期刊
COMPUTATIONAL MECHANICS
卷 54, 期 6, 页码 1497-1514出版社
SPRINGER
DOI: 10.1007/s00466-014-1071-8
关键词
Composite materials; Finite deformations; Lippmann-Schwinger equation; FFT
资金
- German Research Foundation (DFG), Federal Cluster of Excellence MERGE Technologies for Multifunctional Lightweight Structures [EXC 1075]
In recent years the FFT-based homogenization method of Moulinec and Suquet has been established as a fast, accurate and robust tool for obtaining effective properties in linear elasticity and conductivity problems. In this work we discuss FFT-based homogenization for elastic problems at large deformations, with a focus on the following improvements. Firstly, we exhibit the fixed point method introduced by Moulinec and Suquet for small deformations as a gradient descent method. Secondly, we propose a Newton-Krylov method for large deformations. We give an example for which this methods needs approximately 20 times less iterations than Newton's method using linear fixed point solvers and roughly 100 times less iterations than the non-linear fixed point method. However, the Newton-Krylov method requires 4 times more storage than the non-linear fixed point scheme. Exploiting the special structure we introduce a memory-efficient version with 40% memory saving. Thirdly, we give an analytical solution for the micromechanical solution field of a two-phase isotropic St. Venant-Kirchhoff laminate. We use this solution for comparison and validation, but it is of independent interest. As an example for a microstructure relevant in engineering we discuss finally the application of the FFT-based method to glass fiber reinforced polymer structures.
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