H. Moulinec et P. Suquet, A NUMERICAL-METHOD FOR COMPUTING THE OVERALL RESPONSE OF NONLINEAR COMPOSITES WITH COMPLEX MICROSTRUCTURE, Computer methods in applied mechanics and engineering, 157(1-2), 1998, pp. 69-94
The local and overall responses of nonlinear composites are classicall
y investigated by the Finite Element Method. We propose an alternate m
ethod based on Fourier series which avoids meshing and which makes dir
ect use of microstructure images. It is based on the exact expression
of the Green function of a linear elastic and homogeneous comparison m
aterial. First, the case of elastic nonhomogeneous constituents is con
sidered and an iterative procedure is proposed to solve the Lippman-Sc
hwinger equation which naturally arises in the problem. Then, the meth
od is extended to non-linear constituents by a step-by-step integratio
n in time. The accuracy of the method is assessed by varying the spati
al resolution of the microstructures. The flexibility of the method al
lows it to serve for a large variety of microstructures. (C) 1998 Else
vier Science S.A.