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An FFT‐based method for computing weighted minimal surfaces in microstructures with applications to the computational homogenization of brittle fracture
Author(s) -
Schneider Matti
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6270
Subject(s) - homogenization (climate) , fast fourier transform , anisotropy , fourier transform , fracture mechanics , computer science , mathematics , mathematical analysis , algorithm , materials science , composite material , physics , biodiversity , ecology , quantum mechanics , biology
Summary Cell formulae for the effective crack resistance of a heterogeneous medium obeying Francfort‐Marigo's formulation of linear elastic fracture mechanics have been proved recently, both in the context of periodic and stochastic homogenization. This work proposes a numerical strategy for computing the effective, possibly anisotropic, crack resistance of voxelized microstructures using the fast Fourier transform (FFT). Based on Strang's continuous minimum cut—maximum flow duality, we explore a primal‐dual hybrid gradient method for computing the effective crack resistance, which may be readily integrated into an existing FFT‐based code for homogenizing thermal conductivity. We close with demonstrative numerical experiments.