Determination of crack tip asymptotic stress field by fractal finite element method

Abstract

A semianalytical method is used for the determination of stress intensity factors (SIF) as well as the crack tip asymptotic stress field of a crack in elastic body. In this method, two level displacement interpolations at inter-element level and at intra-element level are employed. The concept of fractal geometry is used to automatically generate an infinitesimal mesh with large number of degrees of freedom (DOF) around the singular crack tip region. An effective and efficient transformation method is used to transform those DOF to a small set of generalized coordinates that is associated with coefficients of the global crack tip asymptotic stress function. The first order and the higher order stress fields near the crack tip are solved by finite element method. A typical example is given to illustrate the convergence of the first order and the higher order terms in crack tip asymptotic fields. The accuracy of the first order term has been checked and good agreement between the present and the existing analytical solution is revealed. Significant contribution from the regular stress field to the crack tip asymptotic stress field is discovered.