The definition of a traction-separation relationship is essential in cohesive zone models because it describes the nonlinear fracture process zone. A few models are investigated in this paper and a comparative study is conducted. Among various traction-separation relationships, the one in Abaqus is assessed by evaluating the cohesive traction and its tangent stiffness according to a given separation path. The results demonstrate that the traction-separation relationship in Abaqus can lead to non-physical responses because of a pathological positive tangent stiffness under softening condition. This is reflected in cohesive tractions that increase and decrease repeatedly while the cohesive separation monotonically increases. Thus, together with supporting information, this paper conveys the message that a traction-separation relationship should be developed and selected with great caution, especially under mixed-mode conditions.

Summary To remove mesh bias and provide an accurate crack path representation in mixed‐mode investigation, a novel stress recovery technique is proposed in conjunction with a domain integral and element splits. Based on a domain integral and stress recovery technique, a maximum strain energy release rate is estimated to determine a crack path direction. Then, for a given crack path direction, continuum elements are split, and a cohesive surface element is adaptively inserted. One notes that the proposed stress recovery technique provides a more accurate stress field than a standard stress evaluation procedure. The proposed computational framework is verified and validated by solving mode‐I and mixed‐mode examples. Computational results demonstrate that the domain integral with the stress recovery accurately evaluates a crack path, even with a lower‐quality mesh and under a biaxial stress state. Furthermore, the cohesive surface element approach, with the element split in conjunction with the stress recovery and the domain integral, predicts mixed‐mode fracture behaviors while removing mesh bias in the crack path representation. Additionally, the condition numbers of stiffness matrices are within the same order of magnitude during cohesive fracture simulation.

No abstract

No abstract

The investigation of multiple crack interactions in fracture mechanics is important to predict the safety and reliability of structures. This study aims to investigate the interactions of multiple parallel cracks in a semi-infinite domain in both deterministic and probabilistic ways by using an automated finite element modeling procedure and the Monte Carlo simulation. The stress intensity factor is considered as an indicator of failure and accurately evaluated by using the domain integral technique. The variation of the stress intensity factor according to the position, the length, and the number of cracks is demonstrated. In a probabilistic investigation, the effects of the number of cracks, the random distribution of the crack lengths, and the crack interactions to the failure probability are studied for a semi-infinite domain. The stress redistribution among multiple cracks, the effect of unevenly distributed crack lengths, and the combined effect of crack length uncertainties and a crack shielding effect have been examined.