A fully coupled thermal-electrical-mechanical micromodel for multi-phase periodic thermoelectrical composite materials and devices

This paper introduces a new fully coupled micro thermal-electrical-mechanical (TEM) formulation for periodic multi-phase thermoelectric (TE) material systems and devices. The high fidelity generalized method of cells (HFGMC) micromechanical method is extended to account for the fully (three-way) coupled TEM effects including Seebeck, Peltier, and Joule heat. A special attention is directed towards the induced mechanical field which has often neglected in the literature. The three-dimensional HFGMC formulation is performed by analyzing an isolated periodic volume or a repeated unit-cell (RUC) and by subdividing it into sub-volumes (subcells). Interfacial continuity between adjacent subcells along with periodicity conditions are expressed in terms of average TEM fields and fluxes. The three TEM conservation laws are also expressed in a volume average over the subcell. A three-way coupled set of constitutive equations are used to express the thermoelectric, thermomechanical and electro-mechanical relations for each subcell. Applications are presented for the steady state solutions of the TEM field distributions in two cases. The first for a TE generator device that consists of an array of repeating RUC. The second is for multi-layered laminated composite with a repeating stack of layers including two layers reinforced with p-type and n-type inclusions. The steady-state stress distribution is shown to be a nonlinear solution to the system of coupled TEM governing equations. The new HFGMC-TEM micromodel is effective in establishing the overall (average) TEM constitutive laws for the equivalent homogenized medium along with the spatial distributions of different local fields within the RUC.