A Variational Approach for a Thermo-Mechanical Multiscale Constitutive Model

Abstract

Based on the volume averaging of the microscopic temperature and displacement fields over a local representative volume element (RVE), in this work we present a general variational formulation for multi-scale constitutive models in the thermomechanical setting. In order to describe the RVE material
behavior, we use local continuum constitutive theories. This formulation provides an axiomatic framework within which each class of models is completely defined by a specific choice of kinematical constraints over the RVE. As consequences of the Hill-Mandel Principle of Macro-Homogeneity, we
obtain the equilibrium problems at the RVE level and the homogenization expressions for the heat flux and the effective stress. This approach allows us consider the microscopic temperature fluctuation field in the determination of: effective heat flux, effective stress and the corresponding tangent operators. As a result, the homogenized stress depends explicitly and implicitly on the macroscopic temperature gradient.
Finally, we present a discussion about the thermodynamics implication of this class of multiscale model.