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An accelerated FFT algorithm for thermoelastic and nonlinear composites. (English) Zbl 1195.74302
Summary: A fast numerical algorithm to compute the local and overall responses of nonlinear composite materials is developed. This alternative formulation allows us to improve the convergence of the existing method of e.g. H. Moulinec and P. Suquet [Comput. Methods Appl. Mech. Eng. 157, No. 1–2, 69–94 (1998; Zbl 0954.74079)]. In the present method, a nonlinear elastic (or conducting) material is replaced by infinitely many locally linear thermoelastic materials with moduli that depend on the values of the local fields. This makes it possible to use the advantages of an algorithm developed by D.J. Eyre and G.W. Milton [Eur. Phys. J. Appl. Phys. 6, No. 1, 41–47 (1999)], which has faster convergence. The method is applied to compute the local fields as well as the effective response of nonlinear conducting and elastic periodic composites.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74E30 Composite and mixture properties
74F05 Thermal effects in solid mechanics
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