Eur. Phys. J. B 64, 159-164 (2008)
https://doi.org/10.1140/epjb/e2008-00295-5

An equation of state for anisotropic solids under shock loading

Cranfield University, Cranfield, Bedfordshire MK43 0AL, UK

Received: 12 May 2008
Revised: 7 June 2008
Published online: 30 July 2008

Abstract

An anisotropic equation of state is proposed for accurate extrapolation of high-pressure shock Hugoniot states to other thermodynamics states for shocked single crystals and polycrystalline alloys. The proposed equation of state represents mathematical and physical generalization of the Mie-Grüneisen equation of state for isotropic material and reduces to this equation in the limit of isotropy. Using an anisotropic nonlinear continuum framework and generalized decomposition of a stress tensor [Int. J. Plasticity 24, 140 (2008)], the shock waves propagation along arbitrary directions in anisotropic solids of any symmetry can be examined. The non-associated strength model includes the distortion effect of the yield surface which can be used to describe the anisotropic strength differential effect. A numerical calculation showed that the general pulse shape, Hugoniot Elastic Limits (HELs), and Hugoniot stress levels for aluminum alloy 7010-T6 agree with the experimental data. The results are presented and discussed, and future studies are outlined.