Quasistatic growth of cavities and cracks in the plane

TL;DR

This paper introduces a mathematical model for the slow growth of cavities and cracks in 2D elastic materials, capturing irreversibility and coalescence, with proven existence of solutions for finite cavities.

Contribution

It develops a novel quasistatic growth model for cavities and cracks in nonlinear elasticity, including coalescence and irreversibility, with an existence theorem for finite cavities.

Findings

Existence of quasistatic evolutions for finite cavities

Model accounts for cavity coalescence into cracks

Irreversibility of cavitation and fracture processes

Abstract

We propose a model for quasistatic growth of cavities and cracks in two-dimensional nonlinear elasticity. Cavities and cracks are modeled as discrete and compact subsets of a planar domain, respectively, and deformations are defined only outside of cracks. The model accounts for the irreversibility of both processes of cavitation and fracture and it allows for the coalescence of cavities into cracks. Our main result shows the existence of quasistatic evolutions in the case of a finite number of cavities, under an a priori bound on the number of connected components of the cracks.