Shock formation and the ideal shape of ramp compression waves

Abstract

We derive expressions for shock formation based on the local curvature of the flow characteristics during dynamic compression. Given a specific ramp adiabat, calculated for instance from the equation of state for a substance, the ideal nonlinear shape for an applied ramp loading history can be determined. We discuss the region affected by lateral release, which can be presented in compact form for the ideal loading history. Example calculations are given for representative metals and plastic ablators. Continuum dynamics (hydrocode) simulations were in good agreement with the algebraic forms. Example applications are presented for several classes of laser-loading experiment, identifying conditions where shocks are desired but not formed, and where long duration ramps are desired.

References in corpus (3)

• On the Properties of Plastic Ablators in Laser-Driven Material Dynamics Experiments
• On High Explosive Launching of Projectiles for Shock Physics Experiments
• Numerical solution of shock and ramp compression for general material properties

Cited by in corpus (6)

• Path Integral Monte Carlo and Density Functional Molecular Dynamics Simulations of Warm, Dense MgSiO${}_3$
• High Pressure Phase Diagram of Beryllium from \emph{Ab Initio} Free Energy Calculations
• Femtosecond Diffraction and Dynamic High Pressure Science
• Model of Ramp Compression of Diamond from Ab Initio Simulations
• Non-Iterative Characteristics Analysis for High-Pressure Ramp Loading
• Phase Transition of Iron-based Single Crystals at Extreme Strain Rates under Dynamic Loadings