A general thermodynamical model for finitely-strained continuum with inelasticity and diffusion, its GENERIC derivation in Eulerian formulation, and some application
Authors
- Mielke, Alexander
ORCID: 0000-0002-4583-3888 - Roubiček, Tomáš
2020 Mathematics Subject Classification
- 35Q74 74L05 74F05 74N25 76A10 80A19 86A99
Keywords
- Eulerian mechanics, visco-elastodynamics, Jeffreys rheology, plasticity, poroelasticity, GENERIC, Lie derivatives, Poisson operator, Onsager operator, phase transitions in rocks, martensitic phase transitions
DOI
Abstract
A thermodynamically consistent visco-elastodynamical model at finite strains is derived that also allows for inelasticity (like plasticity or creep), thermal coupling, and poroelasticity with diffusion. The theory is developed in the Eulerian framework and is shown to be consistent with the thermodynamic framework given by General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC). For the latter we use that the transport terms are given in terms of Lie derivatives. Application is illustrated by two examples, namely volumetric phase transitions with dehydration in rocks and martensitic phase transitions in shape-memory alloys. A strategy towards a rigorous mathematical analysis is only very briefly outlined.
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