On the determination of the fourth-order elastic constants

Starting from the equations of small-amplitude waves superposed on a state of homogeneous static deformation (due to hydrostatic pressure or uniaxial stress), exact expressions for the second derivative of the wave velocity with respect to the statically applied stress—at constant temperature—are derived. These equations involve the mixed (adiabatic-isothermal) fourth-order elastic constants, and the equations can be used for their determination. The mixed fourth-order elastic constants lack full symmetry in their indices. Their relations to the adiabatic and isothermal ones are derived.