Two end variable singularity boundary elements and their applications in crack-crack interaction problems

Two new boundary elements have been proposed for simulation of variable order singularities at the two ends of an element in two dimensions. The "rst can model the variable order strain singularity at both the ends of the element. The second element can do both the strain and traction singularities simultaneously. The elements are useful for studying the interaction of singularities as in the case of multiple neighbouring cracks in a domain. They are employed here for the computation of stress intensity factors (SIFs) in the crack}crack interaction problems. To improve the accuracy of such computations further a modi"ed crack closure integral (MCCI) based method for mechanical and/or thermal loading is presented. Examples of mode I crack and mixed mode problems under mechanical loading are studied to illustrate the performance of the proposed elements and the MCCI-based calculations. The e!ects of the order of Gauss quadrature associated with such elements on the accuracy of the SIFs are also reporte