3 results
Search Results
Now showing 1 - 3 of 3
- ItemThermodynamics of multiphase problems in viscoelasticity(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Paoli, Laetitia; Petrov, AdrienThis paper deals with a three-dimensional mixture model describing materials undergoing phase transition with thermal expansion. The problem is formulated within the framework of generalized standard solids by the coupling of the momentum equilibrium equation and the flow rule with the heat transfer equation. A global solution for this thermodynamically consistent problem is obtained by using a fixed-point argument combined with global energy estimates.
- ItemGlobal existence result for phase transformations with heat transfer in shape memory alloys : dedicated to 75th birthday of K. Gröger(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Paoli, Laetitia; Petrov, Adrien; Gröger, K.We consider three-dimensional models for rate-independent processes describing materials undergoing phase transformations with heat transfer. The problem is formulated within the framework of generalized standard solids by the coupling of the momentum equilibrium equation and the flow rule with the heat transfer equation. Under appropriate regularity assumptions on the initial data, we prove the existence a global solution for this thermodynamically consistent system, by using a fixed-point argument combined with global energy estimates.
- ItemGlobal existence result for thermoviscoelastic problems with hysteresis : dedicated to the memory of M. Schatzman(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Paoli, Laetitia; Petrov, Adrien; Schatzman, M.We consider viscoelastic solids undergoing thermal expansion and exhibiting hysteresis effects due to plasticity or phase transformations. Within the framework of generalized standard solids, the problem is described in a 3D setting by the momentum equilibrium equation, the flow rule describing the dependence of the stress on the strain history, and the heat transfer equation. Under appropriate regularity assumptions on the data, a local existence result for this thermodynamically consistent system is established, by combining existence results for ordinary differential equations in Banach spaces with a fixed-point argument. Then global estimates are obtained by using both the classical energy estimate and more specific techniques for the heat equation introduced by Boccardo and Gallouet. Finally a global existence result is derived.