Study on the PDDO-based meshfree method in numerical simulation of shell ductile fracture considering a non-local GTN model

•The average displacement state-based hourglass force is adopted to eliminate zero-energy mode.•The convergence of numerical simulation of fracture is improved based on the non-local GTN model.•Crack propagation under penetration loads is accurately simulated by a multi-crack visualization algorithm. A meshfree method is developed based on the peridynamic differential operator (PDDO) for ductile damage and fracture problems in metal shell structures. The kinematic equations coupled to classical continuum mechanics (CCM) are derived with the motion variables discretized by the PDDO. The elastoplastic and fracture behavior of the material are described by applying the Gurson-Tvergaard-Needleman (GTN) model with shear modification, and the non-local form of the model improves the computational convergence for different modeling scales. The zero-energy model in numerical computations is effectively controlled by introducing an hourglass force based on the average displacement state. The particles contact algorithm and multi-crack visualization algorithm are developed to simulate the fracture of shell structures under collision loads. By comparing with experiments, it is verified that the proposed PDDO-based meshfree method can accurately predict the ductile fracture of shell structures subjected to in-plane and out-of-plane loads.