# Stress regularity in quasi-static perfect plasticity with a pressure dependent yield criterion

## TL;DR

This paper proves a regularity result for the stress tensor in quasi-static perfect plasticity models with pressure-dependent yield criteria, showing the stress gradient is locally square integrable under certain conditions.

## Contribution

It establishes a new regularity result for the stress tensor in perfect plasticity models with Drucker-Prager or Mohr-Coulomb criteria, using advanced mathematical techniques.

## Key findings

- Stress tensor has a locally square integrable gradient.
- Flow rule can be expressed in a strong measure-theoretic form.
- Results apply under suitable assumptions on the data.

## Abstract

This work is devoted to establishing a regularity result for the stress tensor in quasi-static planar isotropic linearly elastic - perfectly plastic materials obeying a Drucker-Prager or Mohr-Coulomb yield criterion. Under suitable assumptions on the data, it is proved that the stress tensor has a spatial gradient that is locally squared integrable. As a corollary, the usual measure theoretical flow rule is expressed in a strong form using the quasi-continuous representative of the stress.