Application of the gradient theory to interface crack between two dissimilar dielectric materials

In the present paper, the interface crack between two dissimilar dielectric materials under a mechanical load is investigated with including flexoelectricity effects. Flexoelectricity is a size dependent electro-mechanical coupling phenomenon, where the electric polarization is induced by a strain gradient in dielectrics. The strain gradients may potentially break the inversion symmetry in centrosymmetric crystals and polarization is observed even in all dielectric mate-rials. The polarization is proportional to the strain gradients in the direct flexoelectricity. Layered composite structures are frequently utilized in microelectronics. Due to a poor adhesion of pro-tection layer and basic material, the interface crack can be created there and for the prediction of failure of these structures it becomes essential to investigate distribution of the interfacial stress and strain fields. Governing equations in the gradient theory contain higher-order derivatives than in the standard continuum mechanics. Therefore, a reliable computational tool is required to solve these boundary-value problems. The mixed finite element method (FEM) is developed, where the standard C0 continuous finite elements are utilized for independent approximations of displacements and strains. The constraints between the displacement gradients and strains are satisfied by collocation at Gaussian integration points inside elements. In numerical examples, a parametric study is performed with respect to flexoelectric and elastic coefficients for both ma-terial regions. The influence of these parameters on the crack opening displacement is discussed.

Automated summary

In this paper, the interface crack between two dissimilar dielectric materials under mechanical load is investigated, with a focus on the flexoelectricity effects. The study explores the size-dependent electro-mechanical coupling phenomenon and its influence on interfacial stress and strain fields. The mixed finite element method is developed as a reliable computational tool to solve the governing equations in the gradient theory. Numerical examples are provided to analyze the impact of flexoelectric and elastic coefficients on the crack opening displacement.