An artificial viscosity approach to quasistatic crack growth

TL;DR

This paper presents a novel model for quasistatic crack growth using an artificial viscosity approach, where crack evolution is derived as a limit of a modified gradient flow as viscosity vanishes.

Contribution

It introduces a new mathematical framework for modeling irreversible crack growth based on a viscosity-regularized gradient flow approach.

Findings

Crack evolution can be obtained as a limit of a viscosity-regularized flow.

The model captures irreversible crack growth dynamics.

Mathematical analysis of the limit process is provided.

Abstract

We introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\epsilon$-gradient flow of the energy functional, as the "viscosity" parameter $\epsilon$ tends to zero.