The Hugoniot of a Solid Determined by Means of a Variational Principle
Abstract
The formulation of the Gruneisen coefficient based on the velocity doubling approximation is used to define a normalized Gruneisen coefficient. A new integral formulation for the free surface velocity is than written in terms of this normalized coefficient. On the assumption that the specific energy of the solid at 0K is a known function of the specific volume and that the bulk sound speed in the uncompressed state is a known quantity, the Hugoniot of the solid is chosen to be that curve, among a family of curves lying on a Mie- Gruneisen constraint surface, which maximizes the free surface velicity. A differential equation for the resulting Hugoniot is determined and its solution is approximated by the first three terms of a series expansion. This expansion furnishes a quadratic expression for the shock velocity in terms of the particle velocity all of whose coefficients are given by formulas involving physically meaningful quantities. Calculations have been made in the case of aluminum and have been found to agree with the experimental data out to 340 kb very closely. A preliminary check for sodium metal is also given
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1971
- Accession Number
- AD0743027
Entities
People
- James F. Heyda
Organizations
- University of Dayton