Dynamic crack growth in viscoelastic materials with memory

TL;DR

This paper presents a model for dynamic crack growth in viscoelastic materials with memory effects, establishing an existence theorem under certain regularity conditions in two dimensions.

Contribution

It introduces a novel model incorporating history-dependent damping and proves an existence theorem for crack evolution in two-dimensional viscoelastic materials.

Findings

Model captures memory effects in crack growth

Proves existence of solutions under regularity constraints

Advances understanding of viscoelastic fracture dynamics

Abstract

In this paper we introduce a model of dynamic crack growth in viscoelastic material, where the damping term depends on the history of the deformation. The model is based on a dynamic energy dissipation balance and on a maximal dissipation condition. Our main result is an existence theorem in dimension two under some a priori regularity constraints on the cracks.