Relationship between third-order elastic coefficients and stress-induced changes on second-order elastic coefficients

The second-order elastic coefficients (SOECs) must be modified to account for the medium deformation to describe acoustic wave propagation in a medium under stress or strain. Early studies have shown this can be achieved by introducing additional third-order elastic coefficient (TOEC) related terms (e.g., [1]). This study reevaluates these formulations and provides ab initio verifications. We first examine the effect of hydrostatic stress on the pressure derivative of SOECs. Then, as a more general case, we investigate the modifications needed to obtain SOECs under hydrostatic and deviatoric stress. We show, in both cases, the change applied to SOECs is a linear combination of SOECs and TOECs. These relationships are tested with ab initio calculations of SOECs and TOECs vs. pressure on NaCl and MgO. The method to compute finite-pressure TOECs is also self-consistently tested.

 

[1] R. N. Thurston, K. Brugger, Phys. Rev. 133, A1604–A1610 (1964).