Multi-phase-field modelling of the elastic and buckling behaviour of laminates with ply cracks.

• A simulation of multiple transverse ply cracking in laminates is presented. • Many phase-field variables are used, each one describes the crack of the layer. • Some interesting phenomenons when the cracks appear at different layers of the structure are shown out. The phase-field theory is a well-known mathematical model for solving interface problems, including crack problems in fracture mechanics. In this study, the formula is derived by variational approaches based on the Reissner-Mindlin plate kinematics and the multi-phase-field theory for simulation of the buckling phenomenon in cracked laminates. Phase-field parameters are defined independently in different plies of laminate to capture the crack behavior of each ply. Simulation is carried out to numerically investigate the stiffness reduction and buckling behavior of transverse cracked laminated composite plates. This paper focuses on the consideration of laminated composite plates, which have a crack in each layer. Therefore, this work is more complicated than the case of the plate has one crack throughout the plate thickness. The significant advancement of the phase-field approach for laminated composite plates with complex crack geometries is demonstrated. [ABSTRACT FROM AUTHOR]