Hydrodynamic meshfree method for high-rate solid dynamics using a Rankine-Hugoniot enhancement in a Riemann-SCNI framework

Many challenging engineering and scientific problems involve the response of nonlinear solid materials to high-rate dynamic loading. Accompanying hydrodynamic effects are crucial, where shock-driven pressures may dominate material response. In this work, a hydrodynamic meshfree formulation is developed under the Lagrangian reproducing kernel particle method framework. The volumetric stress divergence is enhanced using a Rankine-Hugoniot-enriched Riemann solution that introduces the essential physics; oscillation control is introduced through appropriate state and field variable approximations that define the Riemann problem initial conditions. Consequently, non-physical numerical parameters and length scales required in the traditional artificial viscosity technique for shock modeling are avoided here. Several numerical examples are provided to verify the formulation accuracy across a range of shock loading conditions. Copyright (C) 2016 John Wiley & Sons, Ltd.