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Global existence result for thermoviscoelastic problems with hysteresis

Please always quote using this URN:urn:nbn:de:0296-matheon-8798
  • 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.

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Metadaten
Author:Laetitia Paoli, Adrien Petrov
URN:urn:nbn:de:0296-matheon-8798
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2015/12/23
Release Date:2015/12/23
Tag:Existence result; doubly nonlinear equations; enthalpy transformation; generalized standard materials; heat equation; maximal monotone operators; plasticity; shape-memory alloys
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Axx General topics / 35A01 Existence problems: global existence, local existence, non-existence
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q80 PDEs in connection with classical thermodynamics and heat transfer
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)
Preprint Number:1084
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