Effective predictions of heterogeneous flexoelectric multilayered composite with generalized periodicity. (1st September 2020) - Guinovart-Sanjuán, D.; Vajravelu, K.; Rodríguez-Ramos, R.; Guinovart-Díaz, R.; Bravo-Castillero, J.; Lebon, F.; Sabina, F.J.; Merodio, J.
Highlights: The manuscript presents a methodology to find the effective properties of flexoelectric composites with generalized periodicity using the two-scales asymptotic homogenization method. The manuscript offers detailed descriptions of the steps to find the local problems and to derive the effective flexoelectric properties. The methodology is used to solve the local problems of a stratified composite with complex geometry and perfect contact at the interface. A comparison between the behavior of the effective properties for a rectangular and a wavy flexoelectric composite is shown. Graphical abstract: Abstract: In this work, the general mathematical statements for flexoelectric heterogeneous equilibrium boundary value problems are reported. A methodology to find the local problems and the effective properties of flexoelectric composites with generalized periodicity is presented, using the two-scales asymptotic homogenization method. The statement of the homogenized boundary values problem is given. A procedure to solve the local problems of stratified multilayered composites with complex geometry and perfect contact at the interface is proposed. Consequently, the analytical expressions of the effective coefficients are obtained. The piezoelectric limit case for rectangular bi-laminated composites is validated. Finally, numerical analysis to illustrate the behavior of the effective properties for rectangular and wavy flexoelectric bi-layered structures are shown.