A constitutive model for predicting shear modulus of metals using aluminum as the prototype

Abstract

With a two-step approach，a pressure，P，and temperature，T，dependent constitutive model of shear modulus，G，applicable to metals was developed in this work. The goal of the first step is to find the relation of G with P along 0 K isotherm，i.e. the functional form of G1=G1（P，0 K），and the second one is to find the relation of G，starting from a given state of （P，0 K） with a value that was already determined in the first step，with T along the isobar of P，i.e. the functional form of G=G（P，T） or the constitutive model proposed by us. In both steps，results of supersonic measurement and first principles calculation were used. Aluminum，as a model material，was utilized to validate the rationality of this model. It is demonstrated that the predicted results of this model are in satisfactory agreement with the measured and numerically simulated G despite whether it evolves along shock compressed，isentropic，isothermal，or isobaric loci，thereby displaying the rationality and the universal nature of this constitutive model.