Thermodynamically consistent multiscale formulation of a thermo-mechanical problem with phase transformations

Abstract

A multiscale framework for thermo-mechanical analysis with phase transformations is proposed in this work. The formulation covers those cases including coupled constitutive equations for simulating thermo-mechanical processes considering phase transformation phenomena. The general case of temperature- and phase-dependent procedures, involving nonlinear plasticity concepts, is considered as main framework in order to formulate the material dissipation at both micro- and macroscopic level of observation. Thermodynamic consistency conditions for computational up/downscaling between micro- and macroscales are presented, with special focus on phase transformation phenomena, for both the mechanical and thermal homogenization. Classical Coleman–Gurtin thermodynamics is employed at the microscale, whereas an extended framework is considered at the macroscale due to the temperature gradient dependency of the macro stress. The multiscale procedure is based on a variational approach largely discussed in the literature. The overall coupled process at both micro- and macroscopic scales, averaging criteria, thermal, mechanical and phase change constitutive expressions, as well as the corresponding homogenization rules, are discussed and derived in detail.