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We propose a scheme based on recursively applying analytical formulae for effective properties to a class of porous ceramics for calculating their energy harvesting figures of merit. We approximate the structure of freeze-cast PZT parallel laminae joined by links (or bridges) by a model that can be broken down into two directions along which the structure resembles a laminate. The effective coefficients obtained in the first step of the recursion are then used as input on the second step which gives the final effective moduli. The comparison of those with calculations via Finite Element Method (FEM) on a non-recursive model shows good agreement. Finally, we calculate the piezoelectric and pyroelectric figures of merit and compare them with experimental results. The proposed scheme is a good alternative since it relies only on known simple analytical formulae and has a very low computational cost with respect to other methods that may be applied to such a geometry.

A simple scheme for calculating the energy harvesting figures of merit of porous ceramics