A consistent multi-phase-field formulation for anisotropic brittle fracture

Abstract

Anisotropic fracture modelling constitutes an important problem in fracture mechanics as many natural, composite and architected materials exhibit fracture anisotropy. The multi-phase-field technique offers a seemingly straightforward and easy-to-implement approach for handling a range of fracture anisotropies, some of which would otherwise necessitate the use of higher-order damage formulation. However, a closer examination reveals that the formulation contains a few inconsistencies, which hinder the establishment of precise definitions for crack through phase-fields and fracture toughness. In this article, we present modifications to the multi-phase-field approach aimed at rectifying these issues. Our model introduces a new degradation function, enabling an unambiguous definition of crack and leading to an analytical expression of the modelled fracture toughness. We conduct an in-depth analysis of several key components of the present formulation and discuss the nature of anisotropy it can handle in its current form, and also outline a roadmap for expanding its capability. A limited set of numerical simulations is also provided to illustrate the effectiveness of the current proposition.