Consistent macroscopic tangent computation for FFT‐based computational homogenization at finite strains

Consistent macroscopic tangent computation for FFT‐based computational homogenization at finite... The present work addresses the efficient computation of effective properties of periodic microstructures by the use of Fast Fourier Transforms. While effective quantities in terms of stresses and deformations can be computed from surface integrals along the boundary of an RVE, the computation of the associated moduli is not straight‐forward. The contribution of the present paper is thus the derivation and implementation of an algorithmically consistent macroscopic tangent operator that comprises the effective properties of the RVE. In contrast to finite‐difference based approaches, an exact solution for the macroscopic tangent is derived by means of the classical Lippmann‐Schwinger equation. The problem then reduces to the solution of a system of linear equations even for nonlinear material behaviour. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

Consistent macroscopic tangent computation for FFT‐based computational homogenization at finite strains

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710264
Publisher site
See Article on Publisher Site

Abstract

The present work addresses the efficient computation of effective properties of periodic microstructures by the use of Fast Fourier Transforms. While effective quantities in terms of stresses and deformations can be computed from surface integrals along the boundary of an RVE, the computation of the associated moduli is not straight‐forward. The contribution of the present paper is thus the derivation and implementation of an algorithmically consistent macroscopic tangent operator that comprises the effective properties of the RVE. In contrast to finite‐difference based approaches, an exact solution for the macroscopic tangent is derived by means of the classical Lippmann‐Schwinger equation. The problem then reduces to the solution of a system of linear equations even for nonlinear material behaviour. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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