Determination of coefficients of crack tip asymptotic fields using the scaled boundary finite element method

Coefficients of the Williams expansion of the linear elastic crack tip asymptotic field can only be evaluated analytically for a few simple cases. Numerical solution is necessary in the general case, and the presence of the singular term presents numerical difficulties. The scaled boundary finite element method is a new semi-analytical approach to computational mechanics developed by Wolf and Song. This paper shows that when the scaling centre is located at the crack tip, the scaled boundary finite element solution converges to the Williams expansion. Consequently the coefficients of the Williams expansion, including the stress intensity factor and the T-stress, can be determined directly without further processing. The technique is applied to several problems for which coefficients of the Williams expansion are available, and close agreement with existing results is obtained with very few degrees of freedom.