UCLA

Many of today's challenging engineering and scientific problems involve the response of nonlinear solid materials to high-rate dynamic loading. Accompanying hydrodynamic effects are crucial, where the shock-driven pressure dominates material response. In this work a hydrodynamic meshfree formulation is developed under the Lagrangian reproducing kernel particle method (RKPM) framework. The volumetric stress divergence is enhanced to capture the high-pressure shock response, and the deviatoric portion is retained to describe strength effects of the solid material. A shock modeling formulation for scalar conservation laws is first constructed. In the scalar formulation the reproducing kernel particle method is formulated to address two key shock modeling issues, that is, accurate representation of the essential shock physics and control of the numerical oscillations due to Gibbs phenomenon at the jump. This is achieved by forming a smoothed flux divergence under the meshfree stabilized conforming nodal integration (SCNI) framework, and then enriching the flux divergence with a Riemann solution. The Riemann-enriched flux divergence is embedded into a velocity corrector adaptively applied at the shock front. As a consequence the shock solution is locally corrected while the smooth solution away from the shock is unaffected. For shocks in solids, developments from the scalar formulation were extended to the Cauchy's equation of motion. Shock effects in solids are pressure dominated, so that the shock solution is enhanced through the volumetric stress divergence. The volumetric stress divergence correction is formulated using a Rankine-Hugoniot enriched Riemann solution that introduces the essential shock physics to the formulation. Oscillation control is introduced through the state and field variable approximations that utilize the Riemann problem initial conditions, and therefore non-physical numerical parameters and length scales required in the traditional artificial viscosity technique are avoided. Further, because the proposed method for oscillation control is linked to the essential physics, the two key issues for accurate shock modeling are addressed in a unified and consistent way. For the nonlinear solids formulation, several benchmark problems are solved and the numerical results are verified by comparison to experimental data or analytical solutions. A range of shock conditions are studied to show the versatility of the proposed method for modeling conditions ranging from weak elastic-plastic shocks to strong shocks generated by hypervelocity impact.