An energy-equivalent bridging map formulation for modelling delamination in through-thickness reinforced composite laminates

A new multi-scale framework to numerically model the bridging effect in through-thickness reinforced (TTR) composite laminates with zpins is presented. The framework first establishes a library of bridging maps, calculated by a micromechanical semi-analytical constitutive bridging model. For the macro-scale, a tri-linear cohesive law has been developed to model initiation and propagation of the interfacial damage in the presence of z-pins. The cohesive law takes into account the energy dissipated by delamination propagation through the matrix in the interlaminar region, plus the energy contributed by the z-pin bridging up to complete pull-out from the laminate or z-pin failure. The information regarding the failure mode and the consequent dissipated energy comes from the library of bridging maps. The tri-linear cohesive law has been implemented in a user material subroutine of a commercial finite element software. The framework has been validated against experimental data and an excellent correlation has been achieved.