Existence result for a class of generalized standard materials with thermomechanical coupling
- Paoli, Laetitia
- Petrov, Adrien
2010 Mathematics Subject Classification
- 35A01 35K55 74F05
- Existence result, generalized standard materials, doubly nonlinear equations, heat equation
This paper deals with the study of a three-dimensional model of thermomechanical coupling for viscous solids exhibiting hysteresis effects. This model is written in accordance with the formalism of generalized standard materials. It is composed by the momentum equilibrium equation combined with the flow rule, which describes some stress-strain dependance, and the heat-transfer equation. An existence result for this thermodynamically consistent problem is obtained by using a fixed-point argument and some qualitative properties of the solutions are established.