Modeling the interaction between inclusions and nanocracks in flexoelectric solid

Natural defects such as nano inclusions and nanocracks are inevitable in dielectric materials. When materials are subjected to mechanical loading, the strain gradient around crack tips and inclusions would become large and induce significant flexoelectric fields. In contrast to classical crack-inclusion problems, the interactions between these flexoelectric fields may locally change the electromechanical behaviors of materials, and result in some interesting phenomena. To better understand the crack-inclusion interactions in flexoelectric solids, in this work, we use a collocation mixed finite element method to model and analyze the flexoelectric fields around the crack tip and inclusion. Based on the J-integral, we analyze how the flexoelectric effect affect the interactions energy between nanocracks and nearby nano inclusions. This work proposes a new coupling mechanism in crack-inclusion problems and may inspire future experiments in flexoelectric solids.