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Effective constants in the theory of geometrically nonlinear solids. (English. Russian original) Zbl 0469.73010

Sov. Appl. Mech. 17, 439-444 (1981); translation from Prikl. Mekh. 17, No. 5, 45-50 (1981).

MSC:

74B20 Nonlinear elasticity
74E05 Inhomogeneity in solid mechanics
Full Text: DOI

References:

[1] A. N. Guz’, Stability of Elastic Bodies under Finite Deformations [in Russian], Naukova Dumka, Kiev (1973).
[2] A. N. Guz’, F. G. Makhort, and O. P. Gushcha, Introduction to Acoustical Elasticity [in Russian], Naukova Dumka, Kiev (1977).
[3] B. P. Maslov, ?Third order macroscopic elastic moduli,? Prikl. Mekh.,15, 57?61 (1979).
[4] B. P. Maslov and L. P. Khoroshun, ?Effective characteristics of elastic physically nonlinear inhomogeneous media,? Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 149?154 (1977).
[5] C. Truesdell, A First Course in Rational Continuum Mechanics, Academic Press, New York (1972).
[6] S. Bharata and M. Levinson, ?Signorini’s perturbation scheme for a general reference configuration in finite electrostatics,? Arch. Rat. Mech. Anal.,67, 365?394 (1978).
[7] A. E. Green and J. E. Adkins, Large Elastic Deformations, Clarendon Press, Oxford (1970).
[8] R. Hill, ?On constitutive macrovariables for heterogeneous solids at finite strain,? Proc. Roy. Soc. Ser. A,326, 131?147 (1972). · Zbl 0229.73004 · doi:10.1098/rspa.1972.0001
[9] R. W. Ogden, ?On the overall moduli of nonlinear elastic composite materials,? J. Mech. Phys. Solids,22, 541?554 (1974). · Zbl 0293.73003 · doi:10.1016/0022-5096(74)90033-7
[10] R. S. Rivlin, ?The solution of problems in second order elasticity theory,? in: Continuum Mechanics IV: Problems in Nonlinear Elasticity, Gordon and Breach, New York (1965), pp. 110?139.
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