The Linear US-uP Relation in Shock-Wave Physics

Abstract

A linear relation between shock velocity US and particle velocity UP is often regarded as the "typical" or "standard" material response in the shock-wave literature. It has even been proposed that this linearity follows from some kind of universal equation of state (EOS) principle. This report presents a theoretical analysis of this issue and a survey of the Hugoniot data for all the elements. It demonstrates that linearity follows from the fact that US-UP plots are rather insensitive to material properties, not from any universal EOS. The effects of pressure and material properties on the shock response are more easily seen and analyzed by plotting UF = US - UP as a function of UP. The data survey shows that linear behavior is only observed in 20% of all the elements and is not at all universal.