Global existence result for phase transformations with heat transfer in shape memory alloys

2011/04/28 by Lætitia Paoli, Laetitia Paoli, Paoli, Laetitia +2 · 1 citation
Computer Science · Materials Science · Mathematics · #Contact Mechanics and Variational Inequalities #Shape Memory Alloy Transformations #Solidification and crystal growth phenomena #math.AP #msc:35K55 #msc:74C05 #msc:74C10 #msc:74F05 #msc:74N30 #msc:80A17

paper · pdf · doi:10.48550/arxiv.1104.5408

arxiv created 2011/04/28 · arxiv updated 2011/04/29

Abstract

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.

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