Shear modulus and elastic constants in lead from first principles

The behavior of a material subjected to extreme loadings is linked to its mechanical properties. Particularly, the shear modulus (G) is a part of the overall description used in hydrodynamics codes, dedicated to simulations at high strain rates.

Evolution of G is usually described by constitutive models [1,2], mostly based on the determination of elastic properties from ultrasonic experiments [3,4]. However, such experiments do not allow to understand the underlying physics appearing at microscale like the influence of crystallographic changes induced during shocks. Moreover, experimental data show that G increases with pressure and decreases with temperature. Although the usual constitutive models are able to reproduce these experimental observations, their precision outside the experimental domain cannot be guaranteed (high pressure, high temperature) [5].

Another recent way to evaluate G is to use ab initio calculations. This method allows the determination of elastic constants in each phase thanks to the energy variation of a deformed cell [6].

In this work, G of lead is evaluated by the strain-energy method from first principles. A new adjustment of the SCG constitutive model [1] is proposed in order to take into account the influence of crystallographic changes and the pressure and temperature dependencies given by ab initio calculations.