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FFT-based homogenization for microstructures discretized by linear hexahedral elements

: Schneider, Matti; Merkert, Dennis; Kabel, Matthias


International journal for numerical methods in engineering 109 (2017), No.10, pp.1461-1489
ISSN: 0029-5981
Journal Article
Fraunhofer ITWM ()
elasticity; finite element methods; micromechanics; homogenization; LippmannSchwinger equation; FFT

The FFT-based homogenization method of Moulinec-Suquet has recently emerged as a powerful tool for computing the macroscopic response of complex microstructures for elastic and inelastic problems. In this work, we generalize the method to problems discretized by trilinear hexahedral elements on Cartesian grids and physically nonlinear elasticity problems. We present an implementation of the basic scheme that reduces the memory requirements by a factor of four and of the conjugate gradient scheme that reduces the storage necessary by a factor of nine compared with a naive implementation. For benchmark problems in linear elasticity, the solver exhibits mesh- and contrast-independent convergence behavior and enables the computational homogenization of complex structures, for instance, arising from computed tomography computed tomography (CT) imaging techniques. There exist 3D microstructures involving pores and defects, for which the original FFT-based homogenization scheme does not converge.