Complex fracture nucleation and evolution with nonlocal elastodynamics

TL;DR

This paper introduces a nonlocal elastodynamic model for predicting complex fracture nucleation and evolution without damage variables, capable of simulating multiple interacting dynamic fractures.

Contribution

It presents a novel continuum model based on integral operators and a nonconvex strain energy density, avoiding damage laws and reproducing Griffith fracture in the limit.

Findings

Model is mathematically well-posed.

Capable of simulating multiple dynamic fractures.

Reproduces Griffith fracture in the zero-region limit.

Abstract

A mechanical model is introduced for predicting the initiation and evolution of complex fracture patterns without the need for a damage variable or law. The model, a continuum variant of Newton's second law, uses integral rather than partial differential operators where the region of integration is over finite domain. The force interaction is derived from a novel nonconvex strain energy density function, resulting in a nonmonotonic material model. The resulting equation of motion is proved to be mathematically well-posed. The model has the capacity to simulate nucleation and growth of multiple, mutually interacting dynamic fractures. In the limit of zero region of integration, the model reproduces the classic Griffith model of brittle fracture. The simplicity of the formulation avoids the need for supplemental kinetic relations that dictate crack growth or the need for an explicit damage evolution law.