Effective piezoelecric behaviour due to flexoelectric microstructure - homogenization based modelling

Abstract

The flexoelectricity is a property of all dielectric materials, occurring in both centrosymmetric and asymmetric crystals when strain gradient is generated. Conversely, also a "hyperstress" is generated due to gradient of electric field, contributing to the material stiffness. Both these direct and reverse effects appear at small scales, rather then at the ``macrolevel''. The aim of the present study is to explore behaviour of weakly flexoelectric periodically heterogeneous materials. For this, the asymptotic homogenization method is employed. We consider piezoelectric or dielectric materials with a weak flexoelectric property, constituting the skeleton of general periodic porous structures which enable to generate the strain gradients. Using the asymptotic homogenization, it is shown that effective behaviour of such materials is piezoelectric, whereby the homogenized piezoelectric coefficients are computed using the characteristic responses of the flexoelectric microstructure. Analytic result is derived for a 1D periodic rods designing a porous structure.