An FFT‐based method for computing weighted minimal surfaces in microstructures with applications to the computational homogenization of brittle fracture. (4th December 2019)

• Record Type: Journal Article
• Authors: Schneider, Matti
• Is Part Of: International journal for numerical methods in engineering. Volume 121:Number 7(2020)
• Page Start: 1367
• Page End: 1387
• Publication Date: 2019-12-04
• Subjects: brittle fracture -- computational homogenization -- FFT‐based method -- maximum flow -- primal‐dual algorithms; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6270
• Languages: English
• ISSNs: 0029-5981

Abstract

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.