Non-isothermal cyclic fatigue in an oscillating elastoplastic beam with phase transition

We propose a temperature dependent model for material fatigue accumulation, including phase transition in an oscillating elastoplastic beam. The full system of equations consists of the momentum and energy balance equations, equation for the phase transition, and an evolution equation for the fatigue rate. The fatigue rate is supposed to be proportional to the dissipation rate. Due to the phase transition, fatigue rate can also decrease but only in the case of strong melting