A novel size independent symplectic analytical singular element for inclined crack terminating at bimaterial interface

Abstract

• The analytical symplectic eigen expansion for inclined bimaterial interface crack is solved. • Stress intensity factors for the inclined bimaterial crack derived from the proposed method are provided and discussed. • A novel singular finite element is constructed based on the symplectic eigen solution. • It is proven that the stiffness matrix of the proposed singular element is independent of the element's size. • Stress intensity factors can be calculated directly without any post-processing. Cracks often exist in composite structures, especially at the interface of two different materials. These cracks can significantly affect the load bearing capacity of the structure and lead to premature failure of the structure. In this paper, a novel element for modeling the singular stress state around the inclined interface crack which terminates at the interface is developed. This new singular element is derived based on the explicit form of the high order eigen solution which is, for the first time, determined by using a symplectic approach. The developed singular element is then applied in finite element analysis and the stress intensity factors (SIFs) for a number of crack configurations are derived. It has been concluded that composites with complex geometric configurations of inclined interface cracks can be accurately simulated by the developed method, according to comparison of the results against benchmarks. It has been found that the stiffness matrix of the proposed singular element is independent of the element size and the SIFs of the crack can be solved directly without any post-processing.