A modified FFT-based solver for the mechanical simulation of heterogeneous materials with Dirichlet boundary conditions

Abstract

Fast Fourier transform based algorithms, relying on the initial idea proposed by Moulinec and Suquet in 1998, are very efficient in the context of periodic homogenization in solid mechanics. The purpose of this short note is to propose a simple modification of these algorithms to extend their application domain from periodic boundary conditions (BC) to Dirichlet BC. The method is validated by a direct comparison with standard finite element simulations with prescribed displacements at the boundary. The convergence properties of the iterative algorithm are then analyzed using a simple example (2D matrix–inclusion) as a function of various parameters (material and algorithm parameters).

Keywords

• FFT-based methods
• Dirichlet boundary conditions
• Heterogeneous materials
• Homogenization in solid mechanics