A micromorphic phase-field model for brittle and quasi-brittle fracture

TL;DR

This paper introduces a micromorphic phase-field model for fracture that simplifies numerical implementation and improves accuracy in simulating brittle and quasi-brittle fractures by regularizing the problem and handling irreversibility efficiently.

Contribution

It proposes a novel micromorphic extension of the phase-field model that addresses computational challenges and enhances fracture irreversibility enforcement.

Findings

Effective in simulating brittle fracture

Handles quasi-brittle fracture accurately

Simplifies numerical implementation

Abstract

The phase-field model for fracture, despite its popularity and ease of implementation comes with its set of computational challenges. They are the non-convex energy functional, variational inequality due to fracture irreversibility, the need for extremely fine meshes to resolve the fracture. In this manuscript, the focus is on the numerical treatment of variational inequality. In this context, the popular history-variable approach suffers from variationally inconsistency and non-quantifiable nature of the error introduced. A better alternative, the penalisation approach, has the potential to render the stiffness matrix ill-conditioned. In order to circumvent both aforementioned issues, a micromorphic approach towards phase-field fracture modelling is proposed in this manuscript. Within this approach, a micromorphic extension of the energy functional is carried out. This transforms the phase-field into a local variable, while introducing a micromorphic variable that regularises the fracture problem. This reduction the regularity requirements for the phase-field enables an easier implementation of the fracture irreversibility constraint through simple 'max' operation, with system level precision. Numerical experiments carried out on benchmark brittle and quasi-brittle problems demonstrate the applicability and efficacy of the proposed model for a wide range of fracture problems.