Stress-diffusive regularizations of non-dissipative rate-type materials

Abstract

We consider non-dissipative (elastic) rate-type material models that are derived within the Gibbs-potential-based thermodynamic framework. Since the absence of any dissipative mechanism in the model prevents us from establishing even a local-in-time existence result in two spatial dimensions for a spatially periodic problem, we propose two regularisations.

For such reg- ularized problems we obtain well-posedness of the planar, spatially periodic problem. In contrast with existing results, we prove ours for a regularizing term present solely in the evolution equation for the stress.

Keywords

• Non-dissipative material
• rate-type material
• regularization
• stress diffusion
• spatially-periodic problem
• well-posedness.