Improvements of cohesive zone model on artificial compliance and discontinuous force

The cohesive zone model (CZM) has been used widely and successfully in fracture propagation, but some basic problems are still to be solved. In this paper, artificial compliance and discontinuous force in CZM are investigated. First, theories about the cohesive element (local coordinate system, stiffness matrix, and internal nodal force) are presented. The local coordinate system is defined to obtain local separation; the stiffness matrix for an eight-node cohesive element is derived from the calculation of strain energy; internal nodal force between the cohesive element and bulk element is obtained from the principle of virtual work. Second, the reason for artificial compliance is explained by the effective stiffnesses of zero-thickness and finite-thickness cohesive elements. Based on the effective stiffness, artificial compliance can be completely removed by adjusting the stiffness of the finite-thickness cohesive element. This conclusion is verified from 1D and 3D simulations. Third, three damage evolution methods (monotonically increasing effective separation, damage factor, and both effective separation and damage factor) are analyzed. Under constant unloading and reloading conditions, the monotonically increasing damage factor method without discontinuous force and healing effect is a better choice than the other two methods. The proposed improvements are coded in LS-DYNA user-defined material, and a drop weight tear test verifies the improvements.