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A fast numerical method for computing the linear and nonlinear mechanical properties of composites. (English. Abridged French version) Zbl 0799.73077
Summary: This note is devoted to a new iterative algorithm to compute the local and overall response of a composite from images of its (complex) microstructure. The elastic problem for a heterogeneous material is formulated with the help of a homogeneous reference medium and written under the form of a periodic Lippman-Schwinger equation. Using the fact that the Green’s function of the pertinent operator is known explicitly in Fourier space, this equation is solved iteratively. The method is extended to the case where the individual constituents are elastic- plastic von Mises materials with isotropic hardening.

74S30 Other numerical methods in solid mechanics (MSC2010)
74E30 Composite and mixture properties
74A60 Micromechanical theories
74M25 Micromechanics of solids