Finite plasticity in $P^T P$

TL;DR

This paper introduces a finite-plasticity model based on the symmetric tensor P^T P, which simplifies the mathematical structure and is invariant under frame transformations, with rigorous analysis of solutions and linearization.

Contribution

The paper proposes a novel finite-plasticity model using P^T P instead of classical plastic strain, providing existence results and a rigorous linearization analysis.

Findings

Existence of energetic solutions at material-point and boundary-value levels.

Model is lower-dimensional, symmetric, and reference-based.

Rigorous linearization via evolutive-Gamma convergence.

Abstract

We discuss a finite-plasticity model based on the symmetric tensor $P^T P$ instead of the classical plastic strain $P$. Such a model structure arises from assuming that the material behavior is invariant with respect to frame transformations of the intermediate configuration. The resulting variational model is lower-dimensional, symmetric, and based solely on the reference configuration. We discuss the existence of energetic solutions both at the material-point level and for the quasistatic boundary-value problem. These solutions are constructed as limits of time discretizations. Eventually, the linearization of the model for small deformations is ascertained via a rigorous evolutive-$\Gamma$-convergence argument.