Modeling the flexoelectric effect around the tip of nano-cracks using a collocation MFEM

Abstract

Due to the stress concentration and large strain gradient around the crack tip, strong flexoelectric effect would be produced there. Meanwhile, the flexoelectric effect could conversely affect the mechanical fields in materials, thus influence the fracture property of materials. To model the impact of flexoelectricity on crack tip fields and the electromechanical behaviors of materials, intensive mesh refinement is needed around the crack tip. Thus, an efficient numerical method is desired. In this paper, the flexoelectric effect around the tip of nano-cracks is simulated by using a collocation mixed finite element method (MFEM). Our collocation MFEM is based on C0 continuous approximation and does not involve additional degrees of freedom (DOFs), so that it is quite efficient, which has been verified in our previous study (Tian et al., 2021). Using the collocation MFEM, we simulate the electric potential and field distributions around the crack tip in flexoelectric materials, and the influences of the direct flexoelectric effect on the crack tip opening displacement and J-integral are also studied. Numerical results indicate that the flexoelectric effect around the crack tip would be enhanced by increasing the tensile loading and crack length. Besides, the direct flexoelectric effect around the crack tip enhances the local strength of materials, and plays an important role in fracture mechanics of materials.