Shock-wave compression of a porous material

Abstract

Porous materials may exhibit highly nonstationary behavior under shock-wave loading. The majority of existing experiments have measured the dependence between shock-wave velocity and particle velocity to define the Hugoniot for subsequent derivation of an equation of state. Such equations of state are nonconvex, which leads to significant thermodynamic and numerical problems. The present article suggests an experimental configuration and mathematical model, to overcome these difficulties. The experiment is based on a setup resulting in a continuous record of the stress profile with time using embedded manganin gauges. The model employs a homogenization approach enabling us to obtain a hyperbolic system of equations, which is completed with a convex equation of state so as to be suitable for implementation in commercial hydrocodes. Using available data for porous aluminum, an approach is elaborated for construction of constitutive equations. The model is tested with the present stress profiles in sand and demonstrates good agreement.