Skip to main content
Erschienen in: Acta Mechanica Sinica 5/2015

16.09.2015 | Review Paper

Some recent advances in 3D crack and contact analysis of elastic solids with transverse isotropy and multifield coupling

verfasst von: Wei-Qiu Chen

Erschienen in: Acta Mechanica Sinica | Ausgabe 5/2015

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Significant progress has been made in mixed boundary-value problems associated with three-dimensional (3D) crack and contact analyses of advanced materials featuring more complexities compared to the conventional isotropic elastic materials. These include material anisotropy and multifield coupling, two typical characteristics of most current multifunctional materials. In this paper we try to present a state-of-the-art description of 3D exact/analytical solutions derived for crack and contact problems of elastic solids with both transverse isotropy and multifield coupling in the latest decade by the potential theory method in the spirit of V. I. Fabrikant, whose ingenious breakthrough brings new vigor and vitality to the old research subject of classical potential theory. We are particularly interested in crack and contact problems with certain nonlinear features. Emphasis is also placed on the coupling between the temperature field (or the like) and other physical fields (e.g., elastic, electric, and magnetic fields). We further highlight the practical significance of 3D contact solutions, in particular in applications related to modern scanning probe microscopes.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Cheng, A.H.D., Cheng, D.T.: Heritage and early history of the boundary element method. Eng. Anal. Bound. Elem. 29, 268–302 (2005)MATHCrossRef Cheng, A.H.D., Cheng, D.T.: Heritage and early history of the boundary element method. Eng. Anal. Bound. Elem. 29, 268–302 (2005)MATHCrossRef
2.
Zurück zum Zitat Brelot, M.: Potential Theory. Springer, Berlin (2010) Brelot, M.: Potential Theory. Springer, Berlin (2010)
4.
Zurück zum Zitat Muskhelishvili, N.I.: Singular Integral Equations. Noordhoff, Groningen (1953)MATH Muskhelishvili, N.I.: Singular Integral Equations. Noordhoff, Groningen (1953)MATH
5.
Zurück zum Zitat Sneddon, I.N.: Mixed Boundary Value Problems in Potential Theory. North-Holland, Amsterdam (1966)MATH Sneddon, I.N.: Mixed Boundary Value Problems in Potential Theory. North-Holland, Amsterdam (1966)MATH
6.
Zurück zum Zitat Sneddon, I.N., Lowengrub, M.: Crack Problems in the Classical Theory of Elasticity. Wiley, New York (1969)MATH Sneddon, I.N., Lowengrub, M.: Crack Problems in the Classical Theory of Elasticity. Wiley, New York (1969)MATH
7.
Zurück zum Zitat Fabrikant, V.I.: Applications of Potential Theory in Mechanics: A Selection of New Results. Kluwer, Dordrecht (1989)MATH Fabrikant, V.I.: Applications of Potential Theory in Mechanics: A Selection of New Results. Kluwer, Dordrecht (1989)MATH
8.
Zurück zum Zitat Fabrikant, V.I.: Mixed Boundary Value Problem of Potential Theory and Their Applications in Engineering. Kluwer, Dordrecht (1991)MATH Fabrikant, V.I.: Mixed Boundary Value Problem of Potential Theory and Their Applications in Engineering. Kluwer, Dordrecht (1991)MATH
9.
Zurück zum Zitat Fabrikant, V.I.: Crack and Contact Problems in Linear Theory of Elasticity. Bentham Science Publishers, Sharjah (2010) Fabrikant, V.I.: Crack and Contact Problems in Linear Theory of Elasticity. Bentham Science Publishers, Sharjah (2010)
10.
Zurück zum Zitat Chen, W.Q., Ding, H.J.: Potential theory method for 3D crack and contact problems of multi-field coupled media: A survey. J. Zhejiang Univ. Sci. 5, 1009–1021 (2004)CrossRef Chen, W.Q., Ding, H.J.: Potential theory method for 3D crack and contact problems of multi-field coupled media: A survey. J. Zhejiang Univ. Sci. 5, 1009–1021 (2004)CrossRef
11.
Zurück zum Zitat Hanson, M.T.: The elastic field for spherical Hertzian contact including sliding friction for transversely isotropy. J. Tribol. 114, 606–611 (1992)CrossRef Hanson, M.T.: The elastic field for spherical Hertzian contact including sliding friction for transversely isotropy. J. Tribol. 114, 606–611 (1992)CrossRef
12.
Zurück zum Zitat Yong, Z., Hanson, M.T.: Three-dimensional crack and contact problems with a general geometric configuration. Int. J. Solids Struct. 31, 215–239 (1994)MATHCrossRef Yong, Z., Hanson, M.T.: Three-dimensional crack and contact problems with a general geometric configuration. Int. J. Solids Struct. 31, 215–239 (1994)MATHCrossRef
13.
Zurück zum Zitat Chen, W.Q., Ding, H.J.: A penny-shaped crack in a transversely isotropic piezoelectric solid: modes II and III problems. Acta Mech. Sin. 15, 52–58 (1999)CrossRef Chen, W.Q., Ding, H.J.: A penny-shaped crack in a transversely isotropic piezoelectric solid: modes II and III problems. Acta Mech. Sin. 15, 52–58 (1999)CrossRef
14.
Zurück zum Zitat Chen, W.Q., Ding, H.J.: Indentation of a transversely isotropic piezoelectric half-space by a rigid sphere. Acta Mech. Solida Sin. 12, 114–120 (1999) Chen, W.Q., Ding, H.J.: Indentation of a transversely isotropic piezoelectric half-space by a rigid sphere. Acta Mech. Solida Sin. 12, 114–120 (1999)
15.
Zurück zum Zitat Chen, W.Q.: On piezoelastic contact problem for a smooth punch. Int. J. Solids Struct. 37, 2331–2340 (2000)MATHCrossRef Chen, W.Q.: On piezoelastic contact problem for a smooth punch. Int. J. Solids Struct. 37, 2331–2340 (2000)MATHCrossRef
16.
Zurück zum Zitat Kalinin, S.V., Karapetian, E., Kachanov, M.: Nanoelectromechanics of piezoresponse force microscopy. Phys. Rev. B 70, 184101 (2004)CrossRef Kalinin, S.V., Karapetian, E., Kachanov, M.: Nanoelectromechanics of piezoresponse force microscopy. Phys. Rev. B 70, 184101 (2004)CrossRef
17.
Zurück zum Zitat Karapetian, E., Kachanov, M., Kalinin, S.V.: Nanoelectromechanics of piezoelectric indentation and applications to scanning probe microscopies of ferroelectric materials. Philos. Mag. 85, 1017–1051 (2005)CrossRef Karapetian, E., Kachanov, M., Kalinin, S.V.: Nanoelectromechanics of piezoelectric indentation and applications to scanning probe microscopies of ferroelectric materials. Philos. Mag. 85, 1017–1051 (2005)CrossRef
18.
Zurück zum Zitat Pan, E., Chen, W.Q.: Static Green’s Functions in Anisotropic Media. Cambridge University Press, New York (2015)MATH Pan, E., Chen, W.Q.: Static Green’s Functions in Anisotropic Media. Cambridge University Press, New York (2015)MATH
19.
Zurück zum Zitat Selvadurai, A.P.S.: The analytical method in geomechanics. Appl. Mech. Rev. 60, 87–106 (2007)CrossRef Selvadurai, A.P.S.: The analytical method in geomechanics. Appl. Mech. Rev. 60, 87–106 (2007)CrossRef
20.
Zurück zum Zitat Ding, H.J., Chen, W.Q., Zhang, L.C.: Elasticity of Transversely Isotropic Materials. Springer, Dordrecht (2006)MATH Ding, H.J., Chen, W.Q., Zhang, L.C.: Elasticity of Transversely Isotropic Materials. Springer, Dordrecht (2006)MATH
21.
Zurück zum Zitat Ding, H.J., Chen, W.Q.: Three Dimensional Problems of Piezoelasticity. Nova Science Publishers, New York (2001) Ding, H.J., Chen, W.Q.: Three Dimensional Problems of Piezoelasticity. Nova Science Publishers, New York (2001)
22.
Zurück zum Zitat Ding, H.J., Chen, B., Liang, J.: General solutions for coupled equations for piezoelectric media. Int. J. Solids Struct. 33, 2283–2298 (1996)MATHCrossRef Ding, H.J., Chen, B., Liang, J.: General solutions for coupled equations for piezoelectric media. Int. J. Solids Struct. 33, 2283–2298 (1996)MATHCrossRef
23.
Zurück zum Zitat Chen, W.Q.: On the application of potential theory in piezoelasticity. J. Appl. Mech. 66, 808–810 (1999)CrossRef Chen, W.Q.: On the application of potential theory in piezoelasticity. J. Appl. Mech. 66, 808–810 (1999)CrossRef
24.
Zurück zum Zitat Chen, W.Q., Lee, K.Y., Ding, H.J.: General solution for transversely isotropic magneto-electro-thermo-elasticity and the potential theory method. Int. J. Eng. Sci. 42, 1361–1379 (2004)MATHCrossRef Chen, W.Q., Lee, K.Y., Ding, H.J.: General solution for transversely isotropic magneto-electro-thermo-elasticity and the potential theory method. Int. J. Eng. Sci. 42, 1361–1379 (2004)MATHCrossRef
25.
Zurück zum Zitat Ding, H.J., Chen, B., Liang, J.: On the Green’s functions for two-phase transversely isotropic piezoelectric media. Int. J. Solids Struct. 34, 3041–3057 (1997)MATHCrossRef Ding, H.J., Chen, B., Liang, J.: On the Green’s functions for two-phase transversely isotropic piezoelectric media. Int. J. Solids Struct. 34, 3041–3057 (1997)MATHCrossRef
26.
Zurück zum Zitat Chen, W.Q., Lim, C.W.: 3D point force solution for a permeable penny-shaped crack embedded in an infinite transversely isotropic piezoelectric medium. Int. J. Fract. 131, 231–246 (2005)MATHCrossRef Chen, W.Q., Lim, C.W.: 3D point force solution for a permeable penny-shaped crack embedded in an infinite transversely isotropic piezoelectric medium. Int. J. Fract. 131, 231–246 (2005)MATHCrossRef
27.
Zurück zum Zitat Gao, C.F., Wang, M.Z.: Generalized 2D problem of piezoelectric media containing collinear cracks. Acta Mech. Sin. 15, 235–244 (1999)CrossRef Gao, C.F., Wang, M.Z.: Generalized 2D problem of piezoelectric media containing collinear cracks. Acta Mech. Sin. 15, 235–244 (1999)CrossRef
28.
Zurück zum Zitat Qi, H., Fang, D.N., Yao, Z.H.: Analysis of electric boundary condition effects on crack propagation in piezoelectric ceramics. Acta Mech. Sin. 17, 59–70 (2001)CrossRef Qi, H., Fang, D.N., Yao, Z.H.: Analysis of electric boundary condition effects on crack propagation in piezoelectric ceramics. Acta Mech. Sin. 17, 59–70 (2001)CrossRef
29.
Zurück zum Zitat Chen, Y.H., Lu, T.J.: Cracks and fracture in piezoelectrics. Adv. Appl. Mech. 39, 121–215 (2003)CrossRef Chen, Y.H., Lu, T.J.: Cracks and fracture in piezoelectrics. Adv. Appl. Mech. 39, 121–215 (2003)CrossRef
30.
Zurück zum Zitat Huang, Z.Y., Kuang, Z.B.: A mixed electric boundary value problem for an anti-plane piezoelectric crack. Acta Mech. Solida Sin. 16, 110–115 (2003) Huang, Z.Y., Kuang, Z.B.: A mixed electric boundary value problem for an anti-plane piezoelectric crack. Acta Mech. Solida Sin. 16, 110–115 (2003)
31.
Zurück zum Zitat Wang, B.L., Han, J.C., Du, S.Y.: Applicability of the crack face electrical boundary conditions in piezoelectric mechanics. Acta Mech. Solida Sin. 17, 290–296 (2004) Wang, B.L., Han, J.C., Du, S.Y.: Applicability of the crack face electrical boundary conditions in piezoelectric mechanics. Acta Mech. Solida Sin. 17, 290–296 (2004)
32.
Zurück zum Zitat Li, F.X., Sun, Y., Rajapakse, R.K.N.D.: Effect of electric boundary conditions on crack propagation in ferroelectric ceramics. Acta Mech. Sin. 30, 153–160 (2014)MathSciNetCrossRef Li, F.X., Sun, Y., Rajapakse, R.K.N.D.: Effect of electric boundary conditions on crack propagation in ferroelectric ceramics. Acta Mech. Sin. 30, 153–160 (2014)MathSciNetCrossRef
33.
Zurück zum Zitat Zhang, T.Y., Tong, P.: Fracture mechanics for a mode-III crack in a piezoelectric material. Int. J. Solids Struct. 33, 343–359 (1996)MATHCrossRef Zhang, T.Y., Tong, P.: Fracture mechanics for a mode-III crack in a piezoelectric material. Int. J. Solids Struct. 33, 343–359 (1996)MATHCrossRef
34.
Zurück zum Zitat Benveniste, Y.: On the decay of end effects in conduction phenomena: A sandwich strip with imperfect interfaces of low or high conductivity. J. Appl. Phys. 86, 1273–1279 (1999)CrossRef Benveniste, Y.: On the decay of end effects in conduction phenomena: A sandwich strip with imperfect interfaces of low or high conductivity. J. Appl. Phys. 86, 1273–1279 (1999)CrossRef
35.
Zurück zum Zitat Chen, W.Q., Shioya, T.: Fundamental solution for a penny-shaped crack in a piezoelectric medium. J. Mech. Phys. Solids 47, 1459–1475 (1999)MathSciNetMATHCrossRef Chen, W.Q., Shioya, T.: Fundamental solution for a penny-shaped crack in a piezoelectric medium. J. Mech. Phys. Solids 47, 1459–1475 (1999)MathSciNetMATHCrossRef
36.
Zurück zum Zitat Li, X.F., Lee, K.Y.: Three-dimensional electroelastic analysis of a piezoelectric material with a penny-shaped dielectric crack. J. Appl. Mech. 71, 866–878 (2005)MATHCrossRef Li, X.F., Lee, K.Y.: Three-dimensional electroelastic analysis of a piezoelectric material with a penny-shaped dielectric crack. J. Appl. Mech. 71, 866–878 (2005)MATHCrossRef
37.
Zurück zum Zitat Li, X.F., Lee, K.Y.: Electro-elastic behavior induced by an external circular crack in a piezoelectric material. Int. J. Fract. 126, 17–38 (2004)MATHCrossRef Li, X.F., Lee, K.Y.: Electro-elastic behavior induced by an external circular crack in a piezoelectric material. Int. J. Fract. 126, 17–38 (2004)MATHCrossRef
38.
Zurück zum Zitat Li, X.Y.: Fundamental electro-elastic field in an infinite transversely isotropic piezoelectric medium with a permeable external circular crack. Smart Mater. Struct. 21, 065019 (2012)CrossRef Li, X.Y.: Fundamental electro-elastic field in an infinite transversely isotropic piezoelectric medium with a permeable external circular crack. Smart Mater. Struct. 21, 065019 (2012)CrossRef
39.
Zurück zum Zitat Chen, W.Q.: Exact solution of a semi-infinite crack in an infinite piezoelectric body. Arch. Appl. Mech. 69, 309–316 (1999)MATHCrossRef Chen, W.Q.: Exact solution of a semi-infinite crack in an infinite piezoelectric body. Arch. Appl. Mech. 69, 309–316 (1999)MATHCrossRef
40.
Zurück zum Zitat Chen, W.Q., Pan, E.N., Wang, H.M., Zhang, C.Z.: Theory of indentation on multiferroic composite materials. J. Mech. Phys. Solids 58, 1524–1551 (2010)MathSciNetMATHCrossRef Chen, W.Q., Pan, E.N., Wang, H.M., Zhang, C.Z.: Theory of indentation on multiferroic composite materials. J. Mech. Phys. Solids 58, 1524–1551 (2010)MathSciNetMATHCrossRef
41.
Zurück zum Zitat Chen, W.Q., Shioya, T., Ding, H.J.: The elasto-electric field for a rigid conical punch on a transversely isotropic piezoelectric half-space. J. Appl. Mech. 66, 764–771 (1999)CrossRef Chen, W.Q., Shioya, T., Ding, H.J.: The elasto-electric field for a rigid conical punch on a transversely isotropic piezoelectric half-space. J. Appl. Mech. 66, 764–771 (1999)CrossRef
42.
Zurück zum Zitat Gao, H.J., Zhang, T.Y., Tong, P.: Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids 45, 491–510 (1997)CrossRef Gao, H.J., Zhang, T.Y., Tong, P.: Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids 45, 491–510 (1997)CrossRef
43.
Zurück zum Zitat Beom, H.G., Atluri, S.N.: Effect of electric fields on fracture behavior of ferroelectric ceramics. J. Mech. Phys. Solids 51, 1107–1125 (2003)MATHCrossRef Beom, H.G., Atluri, S.N.: Effect of electric fields on fracture behavior of ferroelectric ceramics. J. Mech. Phys. Solids 51, 1107–1125 (2003)MATHCrossRef
44.
Zurück zum Zitat Zhang, T.Y., Zhao, M.H., Gao, C.F.: The strip dielectric breakdown model. Int. J. Fract. 132, 311–327 (2005)MATHCrossRef Zhang, T.Y., Zhao, M.H., Gao, C.F.: The strip dielectric breakdown model. Int. J. Fract. 132, 311–327 (2005)MATHCrossRef
45.
Zurück zum Zitat Dugdale, D.S.: Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8, 100–104 (1960)CrossRef Dugdale, D.S.: Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8, 100–104 (1960)CrossRef
46.
Zurück zum Zitat Li, X.Y., Yang, D., Chen, W.Q., Kang, G.Z.: Penny-shaped Dugdale crack in a transversely isotropic medium. Int. J. Fract. 176, 207–214 (2012)CrossRef Li, X.Y., Yang, D., Chen, W.Q., Kang, G.Z.: Penny-shaped Dugdale crack in a transversely isotropic medium. Int. J. Fract. 176, 207–214 (2012)CrossRef
47.
Zurück zum Zitat Li, X.Y., Guo, S.T., He, Q.C., Chen, W.Q.: Penny-shaped Dugdale crack in a transversely isotropic medium and under axisymmetric loading. Mech. Math. Solids 18, 246–263 (2013)CrossRef Li, X.Y., Guo, S.T., He, Q.C., Chen, W.Q.: Penny-shaped Dugdale crack in a transversely isotropic medium and under axisymmetric loading. Mech. Math. Solids 18, 246–263 (2013)CrossRef
48.
Zurück zum Zitat Zhao, M.H., Shen, Y.P., Liu, G.N., Liu, Y.J.: Dugdale model solutions for a penny-shaped crack in three-dimensional transversely isotropic piezoelectric media by boundary-integral equation method. Eng. Anal. Bound. Elem. 23, 573–576 (1999)MATHCrossRef Zhao, M.H., Shen, Y.P., Liu, G.N., Liu, Y.J.: Dugdale model solutions for a penny-shaped crack in three-dimensional transversely isotropic piezoelectric media by boundary-integral equation method. Eng. Anal. Bound. Elem. 23, 573–576 (1999)MATHCrossRef
49.
50.
Zurück zum Zitat Chen, S.H., Gao, H.J.: Bio-inspired mechanics of reversible adhesion: orientation-dependent adhesion strength for non-slipping adhesive contact with transversely isotropic elastic materials. J. Mech. Phys. Solids 55, 1001–1015 (2005)MATHCrossRef Chen, S.H., Gao, H.J.: Bio-inspired mechanics of reversible adhesion: orientation-dependent adhesion strength for non-slipping adhesive contact with transversely isotropic elastic materials. J. Mech. Phys. Solids 55, 1001–1015 (2005)MATHCrossRef
51.
Zurück zum Zitat Wu, J., Kim, S., Carlson, A., Lu, C.F., Hwang, K.C., Huang, Y.G., Rogers, J.A.: Contact radius of stamps in reversible adhesion. Theor. Appl. Mech. Lett. 1, 011001 (2011)CrossRef Wu, J., Kim, S., Carlson, A., Lu, C.F., Hwang, K.C., Huang, Y.G., Rogers, J.A.: Contact radius of stamps in reversible adhesion. Theor. Appl. Mech. Lett. 1, 011001 (2011)CrossRef
52.
Zurück zum Zitat Wang, J.Z., Yao, J.Y., Gao, H.J.: Specific adhesion of a soft elastic body on a wavy surface. Theor. Appl. Mech. Lett. 2, 014002 (2012)CrossRef Wang, J.Z., Yao, J.Y., Gao, H.J.: Specific adhesion of a soft elastic body on a wavy surface. Theor. Appl. Mech. Lett. 2, 014002 (2012)CrossRef
53.
Zurück zum Zitat Chen, Z.R., Yu, S.W.: Micro-scale adhesive contact of a spherical rigid punch on a piezoelectric half-space. Compos. Sci. Technol. 65, 1372–1381 (2005) Chen, Z.R., Yu, S.W.: Micro-scale adhesive contact of a spherical rigid punch on a piezoelectric half-space. Compos. Sci. Technol. 65, 1372–1381 (2005)
54.
Zurück zum Zitat Johnson, K.L., Kendall, K., Roberts, A.D.: Surface energy and the contact of elastic solids. Proc. R. Soc. Lond. A 324, 301–313 (1971)CrossRef Johnson, K.L., Kendall, K., Roberts, A.D.: Surface energy and the contact of elastic solids. Proc. R. Soc. Lond. A 324, 301–313 (1971)CrossRef
55.
Zurück zum Zitat Chen, W.Q.: Adhesive contact between a rigid indenter and a piezoelectric half-space. In: Yang, W., Feng, X.Q., Qin, Q.H. (eds.) Advances in Damage, Fracture and Nanomechanics, pp. 58–65. Tsinghua University Press, Beijing (2009). (in Chinese) Chen, W.Q.: Adhesive contact between a rigid indenter and a piezoelectric half-space. In: Yang, W., Feng, X.Q., Qin, Q.H. (eds.) Advances in Damage, Fracture and Nanomechanics, pp. 58–65. Tsinghua University Press, Beijing (2009). (in Chinese)
56.
Zurück zum Zitat Maugis, D.: Adhesion of spheres: the JKR-DMT transition using a Dugdale model. J. Colloid Interface Sci. 150, 243–269 (1992)CrossRef Maugis, D.: Adhesion of spheres: the JKR-DMT transition using a Dugdale model. J. Colloid Interface Sci. 150, 243–269 (1992)CrossRef
57.
Zurück zum Zitat Borodich, F.M., Galanov, B.A., Keer, L.M., Suarez-Alvarez, M.M.: The JKR-type adhesive contact problems for transversely isotropic elastic solids. Mech. Mater. 75, 33–44 (2014)CrossRef Borodich, F.M., Galanov, B.A., Keer, L.M., Suarez-Alvarez, M.M.: The JKR-type adhesive contact problems for transversely isotropic elastic solids. Mech. Mater. 75, 33–44 (2014)CrossRef
58.
Zurück zum Zitat Bui, H.D.: An integral equations method for solving the problem of a plane crack of arbitrary shape. J. Mech. Phys. Solids 25, 29–39 (1977)MathSciNetMATHCrossRef Bui, H.D.: An integral equations method for solving the problem of a plane crack of arbitrary shape. J. Mech. Phys. Solids 25, 29–39 (1977)MathSciNetMATHCrossRef
59.
Zurück zum Zitat Vlassak, J.J., Ciavarella, M., Barber, J.R., Wang, X.: The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape. J. Mech. Phys. Solids 51, 1701–1721 (2003)MATHCrossRef Vlassak, J.J., Ciavarella, M., Barber, J.R., Wang, X.: The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape. J. Mech. Phys. Solids 51, 1701–1721 (2003)MATHCrossRef
60.
Zurück zum Zitat Wang, B.: Three-dimensional analysis of a flat elliptical crack in a piezoelectric material. Int. J. Eng. Sci. 30, 781–791 (1992)MATHCrossRef Wang, B.: Three-dimensional analysis of a flat elliptical crack in a piezoelectric material. Int. J. Eng. Sci. 30, 781–791 (1992)MATHCrossRef
61.
Zurück zum Zitat Fabrikant, V.I., Rubin, B.S., Karapetian, E.N.: Half-plane crack under normal load: complete solution. J. Eng. Mech. 119, 2238–2251 (1993)MATHCrossRef Fabrikant, V.I., Rubin, B.S., Karapetian, E.N.: Half-plane crack under normal load: complete solution. J. Eng. Mech. 119, 2238–2251 (1993)MATHCrossRef
62.
Zurück zum Zitat Huang, Z.Y., Bao, R.H., Bian, Z.G.: The potential theory method for a half-plane crack and contact problems of piezoelectric materials. Compos. Struct. 78, 596–601 (2007)CrossRef Huang, Z.Y., Bao, R.H., Bian, Z.G.: The potential theory method for a half-plane crack and contact problems of piezoelectric materials. Compos. Struct. 78, 596–601 (2007)CrossRef
63.
Zurück zum Zitat Fabrikant, V.I., Karapetian, E.N.: Elementary exact method for solving boundary-value problems of potential theory with application to half-plane crack and contact problems. Q. J. Mech. Appl. Math. 47, 159–174 (1994)MathSciNetMATHCrossRef Fabrikant, V.I., Karapetian, E.N.: Elementary exact method for solving boundary-value problems of potential theory with application to half-plane crack and contact problems. Q. J. Mech. Appl. Math. 47, 159–174 (1994)MathSciNetMATHCrossRef
64.
Zurück zum Zitat Zhang, N., Gao, C.F., Jiang, Q.: Solution of a flat elliptical crack in an electrostrictive solid. Int. J. Solids Struct. 51, 786–793 (2014)CrossRef Zhang, N., Gao, C.F., Jiang, Q.: Solution of a flat elliptical crack in an electrostrictive solid. Int. J. Solids Struct. 51, 786–793 (2014)CrossRef
65.
Zurück zum Zitat Zhao, M.H., Zhang, Q.Y., Pan, E., Fan, C.Y.: Fundamental solutions and numerical modeling of an elliptical crack with polarization saturation in a transversely isotropic piezoelectric medium. Eng. Fract. Mech. 131, 627–642 (2014)CrossRef Zhao, M.H., Zhang, Q.Y., Pan, E., Fan, C.Y.: Fundamental solutions and numerical modeling of an elliptical crack with polarization saturation in a transversely isotropic piezoelectric medium. Eng. Fract. Mech. 131, 627–642 (2014)CrossRef
66.
Zurück zum Zitat Kassir, M.K., Sih, G.C.: Three-Dimensional Crack Problems. Noordhoff, Leyden (1975)MATH Kassir, M.K., Sih, G.C.: Three-Dimensional Crack Problems. Noordhoff, Leyden (1975)MATH
67.
Zurück zum Zitat Nuller, B., Karapetian, E., Kachanov, M.: On the stress intensity factor for the elliptical crack. Int. J. Fract. 92, L17–L20 (1998)CrossRef Nuller, B., Karapetian, E., Kachanov, M.: On the stress intensity factor for the elliptical crack. Int. J. Fract. 92, L17–L20 (1998)CrossRef
68.
69.
Zurück zum Zitat Hanson, M.T., Puja, I.W.: The elastic field resulting from elliptical Hertzian contact of transversely isotropic bodies: closed form solutions for normal and shear loading. J. Appl. Mech. 64, 457–465 (1997)MATHCrossRef Hanson, M.T., Puja, I.W.: The elastic field resulting from elliptical Hertzian contact of transversely isotropic bodies: closed form solutions for normal and shear loading. J. Appl. Mech. 64, 457–465 (1997)MATHCrossRef
70.
Zurück zum Zitat Ding, H.J., Hou, P.F., Guo, F.L.: The elastic and electric fields for elliptical contact for transversely isotropic piezoelectric bodies. J. Appl. Mech. 66, 560–562 (1999)CrossRef Ding, H.J., Hou, P.F., Guo, F.L.: The elastic and electric fields for elliptical contact for transversely isotropic piezoelectric bodies. J. Appl. Mech. 66, 560–562 (1999)CrossRef
71.
Zurück zum Zitat Ding, H.J., Hou, P.F., Guo, F.L.: The elastic and electric fields for three-dimensional contact for transversely isotropic piezoelectric materials. Int. J. Solids Struct. 37, 3201–3229 (2000)MATHCrossRef Ding, H.J., Hou, P.F., Guo, F.L.: The elastic and electric fields for three-dimensional contact for transversely isotropic piezoelectric materials. Int. J. Solids Struct. 37, 3201–3229 (2000)MATHCrossRef
72.
73.
Zurück zum Zitat Dyson, F.W.: The potentials of ellipsoids of variable densities. Q. J. Pure Appl. Math. Oxford Ser. 25, 259–288 (1891)MATH Dyson, F.W.: The potentials of ellipsoids of variable densities. Q. J. Pure Appl. Math. Oxford Ser. 25, 259–288 (1891)MATH
74.
Zurück zum Zitat Rahman, M.: Some problems of a rigid elliptical disk-inclusion bonded inside a transversely isotropic space: Part I. J. Appl. Mech. 66, 612–620 (1999)CrossRef Rahman, M.: Some problems of a rigid elliptical disk-inclusion bonded inside a transversely isotropic space: Part I. J. Appl. Mech. 66, 612–620 (1999)CrossRef
75.
Zurück zum Zitat Fabrikant, V.I.: Utilization of divergent integrals and a new symbolism in crack and contact analysis. IMA J. Appl. Math. 72, 180–190 (2007)MathSciNetMATHCrossRef Fabrikant, V.I.: Utilization of divergent integrals and a new symbolism in crack and contact analysis. IMA J. Appl. Math. 72, 180–190 (2007)MathSciNetMATHCrossRef
76.
Zurück zum Zitat Li, X.Y., Wu, F., Jin, X., Chen, W.Q.: 3D coupled field in a transversely isotropic magneto-electro-elastic half space punched by an elliptic indenter. J. Mech. Phys. Solids 75, 1–44 (2015) Li, X.Y., Wu, F., Jin, X., Chen, W.Q.: 3D coupled field in a transversely isotropic magneto-electro-elastic half space punched by an elliptic indenter. J. Mech. Phys. Solids 75, 1–44 (2015)
77.
Zurück zum Zitat Lü, C.F., Chen, W., Zhou, J.X., Qu, S.X., Chen, W.Q.: Editorial: mechanics of soft materials, structures and systems. Theor. Appl. Mech. Lett. 3, 054001 (2013)CrossRef Lü, C.F., Chen, W., Zhou, J.X., Qu, S.X., Chen, W.Q.: Editorial: mechanics of soft materials, structures and systems. Theor. Appl. Mech. Lett. 3, 054001 (2013)CrossRef
78.
Zurück zum Zitat Shi, W.D., Feng, X.Q., Gao, H.J.: Two-dimensional model of vesicle adhesion on curved substrates. Acta Mech. Sin. 22, 529–535 (2006)MATHCrossRef Shi, W.D., Feng, X.Q., Gao, H.J.: Two-dimensional model of vesicle adhesion on curved substrates. Acta Mech. Sin. 22, 529–535 (2006)MATHCrossRef
79.
Zurück zum Zitat Peng, X.L., Huang, J.Y., Qin, L., Xiong, C.Y., Fang, J.: A method to determine Young’s modulus of soft gels for cell adhesion. Acta Mech. Sin. 25, 565–570 (2009)CrossRef Peng, X.L., Huang, J.Y., Qin, L., Xiong, C.Y., Fang, J.: A method to determine Young’s modulus of soft gels for cell adhesion. Acta Mech. Sin. 25, 565–570 (2009)CrossRef
80.
Zurück zum Zitat Suo, Z.: Theory of dielectric elastomers. Acta Mech. Solida Sin. 23, 549–578 (2010)CrossRef Suo, Z.: Theory of dielectric elastomers. Acta Mech. Solida Sin. 23, 549–578 (2010)CrossRef
82.
Zurück zum Zitat Dorfmann, A., Ogden, R.W.: Nonlinear electroelastostatics: incremental equations and stability. Int. J. Eng. Sci. 48, 1–14 (2010)MathSciNetMATHCrossRef Dorfmann, A., Ogden, R.W.: Nonlinear electroelastostatics: incremental equations and stability. Int. J. Eng. Sci. 48, 1–14 (2010)MathSciNetMATHCrossRef
83.
Zurück zum Zitat Zhang, W.L., Qian, J., Chen, W.Q.: Indentation of a compressible soft electroactive half-space: some theoretical aspects. Acta Mech. Sin. 28, 1133–1142 (2012)MathSciNetMATHCrossRef Zhang, W.L., Qian, J., Chen, W.Q.: Indentation of a compressible soft electroactive half-space: some theoretical aspects. Acta Mech. Sin. 28, 1133–1142 (2012)MathSciNetMATHCrossRef
84.
Zurück zum Zitat Chen, W.Q., Dai, H.H.: Waves in pre-stretched incompressible soft electroactive cylinders: exact solution. Acta Mech. Solida Sin. 25, 530–541 (2012)CrossRef Chen, W.Q., Dai, H.H.: Waves in pre-stretched incompressible soft electroactive cylinders: exact solution. Acta Mech. Solida Sin. 25, 530–541 (2012)CrossRef
85.
Zurück zum Zitat Chen, W.Q.: The renaissance of continuum mechanics. J. Zhejiang Univ. Sci. A 15, 231–240 (2014)CrossRef Chen, W.Q.: The renaissance of continuum mechanics. J. Zhejiang Univ. Sci. A 15, 231–240 (2014)CrossRef
86.
Zurück zum Zitat Nan, C.W., Bichurin, M.I., Dong, S.X., Viehland, D., Srinivasan, G.: Multiferroic magnetoelectric composites: historical perspective, status, and future directions. J. Appl. Phys. 103, 031101 (2008)CrossRef Nan, C.W., Bichurin, M.I., Dong, S.X., Viehland, D., Srinivasan, G.: Multiferroic magnetoelectric composites: historical perspective, status, and future directions. J. Appl. Phys. 103, 031101 (2008)CrossRef
87.
Zurück zum Zitat Ma, J., Hu, J., Li, Z., Nan, C.W.: Recent progress in multiferroic magnetoelectric composites: from bulk to thin films. Adv. Mater. 23, 1062–1087 (2011)CrossRef Ma, J., Hu, J., Li, Z., Nan, C.W.: Recent progress in multiferroic magnetoelectric composites: from bulk to thin films. Adv. Mater. 23, 1062–1087 (2011)CrossRef
88.
Zurück zum Zitat Wang, X., Shen, Y.P.: The general solution of three-dimensional problems in magnetoelectroelastic media. Int. J. Eng. Sci. 40, 1069–1080 (2002)MathSciNetMATHCrossRef Wang, X., Shen, Y.P.: The general solution of three-dimensional problems in magnetoelectroelastic media. Int. J. Eng. Sci. 40, 1069–1080 (2002)MathSciNetMATHCrossRef
89.
Zurück zum Zitat Liu, J.X., Liu, X.G., Zhao, Y.B.: Green’s functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack. Int. J. Eng. Sci. 39, 1405–1418 (2001)MATHCrossRef Liu, J.X., Liu, X.G., Zhao, Y.B.: Green’s functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack. Int. J. Eng. Sci. 39, 1405–1418 (2001)MATHCrossRef
90.
Zurück zum Zitat Du, J.K., Shen, Y.P., Gao, B.: Scattering of anti-plane shear waves by a single crack in an unbounded transversely isotropic electro-magneto-elastic medium. Appl. Math. Mech. Eng. Ed. 25, 1344–1353 (2004)MATHCrossRef Du, J.K., Shen, Y.P., Gao, B.: Scattering of anti-plane shear waves by a single crack in an unbounded transversely isotropic electro-magneto-elastic medium. Appl. Math. Mech. Eng. Ed. 25, 1344–1353 (2004)MATHCrossRef
91.
Zurück zum Zitat Zhou, Z.G., Wang, B.: Dynamic behavior of two parallel symmetry cracks in magneto-electro-elastic composites under harmonic anti-plane waves. Appl. Math. Mech. Eng. Ed. 27, 583–591 (2006)MATHCrossRef Zhou, Z.G., Wang, B.: Dynamic behavior of two parallel symmetry cracks in magneto-electro-elastic composites under harmonic anti-plane waves. Appl. Math. Mech. Eng. Ed. 27, 583–591 (2006)MATHCrossRef
92.
Zurück zum Zitat Zhang, P.W., Zhou, Z.G., Wang, B.: Dynamic behavior of two collinear interface cracks between two dissimilar functionally graded piezoelectric/ piezomagnetic material strips. Appl. Math. Mech. Eng. Ed. 28, 615–625 (2007)MATHCrossRef Zhang, P.W., Zhou, Z.G., Wang, B.: Dynamic behavior of two collinear interface cracks between two dissimilar functionally graded piezoelectric/ piezomagnetic material strips. Appl. Math. Mech. Eng. Ed. 28, 615–625 (2007)MATHCrossRef
93.
Zurück zum Zitat Feng, W.J., Nie, H., Han, X.: A penny-shaped crack in a magnetoelectroelastic layer under radial shear impact loading. Acta Mech. Solida Sin. 20, 275–282 (2007)CrossRef Feng, W.J., Nie, H., Han, X.: A penny-shaped crack in a magnetoelectroelastic layer under radial shear impact loading. Acta Mech. Solida Sin. 20, 275–282 (2007)CrossRef
94.
Zurück zum Zitat Fan, C.Y., Zhou, Y.H., Wang, H., Zhao, M.H.: Singular behaviors of interfacial cracks in 2D magnetoelectroelastic bimaterials. Acta Mech. Solida Sin. 22, 232–239 (2009)CrossRef Fan, C.Y., Zhou, Y.H., Wang, H., Zhao, M.H.: Singular behaviors of interfacial cracks in 2D magnetoelectroelastic bimaterials. Acta Mech. Solida Sin. 22, 232–239 (2009)CrossRef
95.
Zurück zum Zitat Pan, S.D., Zhou, Z.G., Wu, L.Z.: Basic solutions of multiple parallel symmetric mode-III cracks in functionally graded piezoelectric/piezomagnetic material plane. Appl. Math. Mech. Eng. Ed. 34, 1201–1224 (2013)MathSciNetMATHCrossRef Pan, S.D., Zhou, Z.G., Wu, L.Z.: Basic solutions of multiple parallel symmetric mode-III cracks in functionally graded piezoelectric/piezomagnetic material plane. Appl. Math. Mech. Eng. Ed. 34, 1201–1224 (2013)MathSciNetMATHCrossRef
96.
Zurück zum Zitat Tang, Y.L., Zhou, Z.G., Wu, L.Z.: The basic solution of a 3-D rectangular permeable crack in a piezoelectric/piezomagnetic composite material. Acta Mech. Solida Sin. 26, 403–418 (2013)CrossRef Tang, Y.L., Zhou, Z.G., Wu, L.Z.: The basic solution of a 3-D rectangular permeable crack in a piezoelectric/piezomagnetic composite material. Acta Mech. Solida Sin. 26, 403–418 (2013)CrossRef
97.
Zurück zum Zitat Chen, W.Q.: Exact 3D thermoelastic solutions for a penny-shaped crack in an infinite magnetoelectric medium. Trans. Nanjing Univ. Aeronaut. Astronaut. 31, 109–117 (2014) Chen, W.Q.: Exact 3D thermoelastic solutions for a penny-shaped crack in an infinite magnetoelectric medium. Trans. Nanjing Univ. Aeronaut. Astronaut. 31, 109–117 (2014)
98.
Zurück zum Zitat Gao, C.F., Kessler, H., Balke, H.: Fracture analysis of electromagnetic thermoelastic solids. Eur. J. Mech. A Solids 22, 433–442 (2003)MATHCrossRef Gao, C.F., Kessler, H., Balke, H.: Fracture analysis of electromagnetic thermoelastic solids. Eur. J. Mech. A Solids 22, 433–442 (2003)MATHCrossRef
99.
Zurück zum Zitat Wang, B.L., Han, J.C.: Discussion on electromagnetic crack face boundary conditions for the fracture mechanics of magneto-electro-elastic materials. Acta Mech. Sin. 22, 233–242 (2006)MATHCrossRef Wang, B.L., Han, J.C.: Discussion on electromagnetic crack face boundary conditions for the fracture mechanics of magneto-electro-elastic materials. Acta Mech. Sin. 22, 233–242 (2006)MATHCrossRef
100.
Zurück zum Zitat Zhao, M.H., Yang, F., Liu, T.: Analysis of a penny-shaped crack in a magneto-electro-elastic medium. Philos. Mag. 86, 4397–4416 (2006)CrossRef Zhao, M.H., Yang, F., Liu, T.: Analysis of a penny-shaped crack in a magneto-electro-elastic medium. Philos. Mag. 86, 4397–4416 (2006)CrossRef
101.
Zurück zum Zitat Hou, P.F., Leung, A.Y.T., Ding, H.J.: The elliptical Hertzian contact of transversely isotropic magnetoelectroelastic bodies. Int. J. Solids Struct. 40, 2833–2850 (2003)MATHCrossRef Hou, P.F., Leung, A.Y.T., Ding, H.J.: The elliptical Hertzian contact of transversely isotropic magnetoelectroelastic bodies. Int. J. Solids Struct. 40, 2833–2850 (2003)MATHCrossRef
102.
Zurück zum Zitat Li, X.Y., Zheng, R.F., Chen, W.Q.: Fundamental solutions to contact problems of a magneto-electro-elastic half-space indented by a semi-infinite punch. Int. J. Solids Struct. 51, 164–178 (2014)CrossRef Li, X.Y., Zheng, R.F., Chen, W.Q.: Fundamental solutions to contact problems of a magneto-electro-elastic half-space indented by a semi-infinite punch. Int. J. Solids Struct. 51, 164–178 (2014)CrossRef
103.
Zurück zum Zitat Rogowski, B., Kaliński, W.: Indentation of piezoelectromagneto-elastic half- space by a truncated conical punch. Int. J. Eng. Sci. 60, 77–93 (2012)MathSciNetCrossRef Rogowski, B., Kaliński, W.: Indentation of piezoelectromagneto-elastic half- space by a truncated conical punch. Int. J. Eng. Sci. 60, 77–93 (2012)MathSciNetCrossRef
104.
Zurück zum Zitat Wang, H.M., Pan, E., Sangghaleh, A., Wang, R., Han, X.: Circular loadings on the surface of an anisotropic and magnetoelectroelastic half-space. Smart Mater. Struct. 21, 075003 (2012)CrossRef Wang, H.M., Pan, E., Sangghaleh, A., Wang, R., Han, X.: Circular loadings on the surface of an anisotropic and magnetoelectroelastic half-space. Smart Mater. Struct. 21, 075003 (2012)CrossRef
105.
Zurück zum Zitat Zhou, Y.T., Lee, K.Y.: Theory of sliding contact for multiferroic materials indented by a rigid punch. Int. J. Mech. Sci. 66, 156–167 (2013)CrossRef Zhou, Y.T., Lee, K.Y.: Theory of sliding contact for multiferroic materials indented by a rigid punch. Int. J. Mech. Sci. 66, 156–167 (2013)CrossRef
106.
Zurück zum Zitat Elloumia, R., Guler, M.A., Kallel-Kamoun, I., El-Borgi, S.: Closed-form solutions of the frictional sliding contact problem for a magneto-electro-elastic half-plane indented by a rigid conducting punch. Int. J. Solids Struct. 50, 3778–3792 (2013)CrossRef Elloumia, R., Guler, M.A., Kallel-Kamoun, I., El-Borgi, S.: Closed-form solutions of the frictional sliding contact problem for a magneto-electro-elastic half-plane indented by a rigid conducting punch. Int. J. Solids Struct. 50, 3778–3792 (2013)CrossRef
107.
Zurück zum Zitat Zhou, Y.T., Zhong, Z.: Frictional indentation of anisotropic magneto-electro- elastic materials by a rigid indenter. J. Appl. Mech. 81, 071001 (2014)CrossRef Zhou, Y.T., Zhong, Z.: Frictional indentation of anisotropic magneto-electro- elastic materials by a rigid indenter. J. Appl. Mech. 81, 071001 (2014)CrossRef
108.
Zurück zum Zitat Suck, J.B., Schreiber, M., Häussler, P.: Quasicrystals: An Introduction to Structure, Physical Properties and Applications. Springer, Berlin (2010) Suck, J.B., Schreiber, M., Häussler, P.: Quasicrystals: An Introduction to Structure, Physical Properties and Applications. Springer, Berlin (2010)
109.
Zurück zum Zitat Dubois, J.M.: Useful Quasicrystals. World Scientific, Singapore (2005)CrossRef Dubois, J.M.: Useful Quasicrystals. World Scientific, Singapore (2005)CrossRef
110.
Zurück zum Zitat Fan, T.Y.: Mathematical Theory of Elasticity of Quasicrystals and Its Applications. Springer, Berlin (2011)CrossRef Fan, T.Y.: Mathematical Theory of Elasticity of Quasicrystals and Its Applications. Springer, Berlin (2011)CrossRef
111.
Zurück zum Zitat Guo, L.H., Fan, T.Y.: Solvability on boundary-value problems of elasticity of three-dimensional quasicrystals. Appl. Math. Mech. Eng. Ed. 28, 1061–1070 (2007)MathSciNetMATHCrossRef Guo, L.H., Fan, T.Y.: Solvability on boundary-value problems of elasticity of three-dimensional quasicrystals. Appl. Math. Mech. Eng. Ed. 28, 1061–1070 (2007)MathSciNetMATHCrossRef
112.
Zurück zum Zitat Guo, Y.C., Fan, T.Y.: A mode- II Griffith crack in decagonal quasicrystals. Appl. Math. Mech. Eng. Ed. 22, 1311–1317 (2001)MATHCrossRef Guo, Y.C., Fan, T.Y.: A mode- II Griffith crack in decagonal quasicrystals. Appl. Math. Mech. Eng. Ed. 22, 1311–1317 (2001)MATHCrossRef
113.
Zurück zum Zitat Fan, T.Y., Tang, Z.Y., Chen, W.Q.: Theory of linear, nonlinear and dynamic fracture for quasicrystals. Eng. Fract. Mech. 82, 185–194 (2012)CrossRef Fan, T.Y., Tang, Z.Y., Chen, W.Q.: Theory of linear, nonlinear and dynamic fracture for quasicrystals. Eng. Fract. Mech. 82, 185–194 (2012)CrossRef
114.
Zurück zum Zitat Zhou, W.M., Fan, T.Y.: Axisymmetric elasticity problem of cubic quasicrystal. Chin. Phys. 9, 294–303 (2000)CrossRef Zhou, W.M., Fan, T.Y.: Axisymmetric elasticity problem of cubic quasicrystal. Chin. Phys. 9, 294–303 (2000)CrossRef
115.
Zurück zum Zitat Zhou, W.M., Fan, T.Y., Yin, S.Y.: Crack problem under shear loading in cubic quasicrystal. Appl. Math. Mech. Eng. Ed. 24, 720–726 (2003)MATHCrossRef Zhou, W.M., Fan, T.Y., Yin, S.Y.: Crack problem under shear loading in cubic quasicrystal. Appl. Math. Mech. Eng. Ed. 24, 720–726 (2003)MATHCrossRef
116.
Zurück zum Zitat Zhou, W.M., Fan, T.Y., Yin, S.Y.: Axisymmetric contact problem of cubic quasicrystalline materials. Acta Mech. Solida Sin. 15, 68–74 (2002) Zhou, W.M., Fan, T.Y., Yin, S.Y.: Axisymmetric contact problem of cubic quasicrystalline materials. Acta Mech. Solida Sin. 15, 68–74 (2002)
117.
Zurück zum Zitat Chen, W.Q., Ma, Y.L., Ding, H.J.: On three-dimensional elastic problems of one-dimensional hexagonal quasicrystal bodies. Mech. Res. Commun. 31, 633–641 (2004)MathSciNetMATHCrossRef Chen, W.Q., Ma, Y.L., Ding, H.J.: On three-dimensional elastic problems of one-dimensional hexagonal quasicrystal bodies. Mech. Res. Commun. 31, 633–641 (2004)MathSciNetMATHCrossRef
118.
119.
Zurück zum Zitat Peng, Y.Z., Fan, T.Y.: Crack and indentation problems for one-dimensional hexagonal quasicrystals. Eur. Phys. J. B 21, 39–44 (2001)CrossRef Peng, Y.Z., Fan, T.Y.: Crack and indentation problems for one-dimensional hexagonal quasicrystals. Eur. Phys. J. B 21, 39–44 (2001)CrossRef
120.
Zurück zum Zitat Li, X.Y., Li, P.D., Wu, T.H., Shi, M.X., Zhu, Z.W.: Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect. Phys. Lett. A 378, 826–834 (2014)MathSciNetMATHCrossRef Li, X.Y., Li, P.D., Wu, T.H., Shi, M.X., Zhu, Z.W.: Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect. Phys. Lett. A 378, 826–834 (2014)MathSciNetMATHCrossRef
121.
Zurück zum Zitat Wu, Y.F., Chen, W.Q., Li, X.Y.: Indentation on one-dimensional hexagonal quasicrystals: general theory and complete exact solutions. Philos. Mag. 93, 858–882 (2013)CrossRef Wu, Y.F., Chen, W.Q., Li, X.Y.: Indentation on one-dimensional hexagonal quasicrystals: general theory and complete exact solutions. Philos. Mag. 93, 858–882 (2013)CrossRef
122.
Zurück zum Zitat Li, X.Y.: Elastic field in an infinite medium of one-dimensional hexagonal quasicrystal with a planar crack. Int. J. Solids Struct. 51, 1442–1455 (2014)CrossRef Li, X.Y.: Elastic field in an infinite medium of one-dimensional hexagonal quasicrystal with a planar crack. Int. J. Solids Struct. 51, 1442–1455 (2014)CrossRef
123.
Zurück zum Zitat Gao, Y., Zhao, B.S.: A general treatment of three-dimensional elasticity of quasicrystals by an operator method. Phys. Stat. Sol. (b) 243, 4007–4019 (2006)CrossRef Gao, Y., Zhao, B.S.: A general treatment of three-dimensional elasticity of quasicrystals by an operator method. Phys. Stat. Sol. (b) 243, 4007–4019 (2006)CrossRef
124.
Zurück zum Zitat Gao, Y., Zhao, B.S.: General solutions of three-dimensional problems for two-dimensional quasicrystals. Appl. Math. Mod. 33, 3382–3391 (2009)MathSciNetMATHCrossRef Gao, Y., Zhao, B.S.: General solutions of three-dimensional problems for two-dimensional quasicrystals. Appl. Math. Mod. 33, 3382–3391 (2009)MathSciNetMATHCrossRef
125.
Zurück zum Zitat Gao, Y., Ricoeur, A.: Three-dimensional analysis of a spheroidal inclusion in a two-dimensional quasicrystal body. Philos. Mag. 92, 4334–4353 (2012)CrossRef Gao, Y., Ricoeur, A.: Three-dimensional analysis of a spheroidal inclusion in a two-dimensional quasicrystal body. Philos. Mag. 92, 4334–4353 (2012)CrossRef
126.
Zurück zum Zitat Li, X.Y., Wu, F., Wu, Y.F., Chen, W.Q.: Indentation on two-dimensional hexagonal quasicrystals. Mech. Mater. 76, 121–136 (2014)CrossRef Li, X.Y., Wu, F., Wu, Y.F., Chen, W.Q.: Indentation on two-dimensional hexagonal quasicrystals. Mech. Mater. 76, 121–136 (2014)CrossRef
127.
Zurück zum Zitat Wang, T.C., Han, X.L.: Crack problems of piezoelectric materials. Acta Mech. Solida Sin. 12, 95–105 (1999) Wang, T.C., Han, X.L.: Crack problems of piezoelectric materials. Acta Mech. Solida Sin. 12, 95–105 (1999)
128.
Zurück zum Zitat Fang, D.N., Soh, A.K., Liu, J.X.: Electromechanical deformation and fracture of piezoelectric-ferroelectric materials. Acta Mech. Sin. 17, 193–213 (2001)CrossRef Fang, D.N., Soh, A.K., Liu, J.X.: Electromechanical deformation and fracture of piezoelectric-ferroelectric materials. Acta Mech. Sin. 17, 193–213 (2001)CrossRef
129.
Zurück zum Zitat Gao, C.F., Balke, H.: Green’s functions of internal electrodes between two dissimilar piezoelectric media. Appl. Math. Mech. Eng. Ed. 26, 234–241 (2005)MATHCrossRef Gao, C.F., Balke, H.: Green’s functions of internal electrodes between two dissimilar piezoelectric media. Appl. Math. Mech. Eng. Ed. 26, 234–241 (2005)MATHCrossRef
130.
Zurück zum Zitat Li, Q., Chen, Y.H.: Analysis of crack-tip singularities for an interfacial permeable crack in metal-piezoelectric bimaterials. Acta Mech. Solida Sin. 20, 247–257 (2007)CrossRef Li, Q., Chen, Y.H.: Analysis of crack-tip singularities for an interfacial permeable crack in metal-piezoelectric bimaterials. Acta Mech. Solida Sin. 20, 247–257 (2007)CrossRef
131.
Zurück zum Zitat Li, Q., Chen, Y.H.: Analysis of a permeable interface crack in elastic dielectric-piezoelectric bimaterials. Acta Mech. Sin. 23, 681–687 (2007)MATHCrossRef Li, Q., Chen, Y.H.: Analysis of a permeable interface crack in elastic dielectric-piezoelectric bimaterials. Acta Mech. Sin. 23, 681–687 (2007)MATHCrossRef
132.
Zurück zum Zitat Wang, B.L., Noda, N., Han, J.C., Du, S.Y.: A penny-shaped crack in a transversely isotropic piezoelectric layer. Eur. J. Mech. A Solids 20, 997–1005 (2001)MATHCrossRef Wang, B.L., Noda, N., Han, J.C., Du, S.Y.: A penny-shaped crack in a transversely isotropic piezoelectric layer. Eur. J. Mech. A Solids 20, 997–1005 (2001)MATHCrossRef
133.
Zurück zum Zitat Yang, J.H., Lee, K.Y.: Penny shaped crack in a three-dimensional piezoelectric strip under in-plane normal loadings. Acta Mech. 148, 187–197 (2001)MATHCrossRef Yang, J.H., Lee, K.Y.: Penny shaped crack in a three-dimensional piezoelectric strip under in-plane normal loadings. Acta Mech. 148, 187–197 (2001)MATHCrossRef
134.
Zurück zum Zitat Li, X.F., Lee, K.Y.: Effects of electric field on crack growth for a penny-shaped dielectric crack in a piezoelectric layer. J. Mech. Phys. Solids 52, 2079–2100 (2004)MathSciNetMATHCrossRef Li, X.F., Lee, K.Y.: Effects of electric field on crack growth for a penny-shaped dielectric crack in a piezoelectric layer. J. Mech. Phys. Solids 52, 2079–2100 (2004)MathSciNetMATHCrossRef
135.
Zurück zum Zitat Wang, B.L., Sun, Y.G., Zhu, Y.: Fracture of a finite piezoelectric layer with a penny-shaped crack. Int. J. Fract. 172, 19–39 (2011) Wang, B.L., Sun, Y.G., Zhu, Y.: Fracture of a finite piezoelectric layer with a penny-shaped crack. Int. J. Fract. 172, 19–39 (2011)
136.
Zurück zum Zitat Zhao, M.H., Li, D.X., Shen, Y.P.: Interfacial crack analysis in three-dimensional transversely isotropic bi-materials by boundary integral equation method. Appl. Math. Mech. Eng. Ed. 26, 1539–1546 (2005)MATHCrossRef Zhao, M.H., Li, D.X., Shen, Y.P.: Interfacial crack analysis in three-dimensional transversely isotropic bi-materials by boundary integral equation method. Appl. Math. Mech. Eng. Ed. 26, 1539–1546 (2005)MATHCrossRef
137.
Zurück zum Zitat Wang, J.H., Chen, C.Q., Lu, T.J.: Indentation response of piezoelectric films. J. Mech. Phys. Solids 56, 3331–3351 (2008)MATHCrossRef Wang, J.H., Chen, C.Q., Lu, T.J.: Indentation response of piezoelectric films. J. Mech. Phys. Solids 56, 3331–3351 (2008)MATHCrossRef
138.
Zurück zum Zitat Wu, Y.F., Yu, H.Y., Chen, W.Q.: Mechanics of indentation for piezoelectric thin films on elastic substrate. Int. J. Solids Struct. 49, 95–110 (2012)CrossRef Wu, Y.F., Yu, H.Y., Chen, W.Q.: Mechanics of indentation for piezoelectric thin films on elastic substrate. Int. J. Solids Struct. 49, 95–110 (2012)CrossRef
139.
Zurück zum Zitat Wu, Y.F., Yu, H.Y., Chen, W.Q.: Indentation responses of piezoelectric layered half-space. Smart Mater. Struct. 22, 015007 (2013)CrossRef Wu, Y.F., Yu, H.Y., Chen, W.Q.: Indentation responses of piezoelectric layered half-space. Smart Mater. Struct. 22, 015007 (2013)CrossRef
140.
Zurück zum Zitat Fabrikant, V.I.: Application of the generalized images method to contact problems for a transversely isotropic elastic layer. J. Strain Anal. 39, 55–70 (2004)CrossRef Fabrikant, V.I.: Application of the generalized images method to contact problems for a transversely isotropic elastic layer. J. Strain Anal. 39, 55–70 (2004)CrossRef
141.
Zurück zum Zitat Fabrikant, V.I.: Tangential contact problem for a transversely isotropic elastic layer bonded to a rigid foundation. Math. Proc. Camb. Philos. Soc. 138, 173–191 (2005)MathSciNetMATHCrossRef Fabrikant, V.I.: Tangential contact problem for a transversely isotropic elastic layer bonded to a rigid foundation. Math. Proc. Camb. Philos. Soc. 138, 173–191 (2005)MathSciNetMATHCrossRef
142.
Zurück zum Zitat Fabrikant, V.I.: Elementary solution of contact problems for a transversely isotropic elastic layer bonded to a rigid foundation. Z. Angew. Math. Phys. 57, 464–490 (2006)MathSciNetMATHCrossRef Fabrikant, V.I.: Elementary solution of contact problems for a transversely isotropic elastic layer bonded to a rigid foundation. Z. Angew. Math. Phys. 57, 464–490 (2006)MathSciNetMATHCrossRef
143.
Zurück zum Zitat Fabrikant, V.I.: Solution of contact problems for a transversely isotropic elastic layer bonded to an elastic half-space. Proc. IMechE Part C. J. Mech. Eng. Sci. 223, 2487–2499 (2009)CrossRef Fabrikant, V.I.: Solution of contact problems for a transversely isotropic elastic layer bonded to an elastic half-space. Proc. IMechE Part C. J. Mech. Eng. Sci. 223, 2487–2499 (2009)CrossRef
144.
Zurück zum Zitat Fabrikant, V.I.: Application of generalized images method to contact problems for a transversely isotropic elastic layer on a smooth half-space. Arch. Appl. Mech. 81, 957–974 (2011)MATHCrossRef Fabrikant, V.I.: Application of generalized images method to contact problems for a transversely isotropic elastic layer on a smooth half-space. Arch. Appl. Mech. 81, 957–974 (2011)MATHCrossRef
145.
Zurück zum Zitat Fabrikant, V.I.: Contact problems for several transversely isotropic elastic layers on a smooth elastic half-space. Meccanica 46, 1239–1263 (2011)MathSciNetMATHCrossRef Fabrikant, V.I.: Contact problems for several transversely isotropic elastic layers on a smooth elastic half-space. Meccanica 46, 1239–1263 (2011)MathSciNetMATHCrossRef
146.
Zurück zum Zitat Fabrikant, V.I.: Tangential contact problems for several transversely isotropic elastic layers bonded to an elastic foundation. J. Eng. Math. 81, 93–126 (2013)MathSciNetCrossRef Fabrikant, V.I.: Tangential contact problems for several transversely isotropic elastic layers bonded to an elastic foundation. J. Eng. Math. 81, 93–126 (2013)MathSciNetCrossRef
148.
Zurück zum Zitat Hu, K.Q., Zhong, Z., Jin, B.: Electroelastic intensification near anti-plane crack in a functionally gradient piezoelectric ceramic strip. Acta Mech. Solida Sin. 16, 197–204 (2003) Hu, K.Q., Zhong, Z., Jin, B.: Electroelastic intensification near anti-plane crack in a functionally gradient piezoelectric ceramic strip. Acta Mech. Solida Sin. 16, 197–204 (2003)
149.
Zurück zum Zitat Feng, W.J., Li, X.G., Wang, S.D.: Torsional impact response of a penny-shaped crack in a functional graded strip. Appl. Math. Mech. Eng. Ed. 25, 1398–1404 (2004)MATHCrossRef Feng, W.J., Li, X.G., Wang, S.D.: Torsional impact response of a penny-shaped crack in a functional graded strip. Appl. Math. Mech. Eng. Ed. 25, 1398–1404 (2004)MATHCrossRef
150.
Zurück zum Zitat Hao, T.H.: Crack tip field in functionally gradient material with exponential variation of elastic constants in two directions. Acta Mech. Sin. 21, 601–607 (2005)MATHCrossRef Hao, T.H.: Crack tip field in functionally gradient material with exponential variation of elastic constants in two directions. Acta Mech. Sin. 21, 601–607 (2005)MATHCrossRef
151.
Zurück zum Zitat Volkov, S., Aizikovich, S., Wang, Y.S., Fedotov, I.: Analytical solution of axisymmetric contact problem about indentation of a circular indenter into a soft functionally graded elastic layer. Acta Mech. Sin. 29, 196–201 (2013)MathSciNetCrossRef Volkov, S., Aizikovich, S., Wang, Y.S., Fedotov, I.: Analytical solution of axisymmetric contact problem about indentation of a circular indenter into a soft functionally graded elastic layer. Acta Mech. Sin. 29, 196–201 (2013)MathSciNetCrossRef
152.
Zurück zum Zitat Ma, J., Ke, L.L., Wang, Y.S.: Frictionless contact of a functionally graded magneto-electro-elastic layered half-plane under a conducting punch. Int. J. Solids Struct. 51, 2791–2806 (2014)CrossRef Ma, J., Ke, L.L., Wang, Y.S.: Frictionless contact of a functionally graded magneto-electro-elastic layered half-plane under a conducting punch. Int. J. Solids Struct. 51, 2791–2806 (2014)CrossRef
153.
Zurück zum Zitat Sankar, T.S., Fabrikant, V.I.: Asymmetric contact problem including wear for nonhomogeneous half space. J. Appl. Math. Mech. 49, 43–46 (1982)MathSciNetMATH Sankar, T.S., Fabrikant, V.I.: Asymmetric contact problem including wear for nonhomogeneous half space. J. Appl. Math. Mech. 49, 43–46 (1982)MathSciNetMATH
154.
Zurück zum Zitat Fabrikant, V.I., Sankar, T.S.: On contact problems in an inhomogeneous half-space. Int. J. Solids Struct. 20, 159–166 (1984)MATHCrossRef Fabrikant, V.I., Sankar, T.S.: On contact problems in an inhomogeneous half-space. Int. J. Solids Struct. 20, 159–166 (1984)MATHCrossRef
155.
Zurück zum Zitat Li, X.Y., Chen, W.Q., Wang, H.Y., Wang, G.D.: Crack tip plasticity of a penny-shaped Dugdale crack in a power-law graded elastic infinite medium. Eng. Fract. Mech. 88, 1–14 (2012)MathSciNetCrossRef Li, X.Y., Chen, W.Q., Wang, H.Y., Wang, G.D.: Crack tip plasticity of a penny-shaped Dugdale crack in a power-law graded elastic infinite medium. Eng. Fract. Mech. 88, 1–14 (2012)MathSciNetCrossRef
156.
157.
Zurück zum Zitat Tao, F.M., Tang, R.J.: The crack-inclusion interaction and the analysis of singularity for the horizontal contact. Appl. Math. Mech. Eng. Ed. 22, 547–556 (2001)MATHCrossRef Tao, F.M., Tang, R.J.: The crack-inclusion interaction and the analysis of singularity for the horizontal contact. Appl. Math. Mech. Eng. Ed. 22, 547–556 (2001)MATHCrossRef
158.
Zurück zum Zitat Zhong, Z.: Analysis of a partially debonded elliptic inhomogeneity in piezoelectric materials. Appl. Math. Mech. Eng. Ed. 25, 445–457 (2004)MATHCrossRef Zhong, Z.: Analysis of a partially debonded elliptic inhomogeneity in piezoelectric materials. Appl. Math. Mech. Eng. Ed. 25, 445–457 (2004)MATHCrossRef
159.
Zurück zum Zitat Hu, Y.T., Li, G.Q., Jiang, S.N., Hu, H.P., Yang, J.S.: Interaction of electric charges in a piezoelectric with rigid external cracks. Appl. Math. Mech. Eng. Ed. 26, 996–1006 (2005)MATHCrossRef Hu, Y.T., Li, G.Q., Jiang, S.N., Hu, H.P., Yang, J.S.: Interaction of electric charges in a piezoelectric with rigid external cracks. Appl. Math. Mech. Eng. Ed. 26, 996–1006 (2005)MATHCrossRef
160.
Zurück zum Zitat Fang, Q.H., Liu, Y.W.: Elastic interaction between wedge disclination dipole and internal crack. Appl. Math. Mech. Eng. Ed. 27, 1239–1247 (2006)MATHCrossRef Fang, Q.H., Liu, Y.W.: Elastic interaction between wedge disclination dipole and internal crack. Appl. Math. Mech. Eng. Ed. 27, 1239–1247 (2006)MATHCrossRef
161.
Zurück zum Zitat Zhou, Z.G., Wang, B.: Basic solution of two parallel non-symmetric permeable cracks in piezoelectric materials. Appl. Math. Mech. Eng. Ed. 28, 417–428 (2007)MathSciNetMATHCrossRef Zhou, Z.G., Wang, B.: Basic solution of two parallel non-symmetric permeable cracks in piezoelectric materials. Appl. Math. Mech. Eng. Ed. 28, 417–428 (2007)MathSciNetMATHCrossRef
162.
Zurück zum Zitat Xiao, W.S., Xie, C., Liu, Y.W.: Interaction between heat dipole and circular interfacial crack. Appl. Math. Mech. Eng. Ed. 30, 1221–1232 (2009)MathSciNetMATHCrossRef Xiao, W.S., Xie, C., Liu, Y.W.: Interaction between heat dipole and circular interfacial crack. Appl. Math. Mech. Eng. Ed. 30, 1221–1232 (2009)MathSciNetMATHCrossRef
163.
Zurück zum Zitat Xu, C.H., Qin, T.Y., Yuan, L., Noda, N.A.: Analysis of multiple interfacial cracks in three-dimensional bimaterials using hypersingular integro-differential equation method. Appl. Math. Mech. Eng. Ed. 30, 293–301 (2009)MATHCrossRef Xu, C.H., Qin, T.Y., Yuan, L., Noda, N.A.: Analysis of multiple interfacial cracks in three-dimensional bimaterials using hypersingular integro-differential equation method. Appl. Math. Mech. Eng. Ed. 30, 293–301 (2009)MATHCrossRef
164.
Zurück zum Zitat Karapetian, E., Hanson, T.: Crack opening displacements and stress intensity factors caused by a concentrated load outside a circular crack. Int. J. Solids Struct. 31, 2035–2052 (1994)MATHCrossRef Karapetian, E., Hanson, T.: Crack opening displacements and stress intensity factors caused by a concentrated load outside a circular crack. Int. J. Solids Struct. 31, 2035–2052 (1994)MATHCrossRef
165.
Zurück zum Zitat Karapetian, E., Kachanov, M.: Three-dimensional interactions of a circular crack with dipoles, centers of dilatation and moments. Int. J. Solids Struct. 33, 3951–3967 (1996)MATHCrossRef Karapetian, E., Kachanov, M.: Three-dimensional interactions of a circular crack with dipoles, centers of dilatation and moments. Int. J. Solids Struct. 33, 3951–3967 (1996)MATHCrossRef
166.
Zurück zum Zitat Kachanov, M., Karapetian, E.: Three-dimensional interactions of a half-plane crack with point forces, dipoles and moments. Int. J. Solids Struct. 34, 4101–4125 (1997)MATHCrossRef Kachanov, M., Karapetian, E.: Three-dimensional interactions of a half-plane crack with point forces, dipoles and moments. Int. J. Solids Struct. 34, 4101–4125 (1997)MATHCrossRef
167.
Zurück zum Zitat Karapetian, E., Kachanov, M.: Green’s functions for the isotropic or transversely isotropic space containing a circular crack. Acta Mech. 126, 169–187 (1998)MATHCrossRef Karapetian, E., Kachanov, M.: Green’s functions for the isotropic or transversely isotropic space containing a circular crack. Acta Mech. 126, 169–187 (1998)MATHCrossRef
168.
Zurück zum Zitat Xiao, Z.M., Fan, H., Zhang, T.L.: Stress intensity factors of two skew-parallel penny-shaped cracks in a 3-D transversely isotropic solid. Mech. Mater. 20, 261–272 (1995)CrossRef Xiao, Z.M., Fan, H., Zhang, T.L.: Stress intensity factors of two skew-parallel penny-shaped cracks in a 3-D transversely isotropic solid. Mech. Mater. 20, 261–272 (1995)CrossRef
169.
Zurück zum Zitat Zhan, S.G., Wang, T.C.: Interactions of penny-shaped cracks in three- dimensional solids. Acta Mech. Sin. 22, 341–353 (2006)MATHCrossRef Zhan, S.G., Wang, T.C.: Interactions of penny-shaped cracks in three- dimensional solids. Acta Mech. Sin. 22, 341–353 (2006)MATHCrossRef
170.
Zurück zum Zitat Fabrikant, V.I.: Interaction of an arbitrary force with a flexible punch or with a penny-shaped crack. Q. J. Mech. Appl. Math. 50, 303–319 (1997)MathSciNetMATHCrossRef Fabrikant, V.I.: Interaction of an arbitrary force with a flexible punch or with a penny-shaped crack. Q. J. Mech. Appl. Math. 50, 303–319 (1997)MathSciNetMATHCrossRef
171.
Zurück zum Zitat Hou, P.F., Ding, H.J., Guan, F.L.: Circular crack in a transversely isotropic piezoelectric space under point forces and point charges. Acta Mech. Sin. 18, 159–169 (2002)CrossRef Hou, P.F., Ding, H.J., Guan, F.L.: Circular crack in a transversely isotropic piezoelectric space under point forces and point charges. Acta Mech. Sin. 18, 159–169 (2002)CrossRef
172.
Zurück zum Zitat Hou, P.F., Pan, X.P., Ding, H.J.: Three-dimensional interactions of a half-plane crack in a transversely isotropic piezoelectric space with resultant sources. Acta Mech. Solida Sin. 18, 265–271 (2005) Hou, P.F., Pan, X.P., Ding, H.J.: Three-dimensional interactions of a half-plane crack in a transversely isotropic piezoelectric space with resultant sources. Acta Mech. Solida Sin. 18, 265–271 (2005)
173.
Zurück zum Zitat Hou, P.F., Ding, H.J., Leung, A.Y.T.: Three-dimensional interactions of circular crack in transversely isotropic piezoelectric space with resultant sources. Appl. Math. Mech. Eng. Ed. 27, 1439–1449 (2006)MATHCrossRef Hou, P.F., Ding, H.J., Leung, A.Y.T.: Three-dimensional interactions of circular crack in transversely isotropic piezoelectric space with resultant sources. Appl. Math. Mech. Eng. Ed. 27, 1439–1449 (2006)MATHCrossRef
174.
Zurück zum Zitat Goryacheva, I.G.: Mechanics of discrete contact. Tribol. Int. 39, 381–386 (2006)CrossRef Goryacheva, I.G.: Mechanics of discrete contact. Tribol. Int. 39, 381–386 (2006)CrossRef
175.
Zurück zum Zitat Bedoidze, M.V., Pozharskii, D.A.: The interaction of punches on a transversely isotropic half-space. J. Appl. Math. Mech. 78, 409–414 (2014)MathSciNetCrossRef Bedoidze, M.V., Pozharskii, D.A.: The interaction of punches on a transversely isotropic half-space. J. Appl. Math. Mech. 78, 409–414 (2014)MathSciNetCrossRef
176.
Zurück zum Zitat Hetnarski, R.B., Eslami, M.R.: Thermal Stresses—Advanced Theory and Applications. Springer, Berlin (2009)MATH Hetnarski, R.B., Eslami, M.R.: Thermal Stresses—Advanced Theory and Applications. Springer, Berlin (2009)MATH
177.
178.
Zurück zum Zitat Barber, J.R.: Elasticity, 3rd revised ed. Springer, Dordrecht (2010) Barber, J.R.: Elasticity, 3rd revised ed. Springer, Dordrecht (2010)
179.
Zurück zum Zitat Chen, W.Q., Ding, H.J., Ling, D.S.: Thermoelastic field of a transversely isotropic elastic medium containing a penny-shaped crack: exact fundamental solution. Int. J. Solids Struct. 41, 69–83 (2004)MATHCrossRef Chen, W.Q., Ding, H.J., Ling, D.S.: Thermoelastic field of a transversely isotropic elastic medium containing a penny-shaped crack: exact fundamental solution. Int. J. Solids Struct. 41, 69–83 (2004)MATHCrossRef
180.
Zurück zum Zitat Chen, W.Q.: On the general solution for piezothermoelasticity for transverse isotropy with application. J. Appl. Mech. 67, 705–711 (2000)MathSciNetMATHCrossRef Chen, W.Q.: On the general solution for piezothermoelasticity for transverse isotropy with application. J. Appl. Mech. 67, 705–711 (2000)MathSciNetMATHCrossRef
181.
Zurück zum Zitat Chen, W.Q., Lim, C.W., Ding, H.J.: Point temperature solution for a penny- shaped crack in an infinite transversely isotropic thermo-piezo-elastic medium. Eng. Anal. Bound. Elem. 29, 524–532 (2005)MATHCrossRef Chen, W.Q., Lim, C.W., Ding, H.J.: Point temperature solution for a penny- shaped crack in an infinite transversely isotropic thermo-piezo-elastic medium. Eng. Anal. Bound. Elem. 29, 524–532 (2005)MATHCrossRef
182.
Zurück zum Zitat Barber, J.R.: Steady-state thermal stresses caused by an imperfectly conducting penny-shaped crack in an elastic solid. J. Therm. Stresses 3, 77–83 (1980)CrossRef Barber, J.R.: Steady-state thermal stresses caused by an imperfectly conducting penny-shaped crack in an elastic solid. J. Therm. Stresses 3, 77–83 (1980)CrossRef
183.
Zurück zum Zitat Shen, S.P., Kuang, Z.B.: Interface crack in bi-piezothermoelastic media. Acta Mech. Solida Sin. 9, 13–26 (1996) Shen, S.P., Kuang, Z.B.: Interface crack in bi-piezothermoelastic media. Acta Mech. Solida Sin. 9, 13–26 (1996)
184.
Zurück zum Zitat Xu, C.H., Qin, T.Y., Hua, Y.L.: Singular integral equations and boundary element method of cracks in thermally stressed planar solids. Appl. Math. Mech. Eng. Ed. 21, 399–406 (2000)MATHCrossRef Xu, C.H., Qin, T.Y., Hua, Y.L.: Singular integral equations and boundary element method of cracks in thermally stressed planar solids. Appl. Math. Mech. Eng. Ed. 21, 399–406 (2000)MATHCrossRef
185.
Zurück zum Zitat Niraula, O.P., Wang, B.L.: A magneto-electro-elastic material with a penny-shaped crack subjected to temperature loading. Acta Mech. 187, 151–168 (2006)MATHCrossRef Niraula, O.P., Wang, B.L.: A magneto-electro-elastic material with a penny-shaped crack subjected to temperature loading. Acta Mech. 187, 151–168 (2006)MATHCrossRef
186.
Zurück zum Zitat Niraula, O.P., Wang, B.L.: Thermal stress analysis in magneto-electro-thermo-elasticity with a penny-shaped crack under uniform heat flow. J. Therm. Stresses 29, 423–437 (2006)CrossRef Niraula, O.P., Wang, B.L.: Thermal stress analysis in magneto-electro-thermo-elasticity with a penny-shaped crack under uniform heat flow. J. Therm. Stresses 29, 423–437 (2006)CrossRef
187.
Zurück zum Zitat Yang, J., Jin, X.Y., Jin, N.G.: A penny-shaped crack in transversely isotropic magneto-electro-thermo-elastic medium subjected to uniform symmetric heat flux. Int. J. Solids Struct. 51, 1792–1808 (2014)CrossRef Yang, J., Jin, X.Y., Jin, N.G.: A penny-shaped crack in transversely isotropic magneto-electro-thermo-elastic medium subjected to uniform symmetric heat flux. Int. J. Solids Struct. 51, 1792–1808 (2014)CrossRef
188.
Zurück zum Zitat Yang, J., Jin, X.Y., Jin, N.G.: A penny-shaped crack in an infinite linear transversely isotropic medium subjected to uniform anti-symmetric heat flux: Closed-form solution. Eur. J. Mech. A Solids 47, 254–270 (2014)MathSciNetCrossRef Yang, J., Jin, X.Y., Jin, N.G.: A penny-shaped crack in an infinite linear transversely isotropic medium subjected to uniform anti-symmetric heat flux: Closed-form solution. Eur. J. Mech. A Solids 47, 254–270 (2014)MathSciNetCrossRef
189.
Zurück zum Zitat Li, X.Y., Chen, W.Q., Wang, H.Y.: General steady state solutions for transversely isotropic thermoporoelastic media in three dimensions and its application. Eur. J. Mech. A Solids 29, 317–326 (2010)CrossRef Li, X.Y., Chen, W.Q., Wang, H.Y.: General steady state solutions for transversely isotropic thermoporoelastic media in three dimensions and its application. Eur. J. Mech. A Solids 29, 317–326 (2010)CrossRef
190.
Zurück zum Zitat Li, X.Y., Wu, J., Chen, W.Q., Wang, H.Y., Zhou, Z.Q.: Exact and complete fundamental solutions for penny-shaped crack in an infinite transversely isotropic thermoporoelastic medium: Mode I problem. Struct. Eng. Mech. 42, 313–334 (2012)CrossRef Li, X.Y., Wu, J., Chen, W.Q., Wang, H.Y., Zhou, Z.Q.: Exact and complete fundamental solutions for penny-shaped crack in an infinite transversely isotropic thermoporoelastic medium: Mode I problem. Struct. Eng. Mech. 42, 313–334 (2012)CrossRef
191.
Zurück zum Zitat Barber, J.R.: Contact problems involving a cooled punch. J. Elasticity 8, 409–423 (1978)MATHCrossRef Barber, J.R.: Contact problems involving a cooled punch. J. Elasticity 8, 409–423 (1978)MATHCrossRef
192.
Zurück zum Zitat Chen, P.J., Chen, S.H.: Thermo-mechanical contact behavior of a finite graded layer under a sliding punch with heat generation. Int. J. Solids. Struct. 50, 1108–1119 (2013)CrossRef Chen, P.J., Chen, S.H.: Thermo-mechanical contact behavior of a finite graded layer under a sliding punch with heat generation. Int. J. Solids. Struct. 50, 1108–1119 (2013)CrossRef
193.
Zurück zum Zitat Karapetian, E., Kalinin, S.V.: Indentation of a punch with chemical or heat distribution at its base into transversely isotropic half-space: Application to local thermal and electrochemical probes. J. Appl. Phys. 113, 187201 (2013)CrossRef Karapetian, E., Kalinin, S.V.: Indentation of a punch with chemical or heat distribution at its base into transversely isotropic half-space: Application to local thermal and electrochemical probes. J. Appl. Phys. 113, 187201 (2013)CrossRef
194.
Zurück zum Zitat Yang, J., Jin, X.Y.: Indentation of a flat circular punch with uniform heat flux at its base into transversely isotropic magneto-electro-thermo-elastic half space. J. Appl. Phys. 115, 083516 (2014)CrossRef Yang, J., Jin, X.Y.: Indentation of a flat circular punch with uniform heat flux at its base into transversely isotropic magneto-electro-thermo-elastic half space. J. Appl. Phys. 115, 083516 (2014)CrossRef
195.
Zurück zum Zitat Fan, T.Y., Mai, Y.W.: Elasticity theory, fracture mechanics, and some relevant thermal properties of quasi-crystalline materials. Appl. Mech. Rev. 57, 325–343 (2004)CrossRef Fan, T.Y., Mai, Y.W.: Elasticity theory, fracture mechanics, and some relevant thermal properties of quasi-crystalline materials. Appl. Mech. Rev. 57, 325–343 (2004)CrossRef
196.
Zurück zum Zitat Li, X.Y.: Fundamental solutions of penny-shaped and half-infinite plane cracks embedded in an infinite space of one-dimensional quasicrystal under thermal loading. Proc. R. Soc. A 469, 20130023 (2013)CrossRef Li, X.Y.: Fundamental solutions of penny-shaped and half-infinite plane cracks embedded in an infinite space of one-dimensional quasicrystal under thermal loading. Proc. R. Soc. A 469, 20130023 (2013)CrossRef
197.
Zurück zum Zitat Li, X.Y., Li, P.D.: Three-dimensional thermo-elastic general solutions of one-dimensional hexagonal quasi-crystal and fundamental solutions. Phys. Lett. A 376, 2004–2009 (2012)MATHCrossRef Li, X.Y., Li, P.D.: Three-dimensional thermo-elastic general solutions of one-dimensional hexagonal quasi-crystal and fundamental solutions. Phys. Lett. A 376, 2004–2009 (2012)MATHCrossRef
198.
Zurück zum Zitat Yang, L.Z., Zhang, L.L., Song, F., Gao, Y.: General solutions for three-dimensional thermoelasticity of two-dimensional hexagonal quasicrystals and an application. J. Therm. Stresses 37, 363–379 (2014)CrossRef Yang, L.Z., Zhang, L.L., Song, F., Gao, Y.: General solutions for three-dimensional thermoelasticity of two-dimensional hexagonal quasicrystals and an application. J. Therm. Stresses 37, 363–379 (2014)CrossRef
199.
Zurück zum Zitat Chen, W.Q., Shioya, T., Ding, H.J.: Integral equations for mixed boundary value problem of a piezoelectric half-space and the applications. Mech. Res. Commun. 26, 583–590 (1999)MathSciNetMATHCrossRef Chen, W.Q., Shioya, T., Ding, H.J.: Integral equations for mixed boundary value problem of a piezoelectric half-space and the applications. Mech. Res. Commun. 26, 583–590 (1999)MathSciNetMATHCrossRef
200.
Zurück zum Zitat Hou, P.F., Zhou, X.H., He, Y.J.: Green’s functions for a semi-infinite transversely isotropic piezothermoelastic material. Smart Mater. Struct. 16, 1915–1923 (2007)CrossRef Hou, P.F., Zhou, X.H., He, Y.J.: Green’s functions for a semi-infinite transversely isotropic piezothermoelastic material. Smart Mater. Struct. 16, 1915–1923 (2007)CrossRef
201.
Zurück zum Zitat Hou, P.F., Luo, W., Leung, A.Y.T.: A point heat source on the surface of a semi-infinite transversely isotropic piezothermoelastic material. J. Appl. Mech. 75, 011013 (2008)CrossRef Hou, P.F., Luo, W., Leung, A.Y.T.: A point heat source on the surface of a semi-infinite transversely isotropic piezothermoelastic material. J. Appl. Mech. 75, 011013 (2008)CrossRef
202.
Zurück zum Zitat Hou, P.F., Leung, A.Y.T., Ding, H.J.: A point heat source on the surface of a semi-infinite transversely isotropic electro-magneto-thermo-elastic material. Int. J. Eng. Sci. 46, 273–285 (2008)MATHCrossRef Hou, P.F., Leung, A.Y.T., Ding, H.J.: A point heat source on the surface of a semi-infinite transversely isotropic electro-magneto-thermo-elastic material. Int. J. Eng. Sci. 46, 273–285 (2008)MATHCrossRef
203.
Zurück zum Zitat Hou, P.F., Yi, T., Leung, A.Y.T.: Green’s functions for semi-infinite transversely isotropic electro-magneto-thermo-elastic material. Int. J. Appl. Electromagnet. Mech. 29, 83–100 (2009) Hou, P.F., Yi, T., Leung, A.Y.T.: Green’s functions for semi-infinite transversely isotropic electro-magneto-thermo-elastic material. Int. J. Appl. Electromagnet. Mech. 29, 83–100 (2009)
204.
Zurück zum Zitat Hou, P.F., Leung, A.Y.T.: Three-dimensional Green’s functions for two-phase transversely isotropic piezothermoelastic media. J. Intell. Mater. Syst. Struct. 20, 11–21 (2009)CrossRef Hou, P.F., Leung, A.Y.T.: Three-dimensional Green’s functions for two-phase transversely isotropic piezothermoelastic media. J. Intell. Mater. Syst. Struct. 20, 11–21 (2009)CrossRef
205.
Zurück zum Zitat Hou, P.F., Li, Q.H., Jiang, H.Y.: Three-dimensional steady-state general solution for isotropic thermoelastic materials with applications II: Green’s functions for two-phase infinite body. J. Therm. Stresses 36, 851–867 (2013)CrossRef Hou, P.F., Li, Q.H., Jiang, H.Y.: Three-dimensional steady-state general solution for isotropic thermoelastic materials with applications II: Green’s functions for two-phase infinite body. J. Therm. Stresses 36, 851–867 (2013)CrossRef
206.
Zurück zum Zitat Hou, P.F., Zhao, M., Ju, J.W.: Three-dimensional Green’s functions for transversely isotropic thermoporoelastic bimaterials. J. Appl. Geophys. 95, 36–46 (2013)CrossRef Hou, P.F., Zhao, M., Ju, J.W.: Three-dimensional Green’s functions for transversely isotropic thermoporoelastic bimaterials. J. Appl. Geophys. 95, 36–46 (2013)CrossRef
207.
Zurück zum Zitat Hou, P.F., Zhao, M., Tong, J., Fu, B.: Three-dimensional steady-state Green’s functions for fluid-saturated, transversely isotropic, poroelastic bimaterials. J. Hydrol. 496, 217–224 (2013)CrossRef Hou, P.F., Zhao, M., Tong, J., Fu, B.: Three-dimensional steady-state Green’s functions for fluid-saturated, transversely isotropic, poroelastic bimaterials. J. Hydrol. 496, 217–224 (2013)CrossRef
208.
Zurück zum Zitat Hou, P.F., Yuan, K., Tian, W.: Three-dimensional Green’s functions for a fluid and pyroelectric two-phase material. Appl. Math. Comput. 249, 303–319 (2014)MathSciNet Hou, P.F., Yuan, K., Tian, W.: Three-dimensional Green’s functions for a fluid and pyroelectric two-phase material. Appl. Math. Comput. 249, 303–319 (2014)MathSciNet
209.
Zurück zum Zitat Hou, P.F., Li, Z.S., Zhang, Y.: Three-dimensional quasi-static Green’s function for an infinite transversely isotropic pyroelectric material under a step point heat source. Mech. Res. Commun. 62, 66–76 (2014)CrossRef Hou, P.F., Li, Z.S., Zhang, Y.: Three-dimensional quasi-static Green’s function for an infinite transversely isotropic pyroelectric material under a step point heat source. Mech. Res. Commun. 62, 66–76 (2014)CrossRef
210.
Zurück zum Zitat Karapetian, E., Kalinin, S.V.: Point force and generalized point source on the surface of semi-infinite transversely isotropic material. J. Appl. Phys. 110, 052020 (2011)CrossRef Karapetian, E., Kalinin, S.V.: Point force and generalized point source on the surface of semi-infinite transversely isotropic material. J. Appl. Phys. 110, 052020 (2011)CrossRef
211.
Zurück zum Zitat Oliver, W.C., Pharr, G.M.: Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564–1583 (1992)CrossRef Oliver, W.C., Pharr, G.M.: Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564–1583 (1992)CrossRef
212.
Zurück zum Zitat Fischer-Cripps, A.C.: Introduction to Contact Mechanics, 2nd edn. Springer, Berlin (2007)MATHCrossRef Fischer-Cripps, A.C.: Introduction to Contact Mechanics, 2nd edn. Springer, Berlin (2007)MATHCrossRef
213.
Zurück zum Zitat Giannakopoulos, A.E., Suresh, S.: Theory of indentation of piezoelectric materials. Acta Mater. 47, 2153–2164 (1999)CrossRef Giannakopoulos, A.E., Suresh, S.: Theory of indentation of piezoelectric materials. Acta Mater. 47, 2153–2164 (1999)CrossRef
214.
Zurück zum Zitat Sridhar, S., Giannakopoulos, A.E., Suresh, S., Ramamurty, U.: Electrical response during indentation of piezoelectric materials: a new method for material characterization. J. Appl. Phys. 85, 380–387 (1999)CrossRef Sridhar, S., Giannakopoulos, A.E., Suresh, S., Ramamurty, U.: Electrical response during indentation of piezoelectric materials: a new method for material characterization. J. Appl. Phys. 85, 380–387 (1999)CrossRef
215.
Zurück zum Zitat Ramamurty, U., Sridhar, S., Giannakopoulos, A.E., Suresh, S.: An experimental study of spherical indentation on piezoelectric materials. Acta Mater. 47, 2417–2430 (1999)CrossRef Ramamurty, U., Sridhar, S., Giannakopoulos, A.E., Suresh, S.: An experimental study of spherical indentation on piezoelectric materials. Acta Mater. 47, 2417–2430 (1999)CrossRef
216.
Zurück zum Zitat Sridhar, S., Giannakopoulos, A.E., Suresh, S.: Mechanical and electrical responses of piezoelectric solids to conical indentation. J. Appl. Phys. 87, 8451–8456 (2000)CrossRef Sridhar, S., Giannakopoulos, A.E., Suresh, S.: Mechanical and electrical responses of piezoelectric solids to conical indentation. J. Appl. Phys. 87, 8451–8456 (2000)CrossRef
217.
Zurück zum Zitat Giannakopoulos, A.E.: Strength analysis of spherical indentation of piezoelectric materials. J. Appl. Mech. 67, 409–416 (2000)MATHCrossRef Giannakopoulos, A.E.: Strength analysis of spherical indentation of piezoelectric materials. J. Appl. Mech. 67, 409–416 (2000)MATHCrossRef
218.
Zurück zum Zitat Giannakopoulos, A.E., Parmaklis, A.Z.: The contact problem of a circular rigid punch on piezomagnetic materials. Int. J. Solids Struct. 44, 4593–4612 (2007)MATHCrossRef Giannakopoulos, A.E., Parmaklis, A.Z.: The contact problem of a circular rigid punch on piezomagnetic materials. Int. J. Solids Struct. 44, 4593–4612 (2007)MATHCrossRef
219.
Zurück zum Zitat Kalinin, S.V., Bonnell, D.A.: Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces. Phys. Rev. B 65, 125408 (2002)CrossRef Kalinin, S.V., Bonnell, D.A.: Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces. Phys. Rev. B 65, 125408 (2002)CrossRef
220.
Zurück zum Zitat Rar, A., Pharr, G.M., Oliver, W.C., Karapetian, E., Kalinin, S.V.: Piezoelectric nanoindentation. J. Mater. Res. 21, 552–556 (2006)CrossRef Rar, A., Pharr, G.M., Oliver, W.C., Karapetian, E., Kalinin, S.V.: Piezoelectric nanoindentation. J. Mater. Res. 21, 552–556 (2006)CrossRef
221.
Zurück zum Zitat Kalinin, S.V., Rodriguez, B.J., Jesse, S., Karapetian, E., Mirman, B., Eliseev, E.A., Morozovska, A.N.: Nanoscale electromechanics of ferroelectric and biological systems: a new dimension in scanning probe microscopy. Annu. Rev. Mater. Res. 37, 189–238 (2007)CrossRef Kalinin, S.V., Rodriguez, B.J., Jesse, S., Karapetian, E., Mirman, B., Eliseev, E.A., Morozovska, A.N.: Nanoscale electromechanics of ferroelectric and biological systems: a new dimension in scanning probe microscopy. Annu. Rev. Mater. Res. 37, 189–238 (2007)CrossRef
222.
Zurück zum Zitat Makagon, A., Kachanov, M., Karapetian, E., Kalinin, S.V.: Indentation of spherical and conical punches into piezoelectric half-space with frictional sliding: applications to scanning probe microscopy. Phys. Rev. B 76, 040511 (2007)CrossRef Makagon, A., Kachanov, M., Karapetian, E., Kalinin, S.V.: Indentation of spherical and conical punches into piezoelectric half-space with frictional sliding: applications to scanning probe microscopy. Phys. Rev. B 76, 040511 (2007)CrossRef
223.
Zurück zum Zitat Karapetian, E., Kachanov, M., Kalinin, S.V.: Stiffness relations for piezoelectric indentation of flat and non-flat punches of arbitrary planform: applications to probing nanoelectromechanical properties of materials. J. Mech. Phys. Solids 57, 673–688 (2009)MathSciNetMATHCrossRef Karapetian, E., Kachanov, M., Kalinin, S.V.: Stiffness relations for piezoelectric indentation of flat and non-flat punches of arbitrary planform: applications to probing nanoelectromechanical properties of materials. J. Mech. Phys. Solids 57, 673–688 (2009)MathSciNetMATHCrossRef
224.
Zurück zum Zitat Makagon, A., Kachanov, M., Karapetian, E., Kalinin, S.V.: Piezoelectric indentation of a flat circular punch accompanied by frictional sliding and applications to scanning probe microscopy. Int. J. Eng. Sci. 47, 221–229 (2009)CrossRef Makagon, A., Kachanov, M., Karapetian, E., Kalinin, S.V.: Piezoelectric indentation of a flat circular punch accompanied by frictional sliding and applications to scanning probe microscopy. Int. J. Eng. Sci. 47, 221–229 (2009)CrossRef
225.
Zurück zum Zitat Pan, K., Liu, Y.Y., Xie, S.H., Liu, Y.M., Li, J.Y.: The electromechanics of piezoresponse force microscopy for a transversely isotropic piezoelectric medium. Acta Mater. 61, 7020–7033 (2013)CrossRef Pan, K., Liu, Y.Y., Xie, S.H., Liu, Y.M., Li, J.Y.: The electromechanics of piezoresponse force microscopy for a transversely isotropic piezoelectric medium. Acta Mater. 61, 7020–7033 (2013)CrossRef
226.
Zurück zum Zitat Kalinin, S.V., Mirman, B., Karapetian, E.: Relationship between direct and converse piezoelectric effect in a nanoscaled electromechanical contact. Phys. Rev. B 76, 212102 (2007)CrossRef Kalinin, S.V., Mirman, B., Karapetian, E.: Relationship between direct and converse piezoelectric effect in a nanoscaled electromechanical contact. Phys. Rev. B 76, 212102 (2007)CrossRef
227.
Zurück zum Zitat Prashanthi, K., Mandal, M., Duttagupta, S.P., Ramgopal Rao, V., Pant, P., Dhale, K., Palkar, V.R.: Nanomechanical characterization of multiferroic thin films for micro-electromechanical systems. Int. J. Nanosci. 10, 1039–1042 (2011)CrossRef Prashanthi, K., Mandal, M., Duttagupta, S.P., Ramgopal Rao, V., Pant, P., Dhale, K., Palkar, V.R.: Nanomechanical characterization of multiferroic thin films for micro-electromechanical systems. Int. J. Nanosci. 10, 1039–1042 (2011)CrossRef
228.
Zurück zum Zitat Nelson, B.A., King, W.P.: Measuring material softening with nanoscale spatial resolution using heated silicon probes. Rev. Sci. Instrum. 78, 023702 (2007)CrossRef Nelson, B.A., King, W.P.: Measuring material softening with nanoscale spatial resolution using heated silicon probes. Rev. Sci. Instrum. 78, 023702 (2007)CrossRef
229.
Zurück zum Zitat Nikiforov, M.P., Jesse, S., Morozovska, A.N., Eliseev, E.A., Germinario, L.T., Kalinin, S.V.: Probing the temperature dependence of the mechanical properties of polymers at the nanoscale with band excitation thermal scanning probe microscopy. Nanotechnology 20, 395709 (2009)CrossRef Nikiforov, M.P., Jesse, S., Morozovska, A.N., Eliseev, E.A., Germinario, L.T., Kalinin, S.V.: Probing the temperature dependence of the mechanical properties of polymers at the nanoscale with band excitation thermal scanning probe microscopy. Nanotechnology 20, 395709 (2009)CrossRef
230.
Zurück zum Zitat Balke, N., Jesse, S., Kim, Y., Adamczyk, L., Tselev, A., Ivanov, I.N., Dudney, N.J., Kalinin, S.V.: Real space mapping of Li-Ion transport in amorphous Si anodes with nanometer resolution. Nano Lett. 10, 3420–3425 (2010)CrossRef Balke, N., Jesse, S., Kim, Y., Adamczyk, L., Tselev, A., Ivanov, I.N., Dudney, N.J., Kalinin, S.V.: Real space mapping of Li-Ion transport in amorphous Si anodes with nanometer resolution. Nano Lett. 10, 3420–3425 (2010)CrossRef
231.
Zurück zum Zitat Kumar, A., Ciucci, F., Morozovska, A.N., Kalinin, S.V., Jesse, S.: Measuring oxygen reduction/evolution reactions on the nanoscale. Nat. Chem. 3, 707–713 (2011)CrossRef Kumar, A., Ciucci, F., Morozovska, A.N., Kalinin, S.V., Jesse, S.: Measuring oxygen reduction/evolution reactions on the nanoscale. Nat. Chem. 3, 707–713 (2011)CrossRef
232.
Zurück zum Zitat Oliver, W.C., Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology. J. Mater. Res. 19, 3–20 (2004)CrossRef Oliver, W.C., Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology. J. Mater. Res. 19, 3–20 (2004)CrossRef
233.
Zurück zum Zitat Chan, E.P., Hu, Y.H., Johnson, P.M., Suo, Z.G., Stafford, C.M.: Spherical indentation testing of poroelastic relaxations in thin hydrogel layers. Soft Matter 8, 1492–1498 (2012)CrossRef Chan, E.P., Hu, Y.H., Johnson, P.M., Suo, Z.G., Stafford, C.M.: Spherical indentation testing of poroelastic relaxations in thin hydrogel layers. Soft Matter 8, 1492–1498 (2012)CrossRef
234.
Zurück zum Zitat Yang, L., Tu, Y.S., Tan, H.L.: Influence of atomic force microscope (AFM) probe shape on adhesion force measured in humidity environment. Appl. Math. Mech. Eng. Ed. 33, 829–844 (2014)MATH Yang, L., Tu, Y.S., Tan, H.L.: Influence of atomic force microscope (AFM) probe shape on adhesion force measured in humidity environment. Appl. Math. Mech. Eng. Ed. 33, 829–844 (2014)MATH
235.
Zurück zum Zitat Borodich, F.M., Keer, L.M.: Evaluation of elastic modulus of materials by adhesive (no-slip) nano-indentation. Proc. R. Soc. Lond. A 460, 507–514 (2004)MathSciNetMATHCrossRef Borodich, F.M., Keer, L.M.: Evaluation of elastic modulus of materials by adhesive (no-slip) nano-indentation. Proc. R. Soc. Lond. A 460, 507–514 (2004)MathSciNetMATHCrossRef
236.
Zurück zum Zitat Borodich, F.M.: The Hertz-type and adhesive contact problems for depth- sensing indentation. Adv. Appl. Mech. 47, 225–366 (2014)CrossRef Borodich, F.M.: The Hertz-type and adhesive contact problems for depth- sensing indentation. Adv. Appl. Mech. 47, 225–366 (2014)CrossRef
237.
Zurück zum Zitat Rogowski, B., Kaliński, W.: The adhesive contact problem for a piezoelectric half-space. Int. J. Press. Vessels Pip. 84, 502–511 (2007)CrossRef Rogowski, B., Kaliński, W.: The adhesive contact problem for a piezoelectric half-space. Int. J. Press. Vessels Pip. 84, 502–511 (2007)CrossRef
238.
Zurück zum Zitat Dundurs, J., Markenscoff, X.: A Green’s function formulation of anticracks and their interaction with load-induced singularities. J. Appl. Mech. 56, 550–555 (1989)MathSciNetMATHCrossRef Dundurs, J., Markenscoff, X.: A Green’s function formulation of anticracks and their interaction with load-induced singularities. J. Appl. Mech. 56, 550–555 (1989)MathSciNetMATHCrossRef
239.
Zurück zum Zitat Rahman, M.: Some problems of a rigid elliptical disk-inclusion bonded inside a transversely isotropic space, Part II: Solutions of the integral equations. J. Appl. Mech. 66, 621–630 (1999)CrossRef Rahman, M.: Some problems of a rigid elliptical disk-inclusion bonded inside a transversely isotropic space, Part II: Solutions of the integral equations. J. Appl. Mech. 66, 621–630 (1999)CrossRef
240.
Zurück zum Zitat Rahman, M.: The normal shift of a rigid elliptical disk in a transversely isotropic solid. Int. J. Solids Struct. 38, 3965–3977 (2001)MATHCrossRef Rahman, M.: The normal shift of a rigid elliptical disk in a transversely isotropic solid. Int. J. Solids Struct. 38, 3965–3977 (2001)MATHCrossRef
241.
Zurück zum Zitat Kaczyński, A.: On 3D anticrack problems in a transversely isotropic solid. Eur. J. Mech. A Solids 43, 142–151 (2014)MathSciNetCrossRef Kaczyński, A.: On 3D anticrack problems in a transversely isotropic solid. Eur. J. Mech. A Solids 43, 142–151 (2014)MathSciNetCrossRef
242.
Zurück zum Zitat Kaczyński, A.: Thermal stress analysis of a three-dimensional anticrack in a transversely isotropic solid. Int. J. Solids Struct. 51, 2382–2389 (2014)CrossRef Kaczyński, A.: Thermal stress analysis of a three-dimensional anticrack in a transversely isotropic solid. Int. J. Solids Struct. 51, 2382–2389 (2014)CrossRef
243.
Zurück zum Zitat Gouldstone, A., Chollacoop, N., Dao, M., Li, J., Minor, A.M., Shen, Y.L.: Indentation across size scales and disciplines: recent developments in experimentation and modeling. Acta Mater. 55, 4015–4039 (2007) Gouldstone, A., Chollacoop, N., Dao, M., Li, J., Minor, A.M., Shen, Y.L.: Indentation across size scales and disciplines: recent developments in experimentation and modeling. Acta Mater. 55, 4015–4039 (2007)
244.
Zurück zum Zitat Wang, J.X., Huang, Z.P., Duan, H.L., Yu, S.W., Feng, X.Q., Wang, G.F., Zhang, W.X., Wang, T.J.: Surface stress effect in mechanics of nanostructured materials. Acta Mech. Solida Sin. 24, 52–81 (2011) Wang, J.X., Huang, Z.P., Duan, H.L., Yu, S.W., Feng, X.Q., Wang, G.F., Zhang, W.X., Wang, T.J.: Surface stress effect in mechanics of nanostructured materials. Acta Mech. Solida Sin. 24, 52–81 (2011)
245.
Zurück zum Zitat Chen, W.Q.: Surface effect on Bleustein–Gulyaev wave in a piezoelectric half-space. Theor. Appl. Mech. Lett. 1, 041001 (2011)CrossRef Chen, W.Q.: Surface effect on Bleustein–Gulyaev wave in a piezoelectric half-space. Theor. Appl. Mech. Lett. 1, 041001 (2011)CrossRef
246.
Zurück zum Zitat Qin, J., Qu, S.X., Feng, X., Huang, Y.G., Xiao, J.L., Hwang, K.C.: A numerical study of indentation with small spherical indenters. Acta Mech. Solida Sin. 22, 18–26 (2009)CrossRef Qin, J., Qu, S.X., Feng, X., Huang, Y.G., Xiao, J.L., Hwang, K.C.: A numerical study of indentation with small spherical indenters. Acta Mech. Solida Sin. 22, 18–26 (2009)CrossRef
247.
Zurück zum Zitat Wei, Y.G., Wang, X.Z., Zhao, M.H., Cheng, C.M., Bai, Y.L.: Size effect and geometrical effect of solids in micro-indentation test. Acta Mech. Sin. 19, 59–70 (2003)CrossRef Wei, Y.G., Wang, X.Z., Zhao, M.H., Cheng, C.M., Bai, Y.L.: Size effect and geometrical effect of solids in micro-indentation test. Acta Mech. Sin. 19, 59–70 (2003)CrossRef
248.
Zurück zum Zitat Zhou, H., Zhang, H.L., Pei, Y.M., Chen, H.S., Zhao, H.W., Fang, D.N.: Scaling relationship among indentation properties of electromagnetic materials at micro- and nanoscale. Appl. Phys. Lett. 106, 081904 (2015)CrossRef Zhou, H., Zhang, H.L., Pei, Y.M., Chen, H.S., Zhao, H.W., Fang, D.N.: Scaling relationship among indentation properties of electromagnetic materials at micro- and nanoscale. Appl. Phys. Lett. 106, 081904 (2015)CrossRef
249.
Zurück zum Zitat Zhao, M.H., Cheng, C.J., Liu, Y.J., Liu, G.N., Zhang, S.S.: The method of analysis of crack problem in three-dimensional non-local elasticity. Appl. Math. Mech. Eng. Ed. 20, 469–475 (1999)MATHCrossRef Zhao, M.H., Cheng, C.J., Liu, Y.J., Liu, G.N., Zhang, S.S.: The method of analysis of crack problem in three-dimensional non-local elasticity. Appl. Math. Mech. Eng. Ed. 20, 469–475 (1999)MATHCrossRef
250.
Zurück zum Zitat Dai, T.M.: The mixed boundary-value problem for non-local asymmetric elasticity. Appl. Math. Mech. Eng. Ed. 21, 27–32 (2000)MATHCrossRef Dai, T.M.: The mixed boundary-value problem for non-local asymmetric elasticity. Appl. Math. Mech. Eng. Ed. 21, 27–32 (2000)MATHCrossRef
252.
Zurück zum Zitat Willis, J.R.: The stress field around an elliptical crack in an anisotropic elastic medium. Int. J. Eng. Sci. 6, 253–263 (1968)MATHCrossRef Willis, J.R.: The stress field around an elliptical crack in an anisotropic elastic medium. Int. J. Eng. Sci. 6, 253–263 (1968)MATHCrossRef
253.
Zurück zum Zitat Barik, S.P., Kanoria, M., Chaudhuri, P.K.: Effect of anisotropy on thermoelastic contact problem. Appl. Math. Mech. Eng. Ed. 29, 501–510 (2008)MATHCrossRef Barik, S.P., Kanoria, M., Chaudhuri, P.K.: Effect of anisotropy on thermoelastic contact problem. Appl. Math. Mech. Eng. Ed. 29, 501–510 (2008)MATHCrossRef
254.
Zurück zum Zitat Fabrikant, V.I.: Non-traditional contact problem for transversely isotropic half-space. Q. J. Mech. Appl. Math. 64, 151–170 (2011)MathSciNetMATHCrossRef Fabrikant, V.I.: Non-traditional contact problem for transversely isotropic half-space. Q. J. Mech. Appl. Math. 64, 151–170 (2011)MathSciNetMATHCrossRef
255.
256.
Zurück zum Zitat Sevostianov, I., Paulo da Silva, U., Aguiar, A.R.: Green’s function for piezoelectric 622 hexagonal crystals. Int. J. Eng. Sci. 84, 18–28 (2014)CrossRef Sevostianov, I., Paulo da Silva, U., Aguiar, A.R.: Green’s function for piezoelectric 622 hexagonal crystals. Int. J. Eng. Sci. 84, 18–28 (2014)CrossRef
257.
258.
Zurück zum Zitat Tian, J.Y., Xie, Z.M.: Dynamic contact stiffness of vibrating rigid sphere contacting semi-infinite transversely isotropic viscoelastic solid. Acta Mech. Solida Sin. 21, 580–588 (2008)CrossRef Tian, J.Y., Xie, Z.M.: Dynamic contact stiffness of vibrating rigid sphere contacting semi-infinite transversely isotropic viscoelastic solid. Acta Mech. Solida Sin. 21, 580–588 (2008)CrossRef
259.
Zurück zum Zitat Zhang, T.Y.: Effects of static electric field on the fracture behavior of piezoelectric ceramics. Acta Mech. Sin. 18, 537–550 (2002)CrossRef Zhang, T.Y.: Effects of static electric field on the fracture behavior of piezoelectric ceramics. Acta Mech. Sin. 18, 537–550 (2002)CrossRef
260.
Zurück zum Zitat Yang, J.S.: An Introduction to the Theory of Piezoelectricity. Springer, New York (2005)MATH Yang, J.S.: An Introduction to the Theory of Piezoelectricity. Springer, New York (2005)MATH
261.
Zurück zum Zitat Dorfmann, L., Ogden, R.W.: Nonlinear Theory of Electroelastic and Magnetoelastic Interactions. Springer, New York (2014)MATHCrossRef Dorfmann, L., Ogden, R.W.: Nonlinear Theory of Electroelastic and Magnetoelastic Interactions. Springer, New York (2014)MATHCrossRef
262.
Zurück zum Zitat Wang, Q.M., Mohan, A.C., Oyen, M.L., Zhao, X.H.: Separating viscoelasticity and poroelasticity of gels with different length and time scales. Acta Mech. Sin. 30, 20–27 (2014)MathSciNetCrossRef Wang, Q.M., Mohan, A.C., Oyen, M.L., Zhao, X.H.: Separating viscoelasticity and poroelasticity of gels with different length and time scales. Acta Mech. Sin. 30, 20–27 (2014)MathSciNetCrossRef
263.
Zurück zum Zitat Touzaline, A.: Analysis of a quasistatic contact problem with adhesion and nonlocal friction for viscoelastic materials. Appl. Math. Mech. Eng. Ed. 31, 623–634 (2010)MathSciNetMATHCrossRef Touzaline, A.: Analysis of a quasistatic contact problem with adhesion and nonlocal friction for viscoelastic materials. Appl. Math. Mech. Eng. Ed. 31, 623–634 (2010)MathSciNetMATHCrossRef
Metadaten
Titel
Some recent advances in 3D crack and contact analysis of elastic solids with transverse isotropy and multifield coupling
verfasst von
Wei-Qiu Chen
Publikationsdatum
16.09.2015
Verlag
The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences
Erschienen in
Acta Mechanica Sinica / Ausgabe 5/2015
Print ISSN: 0567-7718
Elektronische ISSN: 1614-3116
DOI
https://doi.org/10.1007/s10409-015-0509-3

Weitere Artikel der Ausgabe 5/2015

Acta Mechanica Sinica 5/2015 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.