# Crack growth by vanishing viscosity in planar elasticity

## TL;DR

This paper establishes the existence of quasistatic crack evolutions in brittle materials using a vanishing viscosity method within planar linearized elasticity, allowing the crack path to emerge naturally.

## Contribution

It introduces a novel vanishing viscosity approach to model crack growth without prescribing the crack path in planar elasticity.

## Key findings

- Existence of quasistatic evolutions proven
- Crack paths are determined as part of the solution
- Analysis of energy release rate properties

## Abstract

We show the existence of quasistatic evolutions in a fracture model for brittle materials by a vanishing viscosity approach, in the setting of planar linearized elasticity. The crack is not prescribed a priori and is selected in a class of (unions of) regular curves. To prove the result, it is crucial to analyze the properties of the energy release rate.