Piecewise-linear generalizable cohesive element approach for simulating mixed-mode delamination

Abstract

A cohesive element formulation is proposed that provides a general framework to approximate experimentally measured Traction–Separation Law (TSL) shapes. Unlike other approaches, it does not assume specific TSL shapes, such as bi-linear or exponential. The TSL shapes are defined generally, in a piecewise-linear fashion, and Mode I and shear (Mode II and Mode III) TSLs can have different shapes. Furthermore, it provides added generality by enabling coupling with most fracture criteria proposed in the literature. For each material point, the measured Mode I and shear TSLs are scaled based on the fracture criterion chosen and the calculated mode-mixity. If the mode-mixity at a material point changes between damage onset and complete fracture, the Mode I and shear TSLs are scaled such that: (i) energy is dissipated as determined by the mixed-mode fracture criterion, and (ii) artificial healing/damage is prevented. The approach is shown to accurately converge to Linear Elastic Fracture Mechanics for conditions approaching quasi-brittle fracture, confirming its soundness. For conditions approaching brittle–ductile planar fracture, the approach reproduces accurately the general TSLs used as input, under pure Mode I and shear loadings. For mixed-mode conditions, the specified mixed-mode fracture criterion is accurately reproduced ensuring the correct energy is dissipated. The mixed-mode TSL shapes are a function of the Mode I and shear TSLs used, the fracture criterion chosen, and the local mode-mixity. The adaptability of the approach, as evidenced by the preliminary results, suggests that it can be used to simulate a broad range of cohesive responses.