Investigation of J-integrals and SIFs in piezoelectric materials by element differential method

  • Jin, Liang (Beijing Institute of Mechanical and Electrica)
  • Yang, Yi (Dalian University of Technology)
  • Li, YiAn (Dalian University of Technology)
  • Wang, RuoXin (Dalian University of Technology)
  • Lv, Jun (Dalian University of Technology)

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In this paper, an element differential method (EDM) for analyzing the fracture mechanical behavior of a piezoelectric material structure under electro-mechanical load coupling is proposed. This method makes the nodes inside the cell satisfy the electro-mechanica control equations. And it makes the other nodes satisfy the equilibrium conditions of traction and charge as well as the boundary conditions. Thus, the method constructs system equations for solving the electro-mechanical coupling problem. Compared with the traditional finite element method, it is not necessary to establish the solution format of boundary value problem by variational principle and virtual work principle, which has advantages in solving piezoelectric materials fracture problem. Besides, for the fracture parameters of piezoelectric materials, this paper adopts the equivalent region integral method to calculate the J-integral. First, converting the line integral into surface integral, introducing the smooth q-function interpolation, and then using the double Gaussian integral to calculate the J-integral numerical analytic formula. Based on the J-integral, the crack tip asymptotic solution is introduced as the auxiliary field, and then the stress intensity factor is calculated by the interaction integral method. The fracture problem of a typical piezoelectric structure with central crack and edge crack under electromechanical coupling load is numerically analyzed, and the accuracy of the proposed method in calculating the piezoelectric fracture parameters is verified.