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Homogenization of elasticity equations with contrasting coefficients. (English. Russian original) Zbl 0963.74046

Sb. Math. 190, No. 12, 1749-1806 (1999); translation from Mat. Sb. 190, No. 12, 37-92 (1999).
The author considers non-stationary problems of linearized elasticity in an \(\varepsilon\)-periodic \((\varepsilon\ll 1)\) porous medium, the ratio of minimum and maximum values of elasticity moduli being also a small parameter. He derives homogenized equations and estimates the accuracy of this approximation, especially examining the dependence on certain parameters and on geometric properties of pores.

MSC:

74Q10 Homogenization and oscillations in dynamical problems of solid mechanics
74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
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