Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 121, Issue 7, Pages 1367-1387Publisher
WILEY
DOI: 10.1002/nme.6270
Keywords
brittle fracture; computational homogenization; FFT-based method; maximum flow; primal-dual algorithms
Funding
- German Research Foundation [GRK 2078-1, SCHN 1595/2-1]
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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.
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