Shock formation and the ideal shape of ramp compression waves

TL;DR

This paper derives formulas for shock formation during ramp compression, enabling the design of ideal loading profiles to control shock development in materials under dynamic compression.

Contribution

It introduces a method to determine the ideal nonlinear ramp shape for specific materials based on their equation of state and flow characteristics.

Findings

Continuum simulations agree with algebraic shock formation expressions.

Ideal ramp profiles can be designed to avoid shock formation in experiments.

Applications include optimizing laser-driven compression experiments.

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.