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Finally, the effects of the peak compressive stress, the tensile strain rate, and the loading rate on the spallation are more » further investigated. Moreover, the effect of the spall parameter in PAGOSA with FLIP+MPM on the numerical simulation is also analyzed by investigating the free surface velocity. To further show the ability of PAGOSA with FLIP+MPM to predict fracture in ductile material, the numerical results are compared with the experimental results and other published numerical results. The convergences of PAGOSA with FLIP+MPM-based on both the mesh size and the marker density-are investigated by monitoring free surface velocity. Then PAGOSA with FLIP+MPM is used to model complex spall in ductile material, which is a challenging problem in engineering applications. In both of two benchmark problems, the PAGOSA results and analytical solutions are also presented for comparison. Furthermore, the ability of PAGOSA with FLIP+MPM to capture the fracture in material is shown by a simple stretching fracture in ductile material. The merit of PAGOSA with FLIP+MPM to solve the advection problem is first illustrated by a solid piston periodically moving in a sealed tube with air. N this work, a hydrocode PAGOSA with FLIP+MPM is presented and exercised to investigate the fracture in ductile material.