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

Abstract

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

A crack-tip element for modelling arbitrary crack propagations

“…sin( 1) sin( 1) , 3, 5, 7, ... (20) where the explicit expressions of the 20 coefficients A B C , , , ... u u u are referred to [60,70]. The analytical solution to the original problem can be expressed in terms of an eigen expansion…”

“…where the superscript j indicates the jtheigen expanding term and a j is the expanding coefficient. [60] In the construction of a singular element, the eigen expansion (21) with the unknown expanding coefficients is the best choice to define the fields around the crack tip since the singular terms (3 and 4) and other higher order terms are included. A circular singular element termed as the SASE (as illustrated in Fig.…”

“…A circular singular element termed as the SASE (as illustrated in Fig. 5) which is constructed in this way is available in [60], and its formulation is briefly listed here. In practice, Eq.…”

“…Due to the fact that the eigen solutions are solved by using a symplectic analytical approach, this type of element is termed as "symplectic analytical singular element (SASE)". The SASE has been applied for many basic crack problems such as, general cracks [60], fatigue crack growth [61,62], bimaterial crack [63,64], viscoelastic cracks [65], thermal conduction for crack [66,67], dynamic crack problem [68] and cohesive cracks [69]. The solving accuracy and stability of the SASEs have been shown to be highly satisfactory.…”

Determination of high‐order fields for multianisotropic material antiplane V‐notches and inclusions by the asymptotic expansion technique and an overdeterministic method

“…Ju et al conducted an experimental study on the V‐notch stress intensity factors of multimaterial anisotropic wedges. Special finite element method, singular finite element, and singular boundary element were also developed for studying stress analysis in a multimaterial wedge system.…”