Uniform materials and the multiplicative decomposition of the deformation gradient in finite elasto-plasticity

TL;DR

This paper explores the link between the multiplicative decomposition of the deformation gradient in finite elasto-plasticity and the theory of uniform materials, introducing new models and conditions for anisotropic yield criteria.

Contribution

It demonstrates the equivalence of the deformation gradient decomposition with a uniform material model involving two configurations and develops related evolution equations and dissipation conditions.

Findings

Decomposition corresponds to a uniform material with two configurations.

Derived evolution equations for configurations and material metric.

Established conditions for anisotropic yield criteria based on dissipation positivity.

Abstract

In this work we analyze the relation between the multiplicative decomposition $\mathbf F=\mathbf F^{e}\mathbf F^{p}$ of the deformation gradient as a product of the elastic and plastic factors and the theory of uniform materials. We prove that postulating such a decomposition is equivalent to having a uniform material model with two configurations - total $\phi$ and the inelastic $\phi_{1}$. We introduce strain tensors characterizing different types of evolutions of the material and discuss the form of the internal energy and that of the dissipative potential. The evolution equations are obtained for the configurations $(\phi,\phi_{1})$ and the material metric $\mathbf g$. Finally the dissipative inequality for the materials of this type is presented.It is shown that the conditions of positivity of the internal dissipation terms related to the processes of plastic and metric evolution provide the anisotropic yield criteria.