A regularized time-domain BIEM for transient elastodynamic crack analysis in piezoelectric solids

Abstract

A time domain non-hypersingular traction boundary integral equation method (BIEM) is proposed for dynamic crack analysis of piezoelectric solids. Using the boundary integral equation method, the time domain hypersingular integral equations for a dynamic crack in a 2D infinite piezoelectric solid subjected transient loads are derived. Considering the properties of the fundamental solutions, the hypersingular integral equations are reduced to singular integral equations by using the technique of integration by parts, in which the unknown functions are the tangential derivatives of the displacement and electrical potential discontinuities of the crack surfaces. To solve the time domain singular integral equations numerically, the quadrature formula of Lubich is applied for the temporal discretization, while the Gauss–Chebyshev quadrature method is used for the spatial discretization. Numerical examples are carried out to verify the accuracy of the present method by comparing the numerical results obtained by other scholars. Finally, several numerical results are presented and discussed to show the effects of the mechanical impact loading, crack-face conditions and piezoelectric coupling coefficient on the dynamic stress intensity factors.