NUMERICAL SIMULATION OF CRACKS IN 3D PIEZOELECTRIC MEDIA UNDER VARIOUS ELECTRICAL BOUNDARY CONDITIONS

摘要

This paper presents an accurate and efficient numerical procedure for analysis of isolated cracks in three-dimensional, linear piezoelectric media that subjected to various types of electrical boundary conditions, e.g. electrically permeable, electrically impermeable and electrically semi-permeable boundary conditions. The boundary value problem for all cases is set up in a broad context allowing the treatment of general material anisotropy, arbitrary crack configuration and mixed-mode loadings. The problem is then solved numerically by a weakly singular, symmetric Galerkin boundary element method (SGBEM). The implemented technique offers several positive features enhancing both solution accuracy and computational efficiency. The key governing integral equation contains only weakly singular kernels allowing continuous interpolation functions be used in the approximation and rendering simplicity of numerical integration of involved singular integrals. In addition, the governing equation is in a form well-suited for treatment of all three types of electrical boundary conditions in a simple fashion. To further enhance the accuracy of the computed intensity factors, the interpolation functions used to approximate the relative crack-face displacement and the jump of electric potential in a local region near the crack front are enriched by special basis functions that can capture the local field accurately with only few degrees of freedom. In addition, extra degrees of freedom are introduced along the crack front to enable a direct extraction of the intensity factors from the nodal data. The proposed technique is first tested via extensive numerical experiments on various boundary value problems where either analytical or benchmark solutions are available. Results indicate that the proposed technique is promising and, particularly, yields highly accurate intensity factors with use of relatively coarse meshes. The verified technique is then employed to investigate the influence of electrical boundary conditions on the intensity factors along the crack front for various crack configurations and loading conditions.