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

Abstract

Summary 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 © 2016 John Wiley & Sons, Ltd.