Cohesive element approach for dynamic crack propagation: Artificial compliance and mesh dependency

Abstract

Zero thickness cohesive element approach for arbitrary crack propagation has a deficiency of introducing artificial compliance to the model, especially when cohesive elements are inserted into every element interfaces. For dynamic problems, the artificial compliance decreases the stress wave speed and makes the result less accurate. In this paper, the reason of the artificial compliance is examined, and the bilinear and exponential cohesive law are compared. The work shows that by choosing the right cohesive stiffness, element size and using bilinear cohesive law rather than exponential cohesive law, the artificial compliance issue can be limited to a negligible level without greatly increasing the computational time. Three numerical simulations are used to support the argument. The bilinear cohesive law also shows more robust behavior in terms of cyclic loading than exponential law, and a new cyclic loading formulation is proposed to help fix the discontinuity observed in exponential law. According to our finding, in order to limit the artificial compliance and computational time, large element size is recommended, however, in fracture problems, small element size around crack tip is essential to capture the cohesive zone behavior. To escape the dilemma, we modify the cohesive zone enlargement approach presented in the literature (Dugdale, 1960) and adopt it for arbitrary crack propagation. The modified methodology enlarges cohesive zone size by reducing the cohesive strength only around crack tips to allow more cohesive elements inside the cohesive zone. Two benchmark numerical simulations are carried out to verify the modified methodology.