Electrostatic contributions to all first, second and third order elastic constants of hexagonal metals for a range of axial ratios

Abstract

Identities are presented which express the individual Brugger constants for an arbitrary contribution to the free energy in terms of the linear combinations of Brugger constants that are calculated by the method of homogeneous deformation is given. Using Cauchy relations and the new relations between elastic constants of different orders derived by Cousins (1971), the electrostatic contributions to the 17 first, second and third order elastic constants of hexagonal metals are found to involve the calculation of only five quantities: the equilibrium electrostatic energy density and four shear constants. Results are tabulated for a range of axial ratios.