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Mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading. (English) Zbl 1195.74142

Summary: We present a generalization of the classical mathematical homogenization theory aimed at accounting for finite unit cell distortions, which gives rise to a nonperiodic asymptotic expansion. We introduce an auxiliary macro-deformed configuration, where the overall Cauchy stress is defined, and nonperiodic boundary conditions. Verification studies against a direct numerical simulation demonstrate the versatility of the proposed method.

MSC:

74Q05 Homogenization in equilibrium problems of solid mechanics
74E05 Inhomogeneity in solid mechanics

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