Publication at Faculty of Mathematics and Physics |
2019
Abstract
A mathematical model for an elastoplastic continuum subject to large strains is presented. The inelastic response is modelled within the frame of rate-dependent gradient plasticity for non-simple materials.
Heat diffuses through the continuum by the Fourier law in the actual deformed configuration. Inertia makes the nonlinear problem hyperbolic.
The modelling assumption of small elastic Green-Lagrange strains is combined in a thermodynamically consistent way with the possibly large displacements and large plastic strain. The model is amenable to a rigorous mathematical analysis.
The existence of suitably defined weak solutions and a convergence result for Galerkin approximations is proved.