Semi-lagrangian galerkin reproducing kernel formulation and stability analysis for computational penetration mechanics

Stability analyses of Lagrangian and semi-Lagrangian reproducing particle methods using various domain integration methods are performed. The von Neumann stability analysis shows that both Lagrangian and semi-Lagrangian reproducing kernel discretizations of equation of motion are stable when they are integrated using stabilized conforming nodal integration in the weak forms. On the other hand, integrating the weak form of semi-Lagrangian equation of motion with a direct nodal integration yields an unstable discrete system which resembles the tensile instability in SPH. Stable time step estimation for Lagrangian reproducing kernel discretization shows enhanced stability when weak form is integrated by stabilized conforming nodal integration compared to that using direct nodal integration or 1-point Gauss integration. Penetration simulation is performed to demonstrate the applicability of the proposed method to large deformation and fragment impact problems.