On the formulation of coupled thermoplastic problems with phase-change

This paper deals with a numerical formulation for coupled thermoplastic problems including phase-change phenomena. The final goal is to get an accurate, efficient and robust numerical model, allowing the numerical simulation of solidification processes in the metal casting industry. Some of the current issues addressed in the paper are the following. A fractional step method arising from an operator split of the governing differential equations has been used to solve the nonlinear coupled system of equations, leading to a staggered product formula solution algorithm. Nonlinear stability issues are discussed and isentropic and isothermal operator splits are formulated. Within the isentropic split, a strong operator split design constraint is introduced, by requiring that the elastic and plastic entropy, as well as the phase-change induced elastic entropy due to the latent heat, remain fixed in the mechanical problem. The formulation of the model has been consistently derived within a thermodynamic framework. The constitutive behavior has been defined by a thermoelastoplastic free energy function, including a thermal multiphase change contribution. Plastic response has been modeled by a J2 temperature dependent model, including plastic hardening and thermal softening. A brief summary of the thermomechanical frictional contact model is included. The numerical model has been implemented into the computational Finite Element code COMET developed by the authors. A numerical assessment of the isentropic and isothermal operator splits, regarding the nonlinear stability behavior, has been performed for weakly and strongly coupled thermomechanical problems. Numerical simulations of solidification processes show the performance of the computational model developed.