An XFEM/level set strategy for simulating the piezoelectric spring-type interfaces with apparent physical background

The piezoelectric spring-type interface is widely applied to describe the physical phenomenon that the displacement vector and the electric potential suffer jumps across an interface in a certain intelligent material, while both the normal traction vector and the normal electric displacement stay continuous across the same interface. This work is dedicated to accurately depicting the effects of the physics-based piezoelectric spring-type interfaces in arbitrary shapes and to predicting the effective electroelastic moduli of composites containing such interfaces. To achieve this two-fold goal, a computational approach combining the extended finite element method (XFEM) and the level set method (LSM) is developed and interpreted in detail. The accuracy and convergence performance of the elaborated approach are assessed with a benchmark problem for which the exact analytic solution is derived. Eventually, the approach validated is further utilized to explore the size- and shape-dependent effects induced by these spring-type interfaces on the overall couple-field moduli of fibrous piezoelectric composites.