Accurate simulation of delamination with a resin-rich layer-dependent penalty stiffness based on structural cohesive elements

Shell-based cohesive elements tend to overestimate the compression ahead of the crack tip because of approximations in the penalty stiffness. In this study, the higher-order structural cohesive element previously developed by the authors is enhanced with a resin-rich layer-dependent penalty stiffness to improve both computational efficiency and predictive accuracy. The proposed formulation distinguishes between the normal and shear penalty stiffnesses. It extends the resin-rich layer-based penalty stiffness from the layer-wise to the equivalent single-layer framework. This extension is achieved using the through-thickness distributions of the out-of-plane normal and transverse shear stresses derived from beam theory. The proposed method is verified and validated against benchmark problems for Mode I, Mode II, mixed-mode, and reinforced DCB configurations. Compared with the conventional formulation, it exhibits significantly improved mesh convergence and provides more accurate predictions of the compression distribution ahead of the crack tip and the delamination propagation.