Comparison of FFT-based methods for computing the response of composites with highly contrasted mechanical properties

Numerical simulations of the behavior of composite materials have to take into account the complexity of their microstructural geometry. Realistic simulations involve a large number of degrees of freedom. FFT-based methods have proved their efficiency for mechanical problems (composites with linear elastic or elastic-plastic phases), and can often be much more efficient than classical finite element methods. However the iterative method initially proposed in Moulinec and Suquet (C.R. Acad. Sci. Paris II 318 (1994) 1417) requires a number of iterations roughly proportional to the contrast between the moduli of the individual phases. The improved method proposed in Eyre and Milton (J. Phys. III 6 (1999) 41) has a rate of convergence proportional to the square root of the contrast, but still cannot be applied to composites with infinite contrast (like porous materials). An alternate scheme based on augmented Lagrangians and Fourier Transforms has been proposed in Michel et al. (Comput. Modelling Eng. Sci. (2000) accepted) for highly contrasted or even infinitely contrasted materials. The efficiency of these three methods are compared as a function of the contrast between the phases. (C) 2003 Elsevier B.V. All rights reserved.