On the constitutive modeling of coupled thermomechanical phase-change problems

This paper deals with a thermodynamically consistent numerical formulation for coupled thermoplastic problems including phase-change phenomena and fri ctional contact. The final goal is to get an accurate, efficient and robust numerical model, able for the numerical simulation of industrial solidific ation processes. Some of the current issues addressed in the paper are the following. A fractional step method arising from an operator split of the g overning differential equations has been used to solve the nonlinear couple d system of equations, leading to a staggered product formula solution algo rithm. Nonlinear stability issues are discussed and isentropic and isotherm al operator splits are formulated. Within the isentropic split, a strong op erator split design constraint is introduced, by requiring that the elastic and plastic entropy, as well as the phase-change induced elastic entropy d ue to the latent heat, remain fixed in the mechanical problem. The formulat ion of the model has been consistently derived within a thermodynamic frame work. All the material properties have been considered to be temperature de pendent. The constitutive behavior has been defined by a thermoviscous/ ela stoplastic free energy function, including a thermal multiphase change cont ribution. Plastic response has been modeled by a J2 temperature dependent m odel, including plastic hardening and thermal softening. The constitutive m odel proposed accounts for a continuous transition between the initial liqu id state, the intermediate mushy state and the final solid state taking pla ce in a solidification process. In particular, a pure viscous deviatoric mo del has been used at the initial fluid-like state. A thermomecanical contac t model, including a frictional hardening and temperature dependent coupled potential, is derived within a fully consistent thermodinamical theory. Th e numerical model has been implemented into the computational finite elemen t code COMET developed by the authors. Numerical simulations of solidificat ion processes show the good performance of the computational model develope d. (C) 2001 Elsevier Science Ltd. All rights reserved.