Regularized Micromechanical Modeling for the Prediction of Electro-Elastic Behavior of Reinforced Piezoelectric Composites

In this paper, the effective electro-elastic (EE) behavior of piezoelectric composite is predicted and analyzed based on a regularized micromechanical modeling. The mathematical modeling is based on Green’s function approach to derive the localization equation coupled with regularization and conditioned procedure. The ill-conditioned problem is present when going through the inversion of the localization tensor due to the large dispersion between elastic, dielectric, and piezoelectric coefficients. This problem is addressed using the Tikhonov regularization method. The choice of the regularization parameter is studied to be optimal and to assure the solution stability, and the convergence to the desired solution. The Homogenization of effective properties is obtained through the averaged procedure and a regularized Mori-Tanaka model. The effective electro-elastic properties are predicted with respect to the shape of constituents as well as to the volume fraction of inclusions.