Improved cohesive stress integration schemes for cohesive zone elements

•We provide explicit matrices for several improved cohesive stress integration schemes.•GI-based improved methods with 2 integration points (IPs) are numerically more accurate and robust than the standard GI.•NCI-based improved methods need 3 IPs to achieve similar numerical performance of the GI-based methods with 2 IPs.•In general the GI-based improved methods are numerically superior to the respective NCI-based methods.•The improved methods enable the use of element size comparable to the cohesive zone size without much loss of accuracy.

In this paper, several improved stress integration schemes based on Gaussian integration (GI) method and Newton–Cotes integration (NCI) method are presented and demonstrated to be able to improve the numerical performance of linear cohesive elements. The improved methods consider explicitly the evolving crack front within a partially failed cohesive element. The stress integration matrices for both standard integration and improved integration schemes with arbitrary number of integration points have been explicitly derived. It has been demonstrated, through rigorous comparisons with standard integration methods, that the improved integration methods can greatly improve the numerical accuracy, stability, and robustness, especially when mesh sizes are comparable to the cohesive zone sizes. The much improved numerical accuracy and stability thus permit the use of a maximum cohesive element size as large as the cohesive zone size without significant compromise of the numerical accuracy. This is of significant practical importance because it greatly relaxes the current restriction to the cohesive element size, that it be less than 1/3–1/5 of the cohesive zone size.