The present work deals with the modeling of 1-3 periodic composites made of piezoceramic (PZT) fibers embedded in a soft non-piezoelectric matrix (polymer). We especially focus on predicting the effective coefficients of periodic transversely isotropic piezoelectric fiber composites using representative volume element method (unit cell method). In this paper the focus is on square arrangements of cylindrical fibers in the composite. Two ways for calculating the effective coefficients are presented, an analytical and a numerical approach. The analytical solution is based on the asymptotic homogenization method (AHM) and for the numerical approach the finite element method (FEM) is used. Special attention is given on definition of appropriate boundary conditions for the unit cell to ensure periodicity. With the two introduced methods the effective coefficients were calculated for different fiber volume fractions. Finally the results are compared and discussed.

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The piezoelectric effect is studied for bending and traction tests for two types of structure configurations: homogeneous and composite structures. Mechanical displacements are calculated for traction and bending tests, using FEM for the homogeneous body, where the input material properties are taken from the overall coefficients reported by the Asymptotic Homogenization Method (AHM). A brief theoretical description about the basics of the piezoelectric finite elements and the AHM is given. On the other hand, the calculations of the mechanical displacements are done for the composite structure using FEM where the real data of the material parameters for cylindrical fibers (PZT-5) embedded in a matrix (elastic isotropic polymer) were taken from reported references. A comparison between the results obtained using AHM + FEM and FEM for the homogeneous and the composite structures respectively is reported and shows a favorable result.