Abstract
This review examines the elastic response of solids under load. The definitions of isothermal and adiabatic elastic constants of () for a loaded crystal are given. For the case of hydrostatic pressure, two techniques are proposed for calculating the second-, third-, and fourth-order elastic constants from the energy-strain and stress-strain relations. As an example, using the proposed approach within the framework of the density functional theory, the second- to fourth-order elastic constants of bcc tungsten are calculated for the pressure range of 0–600 GPa.
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