Fourier spectral methods for phase field fracture modelling of CMCs

Abstract

Numerical homogenization of multiphase brittle materials, such as ceramic matrix composites is obviously a computationally intensive task. Common approach involving multiscale finite element models remains quite limited to scientific applications instead of being a reasonable alternative for analytical constitutive models. Despite the exponential growth of computational resources (known as Moore’s law) numerical complexity of the underlying algorithms is simply too high to ensure proper scaling to millions of elements. One of the approaches in-between continuous and discrete mechanics is the use of fast Fourier transform (FFT). The aim of this paper is to extend FFT-based methodology beyond its usual elastic regime, using mathematical formalism developed earlier for FE by means of variational principles. Governing equations are formulated in the frequency domain and solved iteratively on a parallel system. Well-known computational specifics of the discrete FFT algorithm itself provide uncompromised efficiency and a first, promising step towards truly multiscale mechanical analysis of random microstructures.