Computation of Effective Properties of Smart Composite Materials with Generalized Periodicity Using the Two-Scales Asymptotic Homogenization Method

In this work, a general mathematical models for flexoelectric heterogeneous equilibrium boundary value problems are considered. A methodology to find the local problems and the effective properties of flexoelectric composites with generalized periodicity is presented, using a two-scales asymptotic homogenization method. The model of the homogenized boundary values problem is presented. A procedure to solve the local problems of stratified multilayered composites with wavy geometry with perfect contact at the interface is proposed. Further, a study of a multilayered piezoelectric composite with imperfect contact at the interface and the influence of the flexoelectric constituents in the behavior of heterogeneous structures are investigated. Consequently, simple closed-form formulas for the effective stiffness, piezoelectric, dielectric, and flexoelectric tensors are obtained, based on the solutions of local problems of stratified multilayered composites with perfect contact at the interface. These formulas provide information for the understanding of the symmetry of the homogenized structure. The piezoelectric limit case for rectangular bi-laminated composites is validated. As a numerical example, a bilaminate composite with layers perpendicular to the z-axis is studied. The known results in the literature are used to analyze some numerical cases of piezoelectric composites with non-uniform imperfect contact at the interface (fractures modes) and laminate composites with fibrous reinforcement. Finally, flexoelectric stratified composites with generalized periodicity are studied and discussed