A fully coupled thermo-mechanical micromechanics model

The development for a micromechanical model with full thermomechanical coupling, which is based on the combined effects of the mechanical and energy equations, is presented. The model is based on a combined approximate kinematic and thermal analysis of a repeating unit cell in a triply periodic array of inclusions. The unit cell is considered to consist of different subregions that can be composed of any desired material. The behavior of the material within the different subregions can be modeled using elastic, plastic, viscoelastic, viscoplastic, or damage constitutive models. The analysis satisfies the equations of motion and the energy equation for the different subregions of the unit cell in an average sense. The interfacial continuity conditions for the velocities, stresses, temperature, and thermal fluxes between the different subregions are also satisfied in an average sense. Arbitrary heat source terms are included in the energy equation to allow for the analysis of reactive materials. The resulting system of governing equations exhibits full coupling between the deformations and the thermal effects. The proposed model is analytical and provides closed-form expressions for the effective macroscopic kinematic and thermal behavior of a particulate composite. The influence of the thermomechanical coupling on behavior at both the macroscopic and microscopic levels is considered. The presence of the coupling can lead to significant localization of the thermal and deformation responses within different regions of the unit cell. It is shown that the presence of inelastic deformations in conjunction with thermomechanical coupling effects can result in appreciable deviation from an isothermal, inelastic analysis.