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phase-field system; phase transition; hysteresis operator; thermo-visco-plasticity; asymptotic behaviour
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.
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