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A class of general algorithms for multi-scale analyses of heterogeneous media. (English) Zbl 1001.74095
Summary: We develop a class of computational algorithms for multi-scale analysis. The two-scale modeling scheme for analysis of heterogeneous media with fine periodic microstructures is generalized by using relevant variational statements. Instead of the method of two-scale asymptotic expansion, we employ mathematical results on the generalized convergence in the two-scale variational description. Accordingly, the global-local type computational schemes can be unified with the homogenization procedure for general nonlinear problems. After formulating a problem in linear elastostatics, a problem with local contact condition, and an elastoplastic problem, we present numerical examples along with computational algorithms consistent with two-scale modeling strategy, as well as some direct approaches.

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