A semi-analytical bridging model for assessing energy dissipation of monolithic and hybrid z-pins in composite laminates

A semi-analytical model is proposed to simulate the bridging behaviour of novel z-pin materials and architectures recently developed to ensure balanced mode I to mode II delamination bridging. The computational model describes these z-pins as Timoshenko beams embedded in an elastic foundation representing the surrounding composite laminate. Governing equations for the behaviour of the z-pins are derived, with appropriate modifications made to the original formulation to account for the bridging actions of the novel z-pins. A genetic algorithm is proposed to calibrate the necessary input parameters of the model, based on the specific type of z-pin being considered. The model is validated through comparison with numerous experimental single z-pin datasets and effectively outputs the ultimate displacement and energy dissipated per unit area, normalised with respect to areal density, for future use in macroscopic modelling simulations, with the underlying assumptions and limitations explicitly acknowledged and discussed.