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

Abstract

Abstract 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.