Shear modulus at all pressures: Generalized Guinan–Steinberg formula

The Guinan–Steinberg (GS) formula for the shear modulus at all pressures is widely used in material strength studies. As we demonstrate here, the GS formula predicts a value for the shear modulus that is higher than its actual value at low to moderate compressions, even if it has the correct ultrahigh pressure limit. We show that the reason for this shortcoming is insufficient negative curvature in the GS shear modulus as a function of pressure, and propose a generalized GS formula which corrects this inaccuracy. Both the (standard) GS formula and new generalized formula are compared to the experimental data and ab initio calculations on the shear moduli of gold, aluminum, cobalt and beryllium. While the standard formula fails, the generalized one is in good agreement with data in each of the four cases.