An FFT‐based method for computing weighted minimal surfaces in microstructures with applications to the computational homogenization of brittle fracture

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 co...

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Published in:International journal for numerical methods in engineering 2020-04, Vol.121 (7), p.1367-1387
Main Author: Schneider, Matti
Format: Article
Language:English
Subjects:
brittle fracture
Computation
computational homogenization
Crack propagation
Fast Fourier transformations
FFT‐based method
Fourier transforms
Fracture mechanics
Homogenization
Linear elastic fracture mechanics
maximum flow
Minimal surfaces
primal‐dual algorithms
Thermal conductivity
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description 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.
doi_str_mv 10.1002/nme.6270
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subjects brittle fracture
Computation
computational homogenization
Crack propagation
Fast Fourier transformations
FFT‐based method
Fourier transforms
Fracture mechanics
Homogenization
Linear elastic fracture mechanics
maximum flow
Minimal surfaces
primal‐dual algorithms
Thermal conductivity
title An FFT‐based method for computing weighted minimal surfaces in microstructures with applications to the computational homogenization of brittle fracture
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