Finite plasticity in $P^{T}P$

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.

47 pages

References in corpus (1)

• Derivation of $\mathbf{F}={\mathbf{F}}^e{\mathbf{F}}^p$ as the continuum limit of crystalline slip

Cited by in corpus (1)

• A two-speed model for finite-strain elasto-plasticity