The generalized descriptions of elastic constitutive model and equation of state for nonaxisymmetrical large deformation of cubic crystals under extreme high pressures

The large deformation behavior of materials under extreme high pressures has become a key focus in high-pressure science research. The diamond anvil cell (DAC) experiments have revealed anomalous volume-pressure (V/V₀ – P) relationships, which have driven the development of more widely applicable high-pressure equations of state with higher precision. Traditional equations of state often could not involve the anisotropic factors appearing in DAC experiments, which is one of the primary reasons for the lack of precision. Based on the theoretical framework of Birch and Murnaghan, this work derives the anisotropic compression large deformation constitutive relations and the equations of state from both the Lagrangian and Eulerian perspectives, and extends them to describe the strain hardening effects on second-order elastic constants and bulk modulus. Using these theoretical descriptions, the volume-pressure relationships for four face-centered cubic (FCC) metals (Au, Ag, Cu, Ni) and four body-centered cubic (BCC) metals (Mo, Fe, W, Ta) are calculated, and validate the volume-pressure relationship through atomic-scale simulations. The impact of nonaxisymmetry on the pressure and volume changes is quantified, and it is revealed that the nonaxisymmetry amplifies the pressure difference for the same deformation and increases the volume difference for the same pressure. Additionally, the changes in second-order elastic constants and bulk modulus are investigated to analyze the anisotropic strengthening of elastic properties in various metal materials due to anisotropic deformation. The discrepancy of the predicted bulk modulus from the third-order Birch and Murnaghan equation evaluated by comparing the precise solutions from the generalized equation of state under nonaxisymmetrical conditions. It is found that the discrepancy increases with enlarging the degree of nonaxisymmetry, and the discrepancy for BCC metals is generally higher than that for FCC metals. The present theoretical models for the elastic constitutive behavior and the equation of state could provide the precise descriptions for the elastic performance under extreme high-pressure conditions and the theoretical supports for the design of pressure-resistant materials.