Influence of flexoelectricity on interface crack problems under a dynamic load

Abstract

In the present paper, the influence of flexoelectricity on behavior of the interface crack between two dissimilar dielectric materials under a dynamic mechanical load is investigated. The induced electric field affects the distribution and evolution of mechanical fields in dielectric materials. Large strain gradients induce the electric polarization in the direct flexoelectricity. Due to the large strain gradients at the crack tip vicinity it is needed to consider the strain gradient theory model. Governing equations in this theory contain higher-order derivatives than in the conventional continuum mechanics approach. The mixed finite element method (FEM) is developed here for a general boundary value problem, where the standard C0 continuous finite elements are applied for independent approximations of displacements and strains. The constraints between them are satisfied by collocation at appropriate internal points in elements. Interface cracks are observed in layered structures frequently due to a poor adhesion of layers. The incorporation of flexoelectricity and micro-inertial effects is needed into the failure analysis of interface cracks in nano-sized structures under dynamic loading. In numerical examples, we discuss the influence of flexoelectricity coefficients as well as the ratio of elastic coefficients and the geometrical size to microstructural (micro-stiffness and micro-inertia) length scale parameters of the bilayer composite on the crack opening displacement, stresses ahead the crack tip and induced electric intensity vector.