WIAS Preprint No. 734, (2002)

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


  • Klein, Olaf
    ORCID: 0000-0002-4142-3603

2010 Mathematics Subject Classification

  • 74N30 35B40 47J40 34C55 35K60 74K05


  • Phase-field systems, phase transitions, hysteresis operators, thermo-visco-plasticity, asymptotic behaviour


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.

Appeared in

  • Appl. Math. 49 (2004) pp. 309--341

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