DYMAT 2009 (2009) 1339-1343
DOI: 10.1051/dymat/2009189

A modified analytic model of the shear modulus

R. Hou^{1, 2, 3}, J. Peng³, J. Zhang², M. Tu², X. Cui³ and Y. Wang<sup>4

1</sup>  School of Science, Wuhan University of Technology, 430070 Wuhan, China
²  The first aeronautic institute of the air force, Xinyang, 464000 Henan, China
³  National key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, PO Box 919-102, Mianyang, 621900 Sichuan, China
⁴  Mechanics and Materials Science Research Center, Ningbo University, Ningbo 315211, Zhejiang, Chiana

Published online: 15 September 2009

Abstract
Although the SCG constitutive model is extensively used for shear modulus computation at high strain rate, researchers also find its limitation: with increasing pressure, the results calculated by SCG model is not consistent with the first-principle analysis at 0 K isothermal state, and also has obvious deviation with the shock experimental results. A modified model is presented. It is based on the understanding that every physical state of a material can be obtained from its initial state at zero temperature and zero pressure through two processes: an isothermal compression process at T = 0 K and then an isobaric thermal expansion process from 0 K. Along isothermal, the shear modulus can be calculated by a power function deduced from theoretical calculation results. Along isobar, the shear modulus and temperature exhibits linear relation. The modified model involves four parameters and two methods for confirming the parameters are introduced. A comparison with shock experimental results and other models was presented for Al and Cu, which indicated that the modified form has shown good universality in different physical conditions.

© EDP Sciences 2009