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Erschienen in: Archive of Applied Mechanics 12/2021

04.09.2021 | Original

Frictional contact problem of one-dimensional hexagonal piezoelectric quasicrystals layer

verfasst von: Rukai Huang, Shenghu Ding, Xin Zhang, Xing Li

Erschienen in: Archive of Applied Mechanics | Ausgabe 12/2021

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Abstract

Based on three-dimensional (3D) general solutions for one-dimensional (1D) hexagonal piezoelectric quasicrystals (PEQCs), this paper studied the frictional contact problem of 1D hexagonal PEQCs layer. The frequency response functions for 1D hexagonal PEQCs layer are analytically derived by applying double Fourier integral transforms to the general solutions and boundary conditions, which are consequently converted to the corresponding influence coefficients. The conjugate gradient method is used to obtain the unknown pressure distribution, while the discrete convolution–fast Fourier transform technique is applied to calculate the displacements and stresses of phonon and phason, electric potentials and electric displacements. Numerical results are given to reveal the influences of layer thickness, material parameters and loading conditions on the contact behavior. The obtained 3D contact solutions are not only helpful for further analysis and understanding of the coupling characteristics of phonon, phason and electric field, but also provide a reference basis for experimental analysis and material development.

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Literatur
1.
Zurück zum Zitat Shechtman, D.G., Blech, I.A., Gratias, D., Cahn, J.: Metallic phason with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53(20), 1951–1953 (1984)CrossRef Shechtman, D.G., Blech, I.A., Gratias, D., Cahn, J.: Metallic phason with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53(20), 1951–1953 (1984)CrossRef
2.
Zurück zum Zitat Levine, D., Steinhardt, P.J.: Quasicrystals: a new class of ordered structures. Phys. Rev. Lett. 53(26), 2477–2480 (1984)CrossRef Levine, D., Steinhardt, P.J.: Quasicrystals: a new class of ordered structures. Phys. Rev. Lett. 53(26), 2477–2480 (1984)CrossRef
3.
Zurück zum Zitat Dubois, J.M.: New prospects from potential applications of quasicrystalline materials. Mater. Sci. Eng. A 294, 4–9 (2000)CrossRef Dubois, J.M.: New prospects from potential applications of quasicrystalline materials. Mater. Sci. Eng. A 294, 4–9 (2000)CrossRef
4.
Zurück zum Zitat Fujiwara, T., Trambly de Laissardière, G., Yamamoto, S.: Electronic Structure and electron transport in quasicrystals. Mater. Sci. Forum 150, 387–394 (1994)CrossRef Fujiwara, T., Trambly de Laissardière, G., Yamamoto, S.: Electronic Structure and electron transport in quasicrystals. Mater. Sci. Forum 150, 387–394 (1994)CrossRef
5.
Zurück zum Zitat Hu, C.Z., Wang, R.H., Ding, D.H., Yang, W.: Piezoelectric elects in quasicrystals. Phys. Rev. B 56(5), 2463 (1997)CrossRef Hu, C.Z., Wang, R.H., Ding, D.H., Yang, W.: Piezoelectric elects in quasicrystals. Phys. Rev. B 56(5), 2463 (1997)CrossRef
6.
Zurück zum Zitat Rao, K.R.M., Rao, P.H., Chaitanya, B.S.K.: Piezoelectricity in quasicrystals: a group-theoretical study. Pramana 68(3), 481–487 (2007)CrossRef Rao, K.R.M., Rao, P.H., Chaitanya, B.S.K.: Piezoelectricity in quasicrystals: a group-theoretical study. Pramana 68(3), 481–487 (2007)CrossRef
7.
Zurück zum Zitat Li, C.L., Liu, Y.Y.: The physical property tensors of one-dimensional quasicrystals. Chin. Phys. 13(006), 924–931 (2004)CrossRef Li, C.L., Liu, Y.Y.: The physical property tensors of one-dimensional quasicrystals. Chin. Phys. 13(006), 924–931 (2004)CrossRef
8.
Zurück zum Zitat Altay, G., Cengiz, D.M.: On the fundamental equations of piezoelasticity of quasicrystal media. Int. J. Solids Struct. 49(23), 3255–3262 (2012)CrossRef Altay, G., Cengiz, D.M.: On the fundamental equations of piezoelasticity of quasicrystal media. Int. J. Solids Struct. 49(23), 3255–3262 (2012)CrossRef
9.
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(6), 633–641 (2004)MathSciNetCrossRef Chen, W.Q., Ma, Y.L., Ding, H.J.: On three-dimensional elastic problems of one-dimensional hexagonal quasicrystal bodies. Mech. Res. Commun. 31(6), 633–641 (2004)MathSciNetCrossRef
10.
Zurück zum Zitat Li, X.Y., Deng, H.: On 2D Green’s functions for 1D hexagonal quasi-crystals. Phys. B 430, 45–51 (2013)CrossRef Li, X.Y., Deng, H.: On 2D Green’s functions for 1D hexagonal quasi-crystals. Phys. B 430, 45–51 (2013)CrossRef
11.
Zurück zum Zitat Gao, Y., Zhao, B.S.: A general treatment of three-dimensional elasticity of quasicrystals by an operator method. Phys. Status Solidi B 243(15), 13 (2006)CrossRef Gao, Y., Zhao, B.S.: A general treatment of three-dimensional elasticity of quasicrystals by an operator method. Phys. Status Solidi B 243(15), 13 (2006)CrossRef
12.
Zurück zum Zitat Wang, X., Pan, E.: Analytical solutions for some defect problems in 1D hexagonal and 2D octagonal quasicrystals. Pramana 70(5), 911–933 (2008)CrossRef Wang, X., Pan, E.: Analytical solutions for some defect problems in 1D hexagonal and 2D octagonal quasicrystals. Pramana 70(5), 911–933 (2008)CrossRef
13.
Zurück zum Zitat Gao, Y., Ricoeur, A.: Three-dimensional Green’s functions for two-dimensional quasi-crystal bimaterials. Proc. R. Soc. A 467(2133), 2622–2642 (2011)MathSciNetCrossRef Gao, Y., Ricoeur, A.: Three-dimensional Green’s functions for two-dimensional quasi-crystal bimaterials. Proc. R. Soc. A 467(2133), 2622–2642 (2011)MathSciNetCrossRef
14.
Zurück zum Zitat Li, X.Y., Li, P.D., Wu, T.H., Zhu, Z.W.: Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect. Phys. Lett. A 378(10), 826–834 (2014)MathSciNetCrossRef Li, X.Y., Li, P.D., Wu, T.H., Zhu, Z.W.: Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect. Phys. Lett. A 378(10), 826–834 (2014)MathSciNetCrossRef
15.
Zurück zum Zitat Zhou, W.M., Fan, T.Y.: Contact problem in decagonal two-dimensional quasicrystal. J. Beijing Inst. Technol. 10(1), 51–55 (2001) Zhou, W.M., Fan, T.Y.: Contact problem in decagonal two-dimensional quasicrystal. J. Beijing Inst. Technol. 10(1), 51–55 (2001)
16.
Zurück zum Zitat Zhao, X.F., Li, X., Ding, S.H.: Two kinds of contact problems in three-dimensional icosahedral quasicrystals. Appl. Math. Mech. 36(12), 1569–1580 (2015)MathSciNetCrossRef Zhao, X.F., Li, X., Ding, S.H.: Two kinds of contact problems in three-dimensional icosahedral quasicrystals. Appl. Math. Mech. 36(12), 1569–1580 (2015)MathSciNetCrossRef
17.
Zurück zum Zitat Zhao, X.F., Li, X., Ding, S.H.: Two kinds of contact problems in dodecagonal quasicrystalline materials of point group 12mm. Acta Mech. Solida Sin. 29(2), 167–177 (2016)CrossRef Zhao, X.F., Li, X., Ding, S.H.: Two kinds of contact problems in dodecagonal quasicrystalline materials of point group 12mm. Acta Mech. Solida Sin. 29(2), 167–177 (2016)CrossRef
18.
Zurück zum Zitat Wu, Y.F., Chen, W.Q., Li, X.Y.: Indentation on one-dimensional hexagonal quasicrystals: general theory and complete exact solutions. Phil. Mag. 93(8), 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. Phil. Mag. 93(8), 858–882 (2013)CrossRef
19.
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
20.
Zurück zum Zitat Hou, P.F., Chen, B.J., Zhang, Y.: An accurate and efficient analytical method for 1D hexagonal quasicrystal coating under the tangential force based on the Green’s function. Int. J. Mech. Sci. 131, 982–1000 (2017)CrossRef Hou, P.F., Chen, B.J., Zhang, Y.: An accurate and efficient analytical method for 1D hexagonal quasicrystal coating under the tangential force based on the Green’s function. Int. J. Mech. Sci. 131, 982–1000 (2017)CrossRef
21.
Zurück zum Zitat Hou, P.F., Chen, B.J., Zhang, Y.: An accurate and efficient analytical method for 1D hexagonal quasicrystal coating based on Green’s function. Z. Angew. Math. Phys. 68(4), 95 (2017)MathSciNetCrossRef Hou, P.F., Chen, B.J., Zhang, Y.: An accurate and efficient analytical method for 1D hexagonal quasicrystal coating based on Green’s function. Z. Angew. Math. Phys. 68(4), 95 (2017)MathSciNetCrossRef
22.
Zurück zum Zitat Li C., Zhou Y. T.: Fundamental solutions and frictionless contact problem in a semi-infinite space of 2D hexagonal piezoelectric QCs. ZAMM: Ztschrift fur angewandte Mathematik und Mechanik, (2019) Li C., Zhou Y. T.: Fundamental solutions and frictionless contact problem in a semi-infinite space of 2D hexagonal piezoelectric QCs. ZAMM: Ztschrift fur angewandte Mathematik und Mechanik, (2019)
23.
Zurück zum Zitat Zhang, X., Wang, Q., Harrison, K.L., Roberts, S.A., Harris, S.J.: Pressure-driven interface evolution in solid-state lithium metal batteries. Cell Rep. Phys. Sci. 1, 100012 (2020)CrossRef Zhang, X., Wang, Q., Harrison, K.L., Roberts, S.A., Harris, S.J.: Pressure-driven interface evolution in solid-state lithium metal batteries. Cell Rep. Phys. Sci. 1, 100012 (2020)CrossRef
24.
Zurück zum Zitat Zhang, X., Wang, Q., Harrison, K.L., Jungjohann, K., Boyce, B.L., Roberts, S.A., Attia, P.M., Harris, S.J.: Rethinking how external pressure can suppress dendrites in lithium metal batteries. J. Electrochem. Soc. 166, 3639–3652 (2019)CrossRef Zhang, X., Wang, Q., Harrison, K.L., Jungjohann, K., Boyce, B.L., Roberts, S.A., Attia, P.M., Harris, S.J.: Rethinking how external pressure can suppress dendrites in lithium metal batteries. J. Electrochem. Soc. 166, 3639–3652 (2019)CrossRef
25.
Zurück zum Zitat Polonsky, I.A., Keer, L.M.: A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques. Wear 231(2), 206–219 (1999)CrossRef Polonsky, I.A., Keer, L.M.: A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques. Wear 231(2), 206–219 (1999)CrossRef
26.
Zurück zum Zitat Liu, S., Wang, Q.: Studying contact stress fields caused by surface tractions with a discrete convolution and fast fourier transform algorithm. J. Tribol. 124(1), 36–45 (2002)CrossRef Liu, S., Wang, Q.: Studying contact stress fields caused by surface tractions with a discrete convolution and fast fourier transform algorithm. J. Tribol. 124(1), 36–45 (2002)CrossRef
27.
Zurück zum Zitat Liu, S., Wang, Q., Liu, G.: A versatile method of discrete convolution and FFT (DC-FFT) for contact analyses. Wear 243, 101–111 (2000)CrossRef Liu, S., Wang, Q., Liu, G.: A versatile method of discrete convolution and FFT (DC-FFT) for contact analyses. Wear 243, 101–111 (2000)CrossRef
28.
Zurück zum Zitat Zhang, X., Wang, Z., Shen, H., Wang, Q.: Frictional contact involving a multiferroic thin film subjected to surface magnetoelectroelastic effects. Int. J. Mech. Sci. 131, 633–648 (2017)CrossRef Zhang, X., Wang, Z., Shen, H., Wang, Q.: Frictional contact involving a multiferroic thin film subjected to surface magnetoelectroelastic effects. Int. J. Mech. Sci. 131, 633–648 (2017)CrossRef
29.
Zurück zum Zitat Zhang, X., Wang, Z.J., Shen, H.M., Wang, Q.: An efficient model for the frictional contact between two multiferroic bodies. Int. J. Solids Struct. 130, 133–152 (2018)CrossRef Zhang, X., Wang, Z.J., Shen, H.M., Wang, Q.: An efficient model for the frictional contact between two multiferroic bodies. Int. J. Solids Struct. 130, 133–152 (2018)CrossRef
30.
Zurück zum Zitat Zhang, X., Wang, Q.: A SAM-FFT based model for 3D steady-state elastodynamic frictional contacts. Int. J. Solids Struct. 170, 53–67 (2019)CrossRef Zhang, X., Wang, Q.: A SAM-FFT based model for 3D steady-state elastodynamic frictional contacts. Int. J. Solids Struct. 170, 53–67 (2019)CrossRef
31.
Zurück zum Zitat Zhang, X., Wang, Q., He, T.: Transient and steady-state viscoelastic contact responses of layer-substrate systems with interfacial imperfections. J. Mech. Phys. Solids 145, 1170 (2020)MathSciNetCrossRef Zhang, X., Wang, Q., He, T.: Transient and steady-state viscoelastic contact responses of layer-substrate systems with interfacial imperfections. J. Mech. Phys. Solids 145, 1170 (2020)MathSciNetCrossRef
32.
Zurück zum Zitat Ding, H.J., Chen, B., Liang, J.: General solutions for coupled equations for piezoelectric media. Int. J. Solids Struct. 33(16), 2283–2298 (1996)CrossRef Ding, H.J., Chen, B., Liang, J.: General solutions for coupled equations for piezoelectric media. Int. J. Solids Struct. 33(16), 2283–2298 (1996)CrossRef
33.
Zurück zum Zitat Jarić, M.V., Nelson, D.R.: Diffuse scattering from quasicrystals. Phys. Rev. B 37(9), 4458–4472 (1988)CrossRef Jarić, M.V., Nelson, D.R.: Diffuse scattering from quasicrystals. Phys. Rev. B 37(9), 4458–4472 (1988)CrossRef
34.
Zurück zum Zitat Coddens, G., Bellissent, R., Calvayrac, Y., Ambroise, J.P.: Evidence for phason hopping in icosahedral AlFeCu quasi-crystals. Europhys. Lett. (EPL) 16(3), 271–276 (1991)CrossRef Coddens, G., Bellissent, R., Calvayrac, Y., Ambroise, J.P.: Evidence for phason hopping in icosahedral AlFeCu quasi-crystals. Europhys. Lett. (EPL) 16(3), 271–276 (1991)CrossRef
35.
Zurück zum Zitat Wang, Q., Sun, L., Zhang, X., Liu, S., Zhu, D.: FFT-based methods for computational contact mechanics. Front. Mech. Eng. 6, 61 (2020)CrossRef Wang, Q., Sun, L., Zhang, X., Liu, S., Zhu, D.: FFT-based methods for computational contact mechanics. Front. Mech. Eng. 6, 61 (2020)CrossRef
36.
Zurück zum Zitat Wang, Z., Yu, C., Wang, Q.: An efficient method for solving three-dimensional fretting contact problems involving multilayered or functionally graded materials. Int. J. Solids Struct. 66, 46–61 (2015)CrossRef Wang, Z., Yu, C., Wang, Q.: An efficient method for solving three-dimensional fretting contact problems involving multilayered or functionally graded materials. Int. J. Solids Struct. 66, 46–61 (2015)CrossRef
37.
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(23), 3201–3229 (2000)CrossRef 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(23), 3201–3229 (2000)CrossRef
38.
Zurück zum Zitat Chen, W., Pan, E., Wang, H., Zhang, C.Z.: Theory of indentation on multiferroic composite materials. J. Mech. Phys. Solids 58(10), 1524–1551 (2010)MathSciNetCrossRef Chen, W., Pan, E., Wang, H., Zhang, C.Z.: Theory of indentation on multiferroic composite materials. J. Mech. Phys. Solids 58(10), 1524–1551 (2010)MathSciNetCrossRef
39.
Zurück zum Zitat Makagon, A., Kachanov, M., Kalinin, S.V., Karapetian, E.: Indentation of spherical and conical punches into piezoelectric half-space with frictional sliding Applications to scanning probe microscopy. Phys. Rev. B 76(6), 064115 (2007)CrossRef Makagon, A., Kachanov, M., Kalinin, S.V., Karapetian, E.: Indentation of spherical and conical punches into piezoelectric half-space with frictional sliding Applications to scanning probe microscopy. Phys. Rev. B 76(6), 064115 (2007)CrossRef
Metadaten
Titel
Frictional contact problem of one-dimensional hexagonal piezoelectric quasicrystals layer
verfasst von
Rukai Huang
Shenghu Ding
Xin Zhang
Xing Li
Publikationsdatum
04.09.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Archive of Applied Mechanics / Ausgabe 12/2021
Print ISSN: 0939-1533
Elektronische ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-021-02018-9

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