Non-linear extension of FFT-based methods accelerated by conjugate gradients to evaluate the mechanical behavior of composite materials

摘要: Abstract FFT-based methods are used to solve the problem of a heterogeneous unit-cell submitted periodic boundary conditions, which is great interest in context numerical homogenization. Recently (in 2010), Brisard and Zeman proposed simultaneously use Conjugate Gradient based solvers order improve convergence properties (when compared basic scheme, initially 1994). The purpose paper extend this idea case non-linear behaviors. method on Newton–Raphson algorithm can be applied various kinds behaviors (time dependant or independent, with without internal variables) through conventional integration procedure as finite element codes. It must pointed out that approach fundamentally different from traditional approaches rely fixed-point (e.g. Eyre Milton accelerated Augmented Lagrangian etc.). scheme basis simple application (a linear elastic spherical inclusion within matrix): low sensitivity reference material an improved efficiency, for soft stiff inclusion, observed. At first prescribed macroscopic strain, then extended mixed loadings.