An FFT-based method for computing the effective crack energy of a heterogeneous material on a combinatorially consistent grid

TL;DR

This paper presents an FFT-based solver for the combinatorial continuous maximum flow method to accurately compute the effective crack energy in heterogeneous materials, addressing issues of discretization artifacts and scalability.

Contribution

It introduces an FFT-accelerated ADMM solver for the combinatorial maximum flow discretization, improving efficiency and adaptability for large-scale heterogeneous microstructure analysis.

Findings

Efficient FFT-based solver for large-scale microstructure problems

Reduction of discretization artifacts in crack energy computation

Successful application to industrial-scale problems

Abstract

We introduce an FFT-based solver for the combinatorial continuous maximum flow discretization applied to computing the minimum cut through heterogeneous microstructures. Recently, computational methods were introduced for computing the effective crack energy of periodic and random media. These were based on the continuous minimum cut-maximum flow duality of G. Strang, and made use of discretizations based on trigonometric polynomials and finite elements. For maximum flow problems on graphs, node-based discretization methods avoid metrication artifacts associated to edge-based discretizations. We discretize the minimum cut problem on heterogeneous microstructures by the combinatorial continuous maximum flow discretization introduced by Couprie et al. Furthermore, we introduce an associated FFT-based ADMM solver and provide several adaptive strategies for choosing numerical parameters. We demonstrate the salient features of the proposed approach on problems of industrial scale.