Structural cohesive element for the modelling of delamination between thin shells without cohesive zone limit
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Cohesive element has been widely-used for the modelling of delamination between plies in a composite laminate. Despite its popularity, cohesive elements suffer from a well-known limit on the mesh density – the element size must be much smaller than the cohesive zone size. Otherwise, the steeply varying stress field in the cohesive zone cannot be integrated accurately, often leading to under-estimation of the peak cohesive stress and hence a delayed prediction of damage onset. This results in non-conservative strength predictions for delamination [1]. Based on the earlier work in 2D [2], this work develops a new set of elements for composite plies and their interfaces. The core insight is that the kinematics of the delaminated interface should follow from the geometries of the surfaces of the neighbouring plies which are slender shell-like structures. This means that the traditional approach of using solid-like cohesive elements (i.e., C0 continuous with polynomial shape functions) for delamination is inappropriate, as they are not designed to represent the kinematics of thin shell surfaces. Therefore, in this work, the plies will be modelled with C1-continous Kirchhoff-Love thin shell elements. A special cohesive element is formulated for the interface which conforms to the shell elements of the plies and shares their degrees of freedom. The proposed method is verified and validated on the classical benchmark problems of Mode I, Mode II and mixed-mode delamination. In addition, the Single-Leg Bending problem of a complex angle-ply laminate is modelled with the proposed method. All the results show that the mesh size with the new method can be several times larger than that allowed by the current limit on mesh density while retaining solution accuracy. This would then enable the accurate modelling of composite delamination without worrying about the current cohesive zone limit on mesh density, thereby saving a lot of computing time. REFERENCES [1] A. Turon, C. G. Davila, P. P. Camanho and J. Costa. An Engineering solution for the mesh size effects in the simulation of delamination using cohesive elements. Engineering Fracture Mechanics, 74(10):1665-1682, 2007. [2] R. Russo and B. Chen. Overcoming the cohesive zone limit in composites delamination: modeling with slender structural elements and higher-order adaptive integration. International Journal for Numerical Methods in Engineering, 121(24):5511–5545, 2020.