Computation of effective thermo-piezoelectric properties of porous ceramics via asymptotic homogenization and finite element methods for energy-harvesting applications

We consider the linear thermo-piezoelectric properties of a ceramic matrix with cylindrical empty pores distributed periodically. The asymptotic homogenization method is applied to an elliptical tensor-weighted boundary value problem in the Stress-Charge-Entropy formulation of the constitutive relations with rapidly oscillating coefficients and free boundary conditions on the surfaces of the pores. For different shapes of the pore cross section, we solve the local problems via finite element method to compute the effective coefficients as functions of the physical properties of the matrix, the shape of the pore cross section and their volume fraction. The numerical results show excellent agreement with analytical formulae. When the effective coefficients are transformed to the Strain-Charge-Entropy formulation of the constitutive relations, they become independent of the shape of the cross section, which further validates the importance of the analytical formulae. We compute the piezoelectric and pyroelectric figures of merit for energy-harvesting applications, which depend on the effective coefficients and are compared with recent experimental results. This contribution could be useful for fine-tuning the properties of this class of materials for energy-harvesting applications.