Using PAGOSA with FLIP+MPM to simulate and analyze the recompression of spall with 3D effects induced by double-shock waves*

Many grid-based methods for fracture/fragmentation induced by shock wave in material simulate the shock waves by converting the discontinuous shock wave to a steep gradient to maintain the continuity hypothesis. This causes an inaccurate prediction of fracture. This work presents a hybrid shock code PAGOSA with FLIP+MPM to accurately predict and explore the recompression of spall with 3D effects induced by double-shock waves. This algorithm seamlessly couples a finite different method and the particle FLIP+MPM method, in which a mapping between Eulerian grid and marker particles is constructed.  The failure particles are removed in an amazing way. We first validate the capabilities of PAGOSA with FLIP+MPM to predict different fracture/fragmentation cases by solving benchmark problems and comparing with the analytical solutions or the experimental results. The convergences and the infinity-norm errors are also investigated. Subsequently, the 3D effects on the numerical results are demonstrated by simulating the spallation in material. Some factors that affect the spallation with 3D effects are discussed. Finally, the recompressions of spall in material with/without 3D effects are systematically simulated and analyzed. The conditions that induce the recompression of spall are explored. Numerical results show that PAGOSA with FLIP+MPM can accurately predict different fracture cases, that the 3D effects play an important role in the fracture/fragmentation, and the recompression of spall is very sensitive to the occurrence conditions, shows great differences when considering 3D effects in real applications. Moreover, the presented algorithm is not limited to the finite different method presented here, but can be easily extended to other grid-based techniques employed for fracture in materials.