A numerical method for computing the overall response of nonlinear composites with complex microstructure. (English) Zbl 0954.74079

Summary: The local and overall responses of nonlinear composites are classically investigated by the finite element method. We propose an alternate method based on Fourier series which avoids meshing and which makes direct use of microstructure images. It is based on the exact expression of the Green function of a linear elastic and homogeneous comparison material. First, the case of elastic nonhomogeneous constituents is considered and an iterative procedure is proposed to solve the Lippmann-Schwinger equation which naturally arises in the problem. Then, the method is extended to nonlinear constituents by a step-by-step integration in time. The accuracy of the method is assessed by varying the spatial resolution of the microstructures. The flexibility of the method allows to use it for a large variety of microstructures.


74S25 Spectral and related methods applied to problems in solid mechanics
74E30 Composite and mixture properties
74M25 Micromechanics of solids
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