Quasistatic evolution for dislocation-free finite plasticity

TL;DR

This paper develops an existence theory for quasistatic evolution in finite plasticity assuming dislocation-free conditions, where plastic strain is compatible and expressed as a gradient, simplifying the analysis without second-order gradients.

Contribution

It introduces a novel existence framework for quasistatic finite plasticity with compatible plastic strains, applicable to dislocation-free scenarios, using only first-order derivatives.

Findings

Existence of quasistatic evolution solutions established.

Compatible plastic strain characterized as a gradient of a deformation map.

Framework accommodates both Lagrangian and Eulerian descriptions.

Abstract

We investigate quasistatic evolution in finite plasticity under the assumption that the plastic strain is compatible. This assumption is well-suited to describe the special case of dislocation-free plasticity and entails that the plastic strain is the gradient of a plastic deformation map. The total deformation can be then seen as the composition of a plastic and an elastic deformation. This opens the way to an existence theory for the quasistatic evolution problem featuring both Lagrangian and Eulerian variables. A remarkable trait of the result is that it does not require second-order gradients.