FFT‐based homogenization for microstructures discretized by linear hexahedral elements. (18th August 2016)

• Record Type: Journal Article
• Authors: Schneider, Matti; Merkert, Dennis; Kabel, Matthias
• Is Part Of: International journal for numerical methods in engineering. Volume 109:Number 10(2017)
• Page Start: 1461
• Page End: 1489
• Publication Date: 2016-08-18
• Subjects: elasticity -- finite element methods -- micromechanics -- homogenization -- Lippmann–Schwinger equation -- FFT; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5336
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: 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. In contrast, for the proposed scheme, convergence is ensured. Also, the solution fields are devoid of the spurious oscillations and checkerboarding artifacts associated to conventional schemes. We demonstrate the power of the approach by computing the elasto‐plastic response of a long‐fiber reinforced thermoplastic material with 172 × 10 6 (displacement) degrees of freedom. Copyright © 2016 John Wiley & Sons, Ltd.