A 2D hypersingular time-domain traction BEM for transient elastodynamic crack analysis

A two-dimensional (2D)hypersingular time-domain traction BEM for transient elastodynamic crack analysis is presented in this paper. Time-domain traction boundary integral equations (BIEs)are applied for this purpose, to both crack-faces and external boundaries of the cracked solid. A numerical solution procedure is developed for solving the hypersingular time-domain traction BIEs. A time-stepping scheme in conjunction with a collocation method is applied. The time-stepping scheme uses a linear temporal shape-function which makes an analytical time-integration of the convolution integrals possible. As spatial shape-functions, two different shape-functions are adopted: a square-root crack-tip shape-function for elements adjacent to crack-tips and a constant shape-function for elements away from crack-tips. In this manner, the local behavior of the crack-opening-displacements (CODs)at crack-tips is correctly approximated by the square-root crack-tip shape-function. This allows us to accurately compute the dynamic stress intensity factors from the CODs. Suitable methods for evaluating the hypersingular and the strongly singular integrals are presented. Numerical examples for unbounded and bounded solids with cracks are given to show the efficiency and the accuracy of the time-domain BEM for transient elastodynamic crack analysis.