Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity

Olaf Klein

Applications of Mathematics (2004)

  • Volume: 49, Issue: 4, page 309-341
  • ISSN: 0862-7940

Abstract

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The asymptotic behaviour for t → ∞ 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.

How to cite

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Klein, Olaf. "Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity." Applications of Mathematics 49.4 (2004): 309-341. <http://eudml.org/doc/33187>.

@article{Klein2004,
abstract = {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.},
author = {Klein, Olaf},
journal = {Applications of Mathematics},
keywords = {phase-field system; phase transition; hysteresis operator; thermo-visco-plasticity; asymptotic behaviour; phase transition; long-time behaviour; energy dissipation},
language = {eng},
number = {4},
pages = {309-341},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity},
url = {http://eudml.org/doc/33187},
volume = {49},
year = {2004},
}

TY - JOUR
AU - Klein, Olaf
TI - Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity
JO - Applications of Mathematics
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 4
SP - 309
EP - 341
AB - 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.
LA - eng
KW - phase-field system; phase transition; hysteresis operator; thermo-visco-plasticity; asymptotic behaviour; phase transition; long-time behaviour; energy dissipation
UR - http://eudml.org/doc/33187
ER -

References

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