Finite element-smoothed particle hydrodynamics adaptive method in simulating debris cloud

The meshless algorithms, especially the smoothed particle hydrodynamics (SPH), are attempted to solve the hypervelocity impact (HVI) problem. However, several limitations of SPH exist in the current studies, such as the tensile instability, the material boundary uncertainty, and the difficulty in defining boundaries. Furthermore, it cannot accurately provide the parameters of the generated fragments. In this paper, we formulate the finite element-smoothed particle hydrodynamics (FEM-SPH) adaptive method to solve the HVI problem by LS-DYNA. It combines the advantages of FEM and SPH by transforming the failed elements into the SPH particles during the simulation. The debris cloud shape is represented by the distribution of the particles in SPH and the exact fragment parameters in FEM, including geometry, temperature, energy, and distribution. By analyzing and optimizing the implementation method, the contact and coupling algorithm, and calculation parameters, we reproduce the experimental results by Piekutowski [39,40] in the numerical simulation. Based on the proposed three typical shapes of the fragments, a systematic statistical analysis is proposed to classify the fragments and analyze their parameters, including speed, momentum, and energy. Risky fragments, i.e., the fragments with large size and high speed, are selected from the overall fragments. We further study the distribution of risky fragments with the details of the evolution in the space and time, which paves the way for further systematic research on the subsequent impact of the debris cloud. Our work shows that the method has a significant and wide application to the debris cloud simulation. The current algorithm can be applied to simulate the Whipple shields with complex structures and advanced material, e.g., sandwich materials, composite materials, foam materials, and gradient materials, or analyze the implosion and fragmentation warhead.