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2021 | OriginalPaper | Buchkapitel

1. Theoretical Basis of the Structural Modeling Method

verfasst von : Vladimir I. Erofeev, Igor S. Pavlov

Erschienen in: Structural Modeling of Metamaterials

Verlag: Springer International Publishing

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Abstract

The principles of the structural modeling method, the development of the theoretical foundations of which this monograph is devoted, are formulated in the first chapter. Moreover, the problem of the applicability of the classical mechanics laws to a theoretical description of media with micro- and nanostructure is discussed here.

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Nächstes Kapitel A 2D Lattice with Dense Packing of the Particles
Fußnoten
1
For comparison—a = 0.54 nm in silicon and a = 0.57 nm in germanium.
 
Literatur
1.
Sedov, L.I.: Mechanics of Continuous Medium, vol. 1. World Scientific Publ, Singapore (1997)
2.
Kunin, I.A.: Elastic Media with Microstructure, 2 volumes. Springer, Berlin (1983)
3.
Nowacki, W.: Theory of Micropolar Elasticity. J. Springer, Wien (1970)
4.
Savin, G.N., Lukashev, A.A., Lysko, E.M.: Propagation of elastic waves in a solid with microstructure. Prikl. Mekh. (Appl. Mech.) 6(7), 48–52 (1970) (in Russian)
5.
Newton, I.: Philosophical Naturalis Principia Mathematica. London, 419 p (1686)
6.
7.
Potapov, A.I., Pavlov, I.S., Maugin, G.A.: Nonlinear wave interactions in 1D crystals with complex lattice. Wave Motion 29, 297–312 (1999)
8.
Cauchy, A.L.: Memoire sur la dispersion de la lumiere. Paris (1830)
9.
Powell, B.: An abstract of the essential principles of A.Cauchy’s view of the undulatory theory, leading to an explanation of the dispersion of light; with remarks. Phil. Mag. 6(3), 31 (1835)
10.
Tomson, S.W.: Popular Lectures and Addresses, vol. I. MacMilan and Co and New York, Constitution of Matter. London (1889)
11.
Born, M., Huang, K.: Dynamical Theory of Crystal Lattices. Clarendon Press, Oxford (1954)
12.
Brillouin, L., Parodi, M.: Wave Propagation in Periodic Structures. McGrawHill, New York (1946)
13.
Cosserat, E., Cosserat, F.: Theorie des Corps Deformables. Librairie Scientifique A. Hermann et Fils, Paris, 226p (1909) (Reprint, 2009)
14.
Mac Cullagh, J.: An essay towards a dynamical theory of crystalline reflection and refraction. Trans. R. Irish. Acad. Sci. 21, 17–50 (1839)
15.
Mossoti, E.: Lezioni di Meccanica Razionale, Firenze (1851)
16.
Clebsch, A.: Theorie der Elastizität tester Korper, Leipzig, 424 p (1862)
17.
Kirchhoff, G.: Vorlesungen uber mathematische Physik, p. 466p. Mechanik, Leipzig (1874)
18.
Duhem, P.: Hidrodynamique, Elasticité. Acoustique, Paris (1891)
19.
Hertz, K.: Die Prinzipien der Mechanik. Leipzig (1894)
20.
Voigt, W.: Theoretische Studien uber die Elastizitatsverhaltnisse der Krystalle. Abn. Ges.Wiss. Gottingen, vol. 34 (1887).
21.
Frenkel, Ya.I.: The Kinetic Theory of Liquids. USSR Academic Press, Moscow (1945) (in Russian).
22.
Anselm, A.I., Porfiryeva, N.N.: Orientational-translational waves in molecular crystals. Soviet Phys. JETP. 19(5), 438–446 (1949) ((in Russian))
23.
Porfiryeva, N.N.: Orientational-translational waves in molecular crystals. Part 2. Dynamics of 2D and 3D lattices. JETP 19(8), 692–702 (1949) (in Russian).
24.
Mechanics of generalized continua. Proceedings of the IUTAM-symposium on the generalized Cosserat continuum and the continuum theory of dislocations with applications. Freudenstadt and Stuttgart, 1967, ed. E. Kroner, Springer-Verlag, Berlin, Heidelberg, New York (1968)
25.
Aero, E.L., Kuvshinskii, E.V.: Fundamental equations of the theory of elastic media with rotationally interacting particles. Soviet Phys. Solid State 2, 1272–1281 (1961).
26.
Kuvshinskiy, E.V., Aero, E.L.: Continuum theory of asymmetric elasticity—the problem of internal rotation. Soviet Phys. Solid State 5, 1892–1897 (1964).
27.
28.
Lee, J.D., Eringen, A.C.: Continuum theory of smectic liquid crystal. J. Chem. Phys. 58(10), 4203–4211 (1973)
29.
Lee, J.D., Eringen, A.C.: Wave propagation in nematic liquid crystals. J. Chem. Phys. 54(12), 5027–5034 (1971)
30.
Akhiezer, A.I., Bar’yakhtar, V.G., Peletminskii, S.V.: Spin Waves. North Holland, Amsterdam (1968)
31.
Green, A.E., Rivlin, R.S.: Multipolar continuum mechanics. Arch. Rat. Mech. Anal. 17, 113–147 (1964)
32.
Koiter, W.T.: Couple-stresses in the theory of elasticity. Proc. Konikl Acad. Wet., Ser. B67, 17 (1964)
33.
Ilyushin, A.A.: Mechanics of Continuous Media. Moscow State Univ, Publ, Moscow (1990).((in Russian))
34.
Ilyushin, A.A., Lomakin, V.A.: Moment theories in mechanics of solids. Strength and Plasticity. Moscow, Nauka, pp. 54–60 (1971)
35.
Lomakin, V.A.: Static Problems in Mechanics of Deformable Solids. Nauka, Moscow (1970).((in Russian))
36.
Mindlin, R.D.: Microstructure in linear elasticity. Arch. Rat. Mech. Anal. 16(7), 51–78 (1964)
37.
Palmov, V.A.: Basic equations of the theory of asymmetrical elasticity. Prikl. Matem. Mekh. 28(3), 401–408 (1964)
38.
Palmov, V.A.: On a model of a medium with complex structure. Prikl. Matem. Mekh. 33(4), 768–773 (1969)
39.
Savin, G.N.: Foundations of the Plane Problem of the Couple Stress Theory of Elasticity. Izd-vo Kiev. Univ, Kiev (1965).((in Russian))
40.
Toupin, R.A.: Theories of elasticity with couple-stresses Arch. Rat. Mech. Anal. 17, 85–112 (1964)
41.
Truesdell, C., Toupin, R.A.: The classical field theories. Springer, Handbuch der Physik. III/I. Berlin (1960)
42.
Eringen, A.C.: Microcontinuum Field Theories. 1: Foundation and solids. Springer, New York (1999).
43.
Eringen, A.C.: Nonlinear theory of continuous media, p. 477p. McGraw-Hill, New York (1962)
44.
Eringen, A.C., Edelen, D.G.B.: On non-local elasticity. Int J. Eng. Sci. 10(3), 233–248 (1972)
45.
Eringen, A.C., Suhubi, E.S.: Nonlinear theory of simple micro-elastic solids. Int. J. Eng. Sci. 2, 189–203, 389–404 (1964)
46.
Kushwaha, M.S., Halevi, P., Martinez, G., Dobrzynski, L., Djafari-Rouhani, B.: Theory of band structure of periodic elastic composites. Phys. Rev. B. 49, 2313 (1994)
47.
Kroner, E., Datta, B.K.: Non-local theory of elasticity for a finite inhomogeneous medium—a derivation from lattice theory. In: J. Simmons, R. de Wit (eds.) Fundamental aspects, of dislocation theory (Conference Proc.), vol. 2, pp. 737–746. National Bureau of Standards, Washington (1970)
48.
Krumhansl, J.A.: Some considerations of the relation between solid state physics and generalized continuum mechanics. Eur. J. Mech. A/Solids 15, 1049–1075 (1996)
49.
Edelen, D.G.B., Green, A.E., Laws, N.: Nonlocal continuum mechanics. Arch. Rat. Mech. Anal. 43(1), 36–44 (1971)
50.
Green, A.E.: Micro-materials and multipolar continuum mechanics. Int. J. Eng. Sci. 3(5), 533–537 (1965)
51.
Bardenhagen, S., Triantafyllidis, N.: Derivation of higher order gradient continuum theories in 2,3-D non-linear elasticity from periodic lattice models. J. Mech. Phys. Solids. 42(1), 111–139 (1994)
52.
Lifshits, I.M.: On heat properties of chain and layered structures at low temperatures. J. Exp. Theoret. Phys. 22(4), 475–486 (1952) (in Russian)
53.
Kosevich, A.M.: 1999. The Crystal Lattice, Wiley-VCH, Berlin (1999)
54.
Leonov, M.Y.: The Mechanics of Deformations and Fracture. Ilim, Frunze (1981).((in Russian))
55.
Slepyan, L.I.: Models and Phenomena in Fracture Mechanics. Springer, Berlin (2002)
56.
Slepyan, L.I.: On discrete models in fracture mechanics. Mech. Solids 45(6), 803–814 (2011)
57.
Korotkina, M.R.: Remark about moment stresses in discrete media. Moscow University Mechanics Bulletin. Allerton Press, Inc. no. 5, pp. 103–109 (1969)
58.
Nazarov, S.A., Paukshto, M.V.: Discrete Models and Averaging in Problems of the Elasticity Theory. Izd. Leningr. Univ, Leningrad (1984).((in Russian))
59.
Berinskii, I.E., Ivanova, E.A., Krivtsov, A.M., Morozov, N.F.: Application of moment interaction to the construction of a stable model of graphite crystal lattice. Mech. Solids 42(5), 663–671 (2007)
60.
Ivanova, E.A., Krivtsov, A.M., Morozov, N.F.: Derivation of macroscopic relations of the elasticity of complex crystal lattices taking into account the moment interactions at the microlevel. J. Appl. Math. Mech. 71(4), 543–561 (2007)
61.
Ivanova, E.A., Krivtsov, A.M., Morozov, N.F., Firsova, A.D.: Description of crystal packing of particles with torque interaction. Mech. Solids 38(4), 76–88 (2003)
62.
Krivtsov, A.M., Podol’skaya, E.A.: Modeling of elastic properties of crystals with hexagonal close-packed lattice. Mech. Solids 45(3), 370–378 (2010)
63.
Porubov, A.V.: Two-dimensional modeling of diatomic lattice. In: dell’Isola F. et al. (eds.) Advances in Mechanics of Microstructured Media and Structures, Advanced Structured Materials vol. 87. Springer International Publishing AG, part of Springer Nature, pp. 263─272 (2018). https://​doi.​org/​10.​1007/​978-3-319-73694-5_​15
64.
Porubov, A.V., Berinskii, I.E.: Nonlinear plane waves in materials having hexagonal internal structure. Int. J. Non-Linear Mech. 67, 27–33 (2014)
65.
Porubov, A.V., Berintskii, I.E.: Two-dimensional nonlinear shear waves in materials having hexagonal lattice structure. Math. Mech. Solids 21(1), 94–103 (2016)
66.
Porubov, A.V., Krivtsov, A.M., Osokina, A.E.: Two-dimensional waves in extended square lattice. Int. J. Non-Linear Mech. 99, 281–287 (2018)
67.
Porubov, A.V., Osokina, A.E.: On two-dimensional longitudinal nonlinear waves in graphene lattice. In: Berezovski A., Soomere T. (eds.) Applied Wave Mathematics II. Mathematics of Planet Earth, vol. 6, pp. 151–166. Springer, Cham (2019)
68.
Vasiliev, A.A, Dmitriev, S.V., Miroshnichenko, A.E.: Multi-field approach in mechanics of structural solids. Int. J. Solids Struct. 47, 510–525 (2010)
69.
Vasiliev, A.A, Dmitriev, S.V., Miroshnichenko, A.E.: Multi-field continuum theory for medium with microscopic rotations. Int. J. Solids Struct. 42, 6245–6260 (2005)
70.
Vasiliev, A.A, Miroshnichenko, A.E., Ruzzene, M.: Multifield model for Cosserat media. J. Mech. Mater. Struct. 3(7), 1365–1382 (2008)
71.
Vasiliev, A.A., Miroshnichenko, A.E., Dmitriev, S.V.: Multi-field modeling of a Cosserat lattice: models, wave filtering, and boundary effects. Euro. J. Mech. A/Solids 46, 96–105
72.
Suiker, A.S.J., Metrikine, A.V., de Borst, R.: Comparison of wave propagation characteristics of the Cosserat continuum model and corresponding discrete lattice models. Int. J. Solids Struct. 38, 1563–1583
73.
Suiker, A.S.J., Metrikine, A.V., de Borst, R.: Dynamic behaviour of a layer of discrete particles. Part 1: Analysis of body waves and eigenmodes. J. Sound Vib. 240(1), 1–18
74.
Morozov, N.F., Paukshto, M.V.: On the crack simulation and solution in the lattice. ASME J. Appl. Mech. 58, 290–292 (1991)
75.
Krivtsov, A.M.: Deformation and destruction of microstructured solids. Moscow, Fizmatlit Publ., 304 p. (2007) (in Russian)
76.
Ostoja-Starzewski, M., Sheng, P.Y., Alzebdeh, K.: Spring network models in elasticity and fracture of composites and polycrystals. Comput. Materi. Sci. 7, 82–93 (1996)
77.
Pouget, J., Maugin, G.A.: Nonlinear dynamics of oriented elastic solid. Part 1,2 J. Elasticity 22, 135–155, 157–183 (1989)
78.
Sayadi, M.K., Pouget, J.: Soliton dynamics in a microstructured lattice model. J. Phys. A: Math. Gen. 24, 2151–2172 (1991)
79.
Askar, A.: A model for coupled rotation-displacement mode of certain molecular crystals. Illustration for KNO3. J. Phys. Chem. Solids 34, 1901–1907 (1973)
80.
Askar, A.: Molecular crystals and the polar theories of continua: experimential values of material coefficients for KNO3. Int. J. Eng. Sc. 10, 293–300 (1972)
81.
Fisher-Hjalmars, I.: Micropolar phenomena in ordered structures. In: Brulin, O., Hsieh, R.K.T. (eds.) Mechanics of Micropolar Media. World Scientific, Singapore, pp. 1–33 (1982)
82.
Fujii, K., Fuka, T., Kondo, H., Ishii, K.: Orientational phase transition in molecular crystal N2. J. Phys. Soc. Jpn. 66, 125–129 (1997)
83.
Berglund, K.: Structural models of micropolar media. In: Brulin, O., Hsieh, R.K.T. (eds.) Mechanics of Micropolar Media. World Scientific, Singapore, pp. 35–86 (1982)
84.
Ugodchikov, A.G.: Moment dynamics of a linearly elastic body. Dokl. Phys. 340(1), 56–58 (1995)
85.
Krylov, A.L., Mazur, N.G., Nikolayevskii, V.N., El’ , G.A.: Gradient-consistent non-linear model of the generation of ultrasound in the propagation of seismic waves. J. Appl. Math. Mech. 57(6), 1057–1066 (1993)
86.
Krylov, A.L., Nikolayevskii, V.N., El’ , G.A.: Mathematical model of nonlinear generation of ultrasound by seismic waves. Dokl. Akad. Nauk SSSR 318(6), 1340–1345 (1991)
87.
Nikolaevsky, V.N.: Geomechanics and Fluidodynamics. Kluwer Academic Publishers, Dordrecht (1996)
88.
Popov, V.L., Psakhie, S.G.: Theoretical aspects of computer simulation of elastic-plastic media on the basis of movable cellular automata I. Homogeneous Media. Phys. Mesomech. 3(1), 17 (2000)
89.
Psakhie, S.G., Horie, Y., Korostelev, S.Y., Smolin, A.Y., Dmitriev, A.I., Shilko, E.V., Alekseev, S.V.: Method of movable cellular automata as a tool for simulation within the framework of mesomechanics. Russ. Phys. J. 38(11), 1157–1168 (1995). https://​doi.​org/​10.​1007/​BF00559396CrossRef
90.
Psakhie, S.G., Horie, Y., Ostermeyer, G.P., Korostelev, S.Y., Smolin, A.Y.: Movable cellular automata method for simulating materials with mesostructure. Theoret. Appl. Fract. Mech. 37(1–3), 311–334 (2001)
91.
Smolin, AYu., Dobrynin, S.A., Psahie, S.G., Roman, N.V.: On rotation in the movable cellular automation method. Phys. Mesomech. 12(3–4), 124–129 (2009)
92.
Smolin, AYu., Smolin, IYu., Eremina, G., Smolina, IYu.: Multiscale simulation of porous ceramics based on movable cellular automaton method. J. Phys. Conf. Ser. 894, 012087 (2017)
93.
Askar, A.: Lattice Dynamics Foundation of Continuum Theory. World-Scientific, Singapore (1985)
94.
Erofeyev, V.I., Potapov, A.I.: Longitudinal strain waves in nonlinearly elastic media with couple stresses. Int. J. Non-Linear Mech. 28(4), 483–489 (1993)
95.
Erofeyev, V.I., Potapov, A.I.: Nonlinear wave processes in elastic media with inner structure. Nonlinear World, vol. 2, pp. 1197–1215. World-Scientific, Singapore (1990)
96.
Gendelman, O.V., Manevitch, L.I.: Linear and nonlinear excitations in a polyethylene crystal. Part I. Vibrational modes and linear equations. Macromol. Theor. Simul. 7, 579–589 (1998)
97.
Lisina, S.A., Potapov, A.I., Nesterenko, V.F.: Nonlinear granular medium with rotations of the particles. One-dimensional model. Phys. Acoust. 47(5), 666–674 (2001)
98.
Pouget, J.: Lattice dynamics and stability of modulated-strain structures for elastic phase transitions in alloys. Phys. Rev. B. 48(2), 864–875 (1993)
99.
Sargsyan, A.H., Sargsyan, S.H.: Dynamic model of micropolar elastic thin plates with independent fields of displacements and rotations. J. Sound Vib. 333(18), 4354–4375 (2014)
100.
Sargsyan, S.H.: Micropolar beam model for nanocrystalline material consisting of linear chains of atoms. Phys. Mesomech. 20(4), 425–431 (2017)
101.
Sargsyan, S.H., Sargsyan, A.A.: General dynamic theory of micropolar elastic thin plates with free rotation and special features of their natural oscillations. Acoust. Phys. 57(4), 473–481 (2011)
102.
Gross, E.F.: Light scattering and relaxation phenomena in liquids Doklady Akademii Nauk SSSR 28(9), 788–793 (1940) (in Russian)
103.
Bernal, J.D., Tamm, G.R.: Zero point energy and physical properties of H2O and D2O. Nature 135, 229 (1935)
104.
Gross, E.F., Korshunov, A.V.: Rotational oscillations of molecules in a crystal lattice of organic substances and scattering spectra. JETP. 16(1), 53–59 (1946)
105.
Gross, E.F.: Izbrannye Trudy (Selected Papers). Nauka, Leningrad (1976).((in Russian))
106.
Gross, E.F., Korshunov, A.V., Sel’kin, V.A.: Raman spectra of small frequencies of crystals of para-, meta- and orthoiodiobenzenes. JETP 20, 293–296 (1950)
107.
Abolinsh, Y.Y., Gross, E.F., Shultin, A.A.: Optic-acoustic effect in crystals. Soviet Phys. Tech. Phys. 28, 2255 (1958)
108.
Savin, G.N., Lukashev, A.A., Lysko, E.M., Veremeenko, S.V., Agas’ev, G.G.: Propagation of elastic waves in the Cosserat continuum with constrained particle rotation. Prikl. Mekh. (Appl. Mech.) 6(6), 37–40 (1970) (in Russian)
109.
Erofeyev, V.I., Rodyushkin, V.M.: Observation of the dispersion of elastic waves in a granular composite and a mathematical model for its description. Sov. Phys. Acoust. 38(6), 611–612 (1992)
110.
Potapov, A.I., Rodyushkin, V.M.: Experimental investigation of strain waves in materials with microstructure. Acoust. Phys. 47(1), 347–352 (2001)
111.
Stroscio, M.A., Dutta, M.: Phonons in Nanostructures. Cambridge University Press, 274 p. (2001)
112.
Lyamov, V.E.: Polarization Effects and Anisotropy of the Interaction of Acoustic Waves in Crystals. Mosk. Gos. Univ., Moscow, 224 p. (1983) (in Russian)
113.
Bagdoev, A.G., Erofeyev, V.I., Shekoyan, A.V.: Wave Dynamics of Generalized Continua. Advanced Structured Materials, vol. 24, 274 p. Springer, Berlin, Heidelberg (2016)
114.
Belyaeva, IYu., Zaitsev, VYu., Ostrovsky, L.A.: Nonlinear acoustical properties of granular media. Acoust. Phys. 39, 11–16 (1993)
115.
Bykov, V.G.: Solitary shear waves in a granular medium. Acoust. Phys. 45(2), 138–142 (1999)
116.
Erofeev, V.I.: Wave Processes in Solids with Microstructure. World Scientific Publishing. New Jersey, London, Singapore, Hong Kong, Bangalore, Taipei (2003)
117.
Nazarov, V.E., Radostin, A.V. Nonlinear Acoustic Waves in Micro-Inhomogeneous Solids. Wiley, 251 p. (2015)
118.
Qiu, C., Zhang, X., Liu, Z.: Far-field imaging of acoustic waves by a two-dimensional sonic crystal. Phys. Rev. B 71, 054302–054311 (2005)
119.
Dragunov, T.N., Pavlov, I.S., Potapov, A.I.: Anharmonic interaction of elastic and orientation waves in one-dimensional crystals. Phys. Solid State 39, 118–124 (1997)
120.
Potapov, A.I., Pavlov, I.S.: Nonlinear waves in 1D oriented media. Acoust. Lett. 19(6), 110–115 (1996)
121.
Potapov, A.I., Pavlov, I.S., Gorshkov, K.A., Maugin, G.A.: Nonlinear interactions of solitary waves in a 2D lattice. Wave Motion 34(1), 83–95 (2001)
122.
Potapov, A.I., Pavlov, I.S., Lisina, S.A.: Acoustic Identification of Nanocrystalline Media. J. Sound Vib. 322(3), 564–580 (2009)
123.
Potapov, A.I., Pavlov, I.S., Lisina, S.A.: Identification of nanocrystalline media by acoustic spectroscopy methods. Acoust. Phys. 56(4), 588–596 (2010)
124.
Ghoniem, N.M., et al.: Multiscale modelling of nanomechanics and micromechanics: an over-view. Phil. Mag. 83(31–34), 3475–3528 (2003)
125.
Cleland, A.N.: Foundations of nanomechanics: from solid-state theory to device applications. Springer, Berlin (2003)
126.
Kittel, C.: Introduction to Solid State Physics, 8th edn. Wiley, Inc. (2005)
127.
Pavlov, P.V., Khokhlov, A.F.: Physics of Solid Body: Textbook, p. 494. Visshaya School, Moscow (2000)
128.
Davydov, A.S.: Quantum Mechanics, 637 p. In: Dirk ter Haar (ed.). Pergamon Press (1976)
129.
Rieth, M.: Nano-Engineering in Science and Technology. An Introduction to the World of Nano-Design. World Scientific, 151 p. (2003)
130.
Golovneva, E.I., Golovnev, I.F., Fomin, V.M.: Peculiarities of application of continuum mechanics methods to the description of nano-structures. Phys. Mesomech. 8(5), 41–48 (2005)
131.
132.
Sedov, L.I.: Mathematical methods for constructing new models of continuous media. Russ. Math. Surv. 20(5), 123–182 (1965)
133.
Sedov, L.I.: Models of continuous media with internal degrees of freedom. J. Appl. Math. Mech. 32(5), 803–819 (1968)
134.
Li, C., Chou, T.W.: Structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct. 40, 2487–2499 (2003)
135.
Erofeev, V.I., Leontyeva, A.V., Malkhanov, A.O., Pavlov I.S. Structural modeling of nonlinear localized strain waves in generalized continua. In: Wolfgang, H., Altenbach, H., Muller, W.H., Abali, B.E. (eds.) Advanced Structured Materials. 2019/High Gradient Materials and Related Generalized Continua. Springer Nature Switzerland AG. Part of Springer, Cham, Switzerland, pp. 55–68.
136.
Moshev, V.V., Garishin, O.K.: Structural mechanics of dispersedly filled elastomeric composites. Uspekhi Mekh. 3(2), 3–36 (2005)
137.
Nikitenkova, S.P., Potapov, A.I.: Dispersion properties of two-dimensional phonon crystals with a hexagonal structure. Acoust. Phys. 56(6), 909–918 (2010)
138.
Pavlov, I.S.: Acoustic identification of the anisotropic nanocrystalline medium with non-dense packing of particles. Acoust. Phys. 56(6), 924–934 (2010)
139.
Pavlov, I.S., Potapov, A.I.: Structural models in mechanics of nanocrystalline media. Doklady Phys. 53(7), 408–412 (2008)
140.
Pavlov, I.S., Potapov, A.I., Maugin, G.A.: A 2D granular medium with rotating particles. Int. J. Solids Struct. 43(20), 6194–6207 (2006)
141.
Pavlov, I.S., Vasiliev, A.A., Porubov, A.V.: Dispersion properties of the phononic crystal consisting of ellipse-shaped particles. J. Sound Vib. 384, 163–176 (2016)
142.
Potapov, A.I., Pavlov, I.S., Nikitenkova, S.P., Shudyaev, A.A.: Structural models in nanoacoustics: control of dispersion properties of phonon crystals. Acoustics of inhomogeneous media. In: Proceedings of the Russian acoustic society. Issue 10. Moscow: GEOS, pp. 9–16 (2009) (in Russian)
143.
Pouget, J., Askar, A., Maugin, G.A.: Lattice model for elastic ferroelectric crystals: Microscopic approach. Phys. Rev. B. 33(9), 6304–6325 (1986)
144.
145.
146.
Vasiliev, A.A., Pavlov, I.S.: Structural and mathematical modeling of Cosserat lattices composed of particles of finite size and with complex connections. IOP Conf. Ser.: Mater. Sci. Eng. 447, 012079 (2018)
147.
Shermergor, T.D.: Theory of Elasticity of Micro-Inhomogeneous Media. Nauka, Moscow (1977).((in Russian))
148.
Miller, R.E., Shenoy, V.B.: Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11, 139–147 (2000)
149.
Solyaev, Yu., Lurie, S.: Numerical predictions for the effective size-dependent properties of piezoelectric composites with spherical inclusions. Compos. Struct. 202, 1099–1108 (2018)
150.
Gulyaev, Yu.V., Lagar’kov, A.N., Nikitov, S.A.: Metamaterials: basic research and potential applications. Herald Russ. Acad. Sci. 78, 268–278 (2008)
151.
Vityaz, P.A., Shelekhina, V.M., Prokhorov, O.A., Gaponenko, N.V.: Preparation of pseudocrystalline materials based on silica. Proc. Natl. Acad. Sci. Belarus. Physical-Technical Ser. 1, 16–20 (2002) (in Russian)
152.
Sidorov, L.N., Yurovskaya, M.A., Borschevskii, A.Y., Trushkov, I.V., Ioffe, I.N.: Fullerenes. Ekzamen, Moscow, 690 p. (2005) (in Russian)
153.
Suzdalev, I.P.: Nanotechnology: Physical Chemistry of Nanoclusters, Nanostructures, and Nanomaterials. KomKniga, Moscow (2006).((in Russian))
154.
Morozov, A.N., Skripkin, A.V.: Behaviour of polymer chains and structures under the influence of random forces. Nonlinear World. 13(7), 33–37 (2015) ((in Russian))
155.
Blank, V.D., Levin, V.M., Prokhorov, V.M., Buga, S.G., Dubitskii, G.A., Serebryanaya, N.R.: Elastic properties of ultrahard fullerites. J. Exp. Theoret. Phys. 87, 741–746 (1998)
156.
Kulbachinskii, V.A., Buga, S.G., Blank, V.D., Dubitsky, G.A., Serebryanaya, N.R.: Superconducting superhard composites based on C60, diamond or boron nitride and MgB2. J. Nanostruct. Polym. Nanocompos. 6(4), 119–122 (2010)
157.
Kobelev, N.P., Soifer, Ya.M., Bashkin, I.O., Moravski, A.P.: Elastic and dissipative properties of C60 fullerite. Nanostruct. Mater. 6(5), 909–912 (1995)
158.
Yildirim, T., Harris, A.B.: Lattice dynamics of solids C60. Phys. Rev. B 46, 7878–7896 (1992)
159.
Mikhalchenko, V.P., Motskin, V.V.: On elastic properties of fullerite C60 f.c.c. phase. J. Thermoelectricity 3, 31–44 (2004)
160.
Koch, E.: Enhancing TC in field-doped fullerenes by applying uniaxial stress. Phys. Rev. B. 66, 081401 (2002)
161.
Kobelev, N.P., Nikolaev, R.K., Soifer, Ya.M., Khasanov, S.S.: Elastic moduli of single-crystal C60. Phys. Solid State 40(1), 154–156 (1998)
162.
Ostrovsky, L.A., Potapov, A.I.: Modulated Waves: Theory and Applications. The Johns Hopkins University Press, Baltimore, MD (1999)
163.
Vinogradova, M.B., Rudenko, O.V., Sukhorukov, A.P.: Theory of Waves. Nauka, Moscow (1990).((in Russian))
164.
165.
Vardoulakis, I., Sulem, J.: Bifurcation Analysis in Geomechanics, p. 459. Blackie Academic and Professional, London (1995)
166.
Chang, C.S., Ma, L.: A micromechanical-based micropolar theory for deformation of granular solids. Int. J. Solids Struct. 28(1), 67–87 (1994)
167.
Christoffersen, J., Mehrabadi, M.M., Nemat-Nasser, S.A.: A micromechanical description of granular material behavior. Trans. ASME. J. Appl. Mech. 48(2), 339–344 (1981)
168.
Sadovskaya, O., Sadovskii, V.: Mathematical Modeling in Mechanics of Granular Materials. Springer, Heidelberg, New York, Dordrecht, London, 390 p. (2012)
169.
Lippman, H.: Cosserat plasticity and plastic spin. Appl. Mech. Rev. 48(11) Part 1, 753–762 (1995)
170.
Bobrovnitskii, Yu.I.: An acoustic metamaterial with unusual wave properties. Acoust. Phys. 60(4), 371–378 (2014)
171.
Bobrovnitskii, Yu.I.: Models and general wave properties of two-dimensional acoustic metamaterials and media. Acoust. Phys. 61(3), 255–264 (2015)
172.
Bobrovnitskii, Yu.I., Tomilina, T.M.: Sound absorption and metamaterials: a review. Acoust. Phys. 64(5), 519–526 (2018)
173.
Cummer, S.A., Christensen, J., Alù, A.: Controlling sound with acoustic metamaterials. Nat. Rev. Mater. 1, 16001 (2016)
174.
Fedotovskii, V.S.: A porous medium as an acoustic metamaterial with negative inertial and elastic properties. Acoust. Phys. 64(5), 548–554 (2018)
175.
Kolken, H.M.A., Zadpoor, A.A.: Auxetic mechanical metamaterials. RSC Adv. 7(9), 5111–5129 (2017)
176.
Zhu, S., Zhang, X.: Metamaterials: artificial materials beyond nature. Natl. Sci. Rev. 5(2), 131 (2018)
177.
Solyaev, Yu., Lurie, S., Ustenko, A.: Numerical modeling of a composite auxetic metamaterials using micro-dilatation theory. Continuum Mech. Thermodyn. 31, 1099–1107 (2019)
178.
Altenbach, H., Maugin, G.A., Erofeev, V.I. (eds.): Mechanics of Generalized Continua. Springer, Berlin, Heidelberg, 350 p. (2011)
179.
Maugin, G.A., Metrikine, A.V. (eds.): Mechanics of Generalized Continua. One Hundred Years After the Cosserats. Springer, 337 p. (2010)
180.
Vakhnenko, V.A.: Diagnosis of the properties of a structurized medium by long nonlinear waves. J. Appl. Mech. Tech. Phys. 37(5), 643–649 (1996)
181.
Destrade, M., Gilchrist, M.D., Saccomandi, G.: Third- and fourth-order constants of incompressible soft solids and the acousto-elastic effect. J. Acoust. Soc. Am. 127(5), 2759–2763 (2010)
182.
Nikitina, N.E.: Acoustoelasticity. Experience of Practical Application. TALAM, Nizhny Novgorod, 208 p (2005) (in Russian)
183.
Erofeev, V.I., Pavlov, I.S.: Rotational waves in microstructured materials. In: dell’Isola, F., Eremeyev, V.A., Porubov, A.V. (eds.) Advances in Mechanics of Microstructured Media and Structures, Advanced Structured Materials, vol. 87, pp. 103–124. Springer, Cham (2018)
184.
Love, A.E.H.: A treatise on the mathematical theory of elasticity, 4th edn. Cambridge University Press, Cambridge (1927)
185.
Broberg, K.B.: The cell model of materials. Comput. Mech. 19, 447–452 (1997)
186.
Gendelman, O.V., Manevitch, L.I.: The description of polyethylene crystal as a continuum with internal degrees of freedom. Int. J. Solids Struct. 33(12), 1781–1798 (1996)
187.
Pavlov, I.S., Potapov, A.I.: Two-dimensional model of a granular medium. Mech. Solids 42(2), 250–259 (2007)
188.
Fedorov, V.I.: Theory of Elastic Waves in Crystals. Nauka, Moscow (1965); Plenum Press, New York (1968)
189.
Goldshtein, R.V., Chentsov, A.V.: A discrete-continual model for a nanotube. Mech. Solids 4, 57–74 (2005)
190.
Erofeev, V.I., Malkhanov, A.O., Zemlyanukhin, A.I., Catcon, V.M.: Nonlinear magnetoelastic waves in a plate. In: Altenbach, H., Eremeyev, V.A. (eds.) Shell-like Structures. Non-classical Theories and Applications. Advanced Structured Materials, vol. 15, pp. 125–134. Springer, Heidelberg, Dordrecht, London, New York (2011)
191.
Maugin, G.A.: Continuum Mechanics of Electromagnetic Solids. North-Holland Amsterdam (1988)
192.
193.
Metadaten
Titel
Theoretical Basis of the Structural Modeling Method
verfasst von
Vladimir I. Erofeev
Igor S. Pavlov
Copyright-Jahr
2021
Buch
Structural Modeling of Metamaterials

Print ISBN: 978-3-030-60329-8

Electronic ISBN: 978-3-030-60330-4

Copyright-Jahr: 2021

DOI
https://doi.org/10.1007/978-3-030-60330-4_1

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