Modified Blatz–Ko Model for High-Pressure Diamond Anvil Cell Materials: Helium and Rhenium

Abstract A modified Blatz–Ko hypoelastic model for the elastic response of isotropic polycrystalline hexagonal close-packed materials under high-pressure conditions is introduced. The model describes the pressure dependence of the elastic constants and is therefore suitable for ultra-high pressure applications. The model is fit to effective isotropic elastic moduli computed as an average of the Voigt and Reuss estimates of single-crystal data obtained from first principles and experimental measurements. Parameterizations are obtained for helium and rhenium, which are of interest due to their use as the pressure transmission medium and gasket material in diamond anvil cell (DAC) experiments. Predicted equations of state are in very good agreement with experiments. The new modified Blatz–Ko models can be coupled with a deformation theory of plasticity approach or a pressure-dependent $J_{2}$ J 2 -flow theory and used in numerical simulations of DAC experiments for design and analysis purposes. (VUMAT routines for the Abaqus finite element code and a numerical example are provided as Supplementary Material.)