Fracture as a pattern formation process

TL;DR

This paper introduces a continuum model for crack propagation that accounts for elastodynamic and viscoelastic effects, providing steady state solutions and exploring different propagation mechanisms using phase field and multipole expansion methods.

Contribution

It presents a novel continuum model incorporating elastodynamic and viscoelastic effects for crack propagation, with solutions for steady state crack shapes and velocities.

Findings

Steady state crack shapes and velocities are obtained.

Different propagation mechanisms are analyzed.

Phase field and multipole expansion methods are used for solutions.

Abstract

A continuum model of crack propagation is presented and discussed. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic and viscoelastic effects are taken into account. Two different mechanism of crack propagation, a first order phase transition and surface diffusion are considered, and we discuss different loading modes. The arising free boundary problems are solved by phase field methods and a sharp interface approach using a multipole expansion technique.