Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity
- Klein, Olaf
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.
- Appl. Math. 49 (2004) pp. 309--341