Research On Smoothed Finite Element Method For Interface Crack In Piezoelectric Bimaterials

The rapid development of high-tech industry has caused the continuous emergence of piezoelectric smart materials,as the core of intelligent material structure and device,piezoelectric materials have been widely used in fields of aerospace,mechanical engineering,civil engineering,etc because of high sensitivity,unique electromechanical performance and other excellent properties.However,piezoelectric materials bring such excellent characteristics at the same time crack defects seriously restrict the application of piezoelectric materials and the performance of related devices,interface crack failure is the main form of its destruction.The uppermost numerical methods for solving fracture mechanical problems in piezoelectric bimaterials with interfaces include finite element method,meshless method,smoothed finite element method,etc.The stiffness matrix of finite element method is overly-rigid,and displacement solution is low.Smoothed finite element method is constructed by finite element method and strain smoothing technology of meshless method.The Gauss divergence theorem is used to transform volume integral to area integral,and the area integral to line integral in the solution domain,and no derivatives of the shape functions are needed,which has high accuracy and been widely concerned by foreign and native scholars.In this paper,the research progress of smoothed finite element method in fracture mechanics is discussed by summarizing the developing status of interface fracture mechanics and smoothed finite element method.Based on the basic theory of piezoelectric materials,electromechanical coupling equilibrium equation of smoothed finite element method is derived.Through the numerical simulation of piezoelectric bimaterials cantileverbeam and perforated piezoelectric plate,it is verified that the smoothed finite element method is feasible and effective for solving the mechanics problem of piezoelectric materials.Consider a center interface crack in double piezoelectric plates,an explicit extrapolating formula of intensity factors for in-plane and anti-plane interface crack in piezoelectric bimaterials are derived,Cell-Based smoothed finite element method is used to simulate the piezoelectric bimaterial plates with center cracks,and compared with the finite element method and analytical solution,It is theoretically proved that Cell-Based smoothed finite element method has high precision.