Fractional step methods for thermo-mechanical damage analyses at transient elevated temperatures

In the interest of computational e ciency this paper describes the implementation of a coupled thermo- damage constitutive model into a coupled time-stepping analysis using fractional step methods. To begin it is demonstrated that a thermo-damage model can be presented in a thermodynamic framework with the evolution equations satisfying the rst and second laws of thermodynamics. The equations of evolution are partitioned in two ways, thus de ning two fractional step methods: an isothermal method and an isentropic method. When implemented into a time-stepping algorithm the isentropic method maintains a precise energy balance for the entire analysis where as the isothermal method can only provide an energy balance at the end of each thermal time step. In addition, a stability analysis shows that the isentropic analysis is unconditionally stable while a isothermal analysis is at best conditionally stable. Simulations of thermal fracture in a restrained specimen under heat show stable growth of damage to failure