# Multiple Independent Cavitation in 2D NeoHookean Materials

## TL;DR

This thesis establishes bounds on stretch factors in 2D incompressible NeoHookean materials to prevent cavitation, using elliptic regularity theory to analyze free boundary problems.

## Contribution

It introduces new bounds for cavitation onset in 2D NeoHookean materials and applies elliptic regularity theory to free boundary problems in elasticity.

## Key findings

- Derived upper bounds for stretch factors preventing cavitation.
- Proved regularity results for free boundary problems in elastic materials.
- Analyzed dependence of estimates on domain geometry.

## Abstract

In this thesis we find an upper bound for the stretch factor of an elastic incompressible material subject to multiaxial traction, under which one can ensure that there is still no coalescence. The problem involves classical elliptic regularity theory (and the analysis of the dependence of the estimates on the domain), from which we get a regularity result for a free boundary problem.