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Effective properties of composite materials with periodic microstructure: A computational approach. (English) Zbl 0964.74054
After a review of the state of knowledge about composites with periodic microstructure, the authors discuss two different numerical methods. For the first one, which is based on the finite element method (FEM), they use the periodicity conditions and the concept of averaged strain or stress, respectively, for linearly elastic, elastoplastic and power-law materials. In the second one, the authors expoit fast Fourier transform method (FFTM) and the concept of homogeneous reference material. At last, three test examples and three advanced ones are analyzed numerically using FEM and FFTM. In the linearly elastic case for a moderate contrast between the phases, the FFTM is must faster than FEM; in the strongly nonlinear case and for a very large contrast between the phases, the FFTM, however, does not converge.

MSC:
74Q15 Effective constitutive equations in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74S25 Spectral and related methods applied to problems in solid mechanics
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