Quasistatic evolution for dislocation-free finite plasticity

¹ Institute of Information Theory and Automation, Czech Academy of Sciences, Pod vodárenskou veží 4, 182 08 Prague, Czechia and Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 166 29 Prague, Czechia.
² Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria.
³ Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, v. Ferrata 1, 27100 Pavia, Italy.

^* Corresponding author: ulisse.stefanelli@univie.ac.at

Received: 8 October 2019
Accepted: 20 May 2020

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.