2016/12/31 by Riccarda Rossi, Rossi, Riccarda
Chemical Engineering · Computer Science · Engineering · #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #Elasticity and Material Modeling #FOS: Mathematics #Rheology and Fluid Dynamics Studies
paper · pdf · doi:10.48550/arxiv.1701.00139
openalex publication_date 2016/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we address a model coupling viscoplasticity with damage in\nthermoviscoelasticity. The associated PDE system consists of the momentum\nbalance with viscosity and inertia for the displacement variable, at small\nstrains, of the plastic and damage flow rules, and of the heat equation. It has\na strongly nonlinear character and in particular features quadratic terms on\nthe right-hand side of the heat equation and of the damage flow rule, which\nhave to be handled carefully. We propose two weak solution concepts for the\nrelated initial-boundary value problem, namely `entropic' and `weak energy'\nsolutions. Accordingly, we prove two existence results by passing to the limit\nin a carefully devised time discretization scheme. Finally, in the case of a\nprescribed temperature profile, and under a strongly simplifying condition, we\nprovide a continuous dependence result, yielding uniqueness of weak energy\nsolutions.\n