Novel special crack-tip elements for interface crack analysis by an efficient boundary element method

This paper presents a new set of novel special crack-tip elements for analysis of interface cracks in linear elastic composite bimaterials by using the boundary element method (BEM). Such interface crack problems present some simulation difficulties based on the conventional numerical methods because the asymptotic crack-tip fields in this case exhibit an oscillatory behavior which is quite different from that in a cracked homogeneous material. The novel special crack-tip elements developed in this study contain the correct local asymptotic behavior of the displacement and stress fields at the tip of an interface crack, and can thus appropriately describe the oscillatory near-tip displacement and stress fields for cracked composite bimaterials. The novel special cracktip elements are implemented into a BEM, which can significantly improve the computational accuracy of the complex stress intensity factor (SIF) for an interface crack even with a relatively coarse mesh. The proposed computational strategy for interface crack analysis based on the novel special crack-tip elements also enables a direct and accurate evaluation of the complex SIF at the collocation point extremely close to the crack-tip. Several numerical examples are presented and discussed to demonstrate that the present method based on the novel special crack-tip elements is pretty simple, highly accurate, and relatively robust with respect to the size of the used crack-tip elements.