A class of general algorithms for multi-scale analyses of heterogeneous media

• Published in: Computer methods in applied mechanics and engineering Vol. 190; no. 40; pp. 5427 - 5464
• Main Authors: Terada, K., Kikuchi, N.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 20.07.2001; Elsevier
• Subjects: Computational techniques; Cross-disciplinary physics: materials science; rheology; Deformation, plasticity, and creep; Exact sciences and technology; Finite-element and galerkin methods; Heterogeneous media; Homogenization theory; Materials science; Mathematical methods in physics; Multi-scale analysis; Nonlinear behavior; Physics; Treatment of materials and its effects on microstructure and properties; Variational methods; Multi-scale analysis; Homogenization theory; Nonlinear behavior; Variational methods; Heterogeneous media; Finite element method; Asymptotic expansion; Heterogeneous medium; Multiscale method; Homogenization; Mechanics; Variational calculus; Modelling; Numerical method; Mechanical contacts; Microstructure; Inhomogeneous materials
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/S0045-7825(01)00179-7

A class of computational algorithms for multi-scale analyses is developed in this paper. The two-scale modeling scheme for the analysis of heterogeneous media with fine periodic microstructures is generalized by using relevant variational statements. Instead of the method of two-scale asymptotic expansion, the mathematical results on the generalized convergence are utilized in the two-scale variational descriptions. Accordingly, the global–local type computational schemes can be unified in association with the homogenization procedure for general nonlinear problems. After formulating the problem in linear elastostatics, that with local contact condition and the elastoplastic problem, we present representative numerical examples along with the computational algorithm consistent with our two-scale modeling strategy as well as some direct approaches.