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Title: Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity (English)
Author: Klein, Olaf
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 49
Issue: 4
Year: 2004
Pages: 309-341
Summary lang: English
Category: math
Summary: The asymptotic behaviour for $t \rightarrow \infty $ of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress law and also in the phase evolution equation are described by using the mathematical theory of hysteresis operators. (English)
Keyword: phase-field system
Keyword: phase transition
Keyword: hysteresis operator
Keyword: thermo-visco-plasticity
Keyword: asymptotic behaviour
MSC: 34C55
MSC: 35B40
MSC: 35K60
MSC: 47J40
MSC: 74K05
MSC: 74N30
idZBL: Zbl 1099.74051
idMR: MR2076488
DOI: 10.1007/s10492-004-6402-1
Date available: 2009-09-22T18:18:22Z
Last updated: 2020-07-02
Stable URL:
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