An Equation of State for Anisotropic Solids under Shock Loading

TL;DR

This paper introduces an anisotropic equation of state for shock-loaded solids, extending the Mie-Grüneisen model to better predict high-pressure states in anisotropic materials like crystals and alloys.

Contribution

It develops a generalized anisotropic equation of state and a nonlinear continuum framework for analyzing shock wave propagation in anisotropic solids of any symmetry.

Findings

Numerical results match experimental data for aluminum alloy 7010-T6

The model accurately predicts Hugoniot elastic limits and stress levels

The approach generalizes isotropic models to anisotropic materials

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-Gr\"{u}neisen 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 \textbf{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.