Observations on the fourth-power scaling of high-pressure shock waves in solids

Abstract

This paper is concerned with the bounds and approximations that are found in the original derivation of the fourth-power scaling of shock waves in solids [D. Grady, Appl. Phys. Lett. 38, 825 (1981)]. The analysis is focused on the framework of the derivation and is independent of constitutive assumption, such as visco-plastic behavior. Results include an upper bound for the shock pressure and a restriction on the range of power coefficient for materials having a power-type function for the shock velocity–particle velocity relation. Relaxation of this restriction is proposed based on the idea that the rise time along the Rayleigh line is strain dependent. The idea led to the application of the Onsager relation to strain rate calculation that in turn resulted in a quadratic function for the strain rate–shock pressure relation. The fourth-power relation is obtained by generalizing the Onsager relation through the introduction of a quadratic dissipative potential in analogy to Rayleigh's dissipative potential.

Document Details

Document Type
Pub Defense Publication
Publication Date
Dec 22, 2021
Source ID
10.1063/5.0071928

Entities

People

  • Y. Horie

Organizations

  • Air Force Research Laboratory
  • Sandia National Laboratories

Tags

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Linear Algebra
  • Structural Dynamics.