Parametric multiphysics finite-volume theory for periodic composites with thermo-electro-elastic phases

The zeroth-order multiphysics finite-volume micromechanics has been proposed to model coupled thermo-electro-mechanical behaviors of unidirectional composites embedded with piezoelectric phases. Parametric mapping is implemented within the multiphysics finite-volume theory's framework, facilitating modeling of multiphase piezoelectric materials with complex microstructures with relatively coarse unit cell discretization. The resulting theory admits piezoelectric materials with complete anisotropy and arbitrary poling direction and enables rapid generation of the entire set of coupled thermo-mechanical, piezoelectric properties, figures of merits, as well as the local fluctuations of fields within the composite microstructures with greater fidelity than its predecessor. The proposed method is verified extensively by comparison with the finite-element homogenization technique, which produces an excellent agreement in a wide range of volume fractions but offers much better stability and efficiency. The contrast with the rectangular theory is also presented and discussed, demonstrating the advantage and the need for the development of parametric formulation. This extension further increases the finite-volume direct averaging micromechanics theory's range of applicability, providing an attractive standard for investigating multiphase and multiphysics problems with different microstructural architectures and scales against which other approaches may be compared.