Elastic constants of a stressed crystal. I. General theory

Abstract

Equations for the derivatives of adiabatic and isothermal elastic constants with respect to the stress tensor for the initially stressed crystal of the arbitrary symmetry are deduced. The relation between the third order elastic constants determined under different thermodynamic boundary conditions are estimated in the general case. The proposed methods of obtaining the derivatives with respect to the stress tensor and the relations between different elastic constants may be applied to the elastic constants of higher order.