Fractional step methods for thermo-mechanical damage analyses at transientelevated temperatures

In the interest of computational efficiency this paper describes the implem entation of a coupled thermo-damage constitutive model into a coupled time- stepping analysis using fractional step methods. To begin it is demonstrate d that a thermo-damage model can be presented in a thermodynamic framework with the evolution equations satisfying the first and second laws of thermo dynamics. The equations of evolution are partitioned in two ways, thus defi ning two fractional step methods: an isothermal method and an isentropic me thod. When implemented into a time-stepping algorithm the isentropic method maintains a precise energy balance for the entire analysis where as the is othermal method can only provide an energy balance at the end of each therm al time step. In addition, a stability analysis shows that the Isentropic a nalysis is unconditionally stable while a isothermal analysis is at best co nditionally stable. Simulations of thermal fracture in a restrained specime n under heat show stable growth of damage to failure. Copyright (C) 2000 Jo hn Wiley & Sons, Ltd.