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

Please always quote using this URN:urn:nbn:de:0296-matheon-8802
  • 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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Metadaten
Author:Laetitia Paoli, Adrien Petrov
URN:urn:nbn:de:0296-matheon-8802
Referee:Carsten Carstensen
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/08/10
Release Date:2011/08/10
Tag:Existence result; doubly nonlinear equations; enthalpy transformation; generalized standard materials; heat equation; maximal monotone operators; shape-memory alloys
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K55 Nonlinear parabolic equations
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Cxx Plastic materials, materials of stress-rate and internal-variable type / 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Cxx Plastic materials, materials of stress-rate and internal-variable type / 74C10 Small-strain, rate-dependent theories (including theories of viscoplasticity)
Preprint Number:814
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