The inverse-deformation approach to fracture

TL;DR

This paper introduces a one-dimensional elastic model with higher gradients that predicts spontaneous fracture through bifurcation analysis, avoiding the need for damage variables or predefined surface energy.

Contribution

It presents a novel inverse-deformation approach with higher gradients for fracture prediction, enabling analysis without additional damage or phase-field variables.

Findings

Fracture occurs at a critical load via bifurcation.

Surface energy arises from higher gradient effects.

Model predicts spontaneous fracture without discontinuous deformations.

Abstract

We propose a one-dimensional, nonconvex elastic constitutive model with higher gradients that can predict spontaneous fracture at a critical load via a bifurcation analysis. It overcomes the problem of discontinuous deformations without additional field variables, such as damage or phase-field variables, and without a priori specified surface energy. Our main tool is the use of the inverse deformation, which can be extended to be a piecewise smooth mapping even when the original deformation has discontinuities describing cracks opening. We exploit this via the inverse-deformation formulation of finite elasticity due to Shield and Carlson, including higher gradients in the energy. The problem is amenable to a rigorous global bifurcation analysis in the presence of a unilateral constraint. Fracture under hard loading occurs on a bifurcating solution branch at a critical applied stretch level and fractured solutions are found to have surface energy arising from higher gradient effects.