Accurate simulation of delamination under mixed-mode loading using a multilinear cohesive law

The complex failure mechanisms involved in failure of interfaces requires the use of an accurate description of the cohesive law. In recent years, there have been many developments to determine the full shape of the cohesive law. However, most of the existing cohesive zone models assume a simplified shape, such as bilinear, trapezoidal or exponential, which are usually simple to model. Their accuracy is found to be rather limited, especially in the presence of a large fracture process zone due to either plastic deformation or fibre bridging. In this work, a new cohesive element description is proposed to formulate a general cohesive zone model to overcome these limitations. The benefit of the new approach is that it allows for convenient implementation of any arbitrary shape of the cohesive law obtained experimentally. The authors present a new procedure based on the superposition of n-bilinear cohesive zones to obtain an equivalent multilinear cohesive law that fits any experimental measurement. The new element formulation has been implemented in the commercial finite element software ABAQUS, using user element subroutine. Verification of the methodology is performed at the single element level and the approach is validated for different material systems (adhesives and composites) using the double cantilever beam, end-notched flexure and mixed-mode bending tests. Excellent correlation between all numerical predictions and experimental results is obtained, demonstrating the robustness of the proposed methodology.