Second- and Higher-Order Effective Elastic Constants of Cubic Crystals under Hydrostatic Pressure

The concept of the pressure-dependent effective elastic constants of a cubic crystal under hydrostatic compression is extended to the effective higher-order elastic constants. These constants describe the non-linear elastic behavior of a cubic crystal in reference to arbitrary finite deformations which are performed in addition to the initial hydrostatic compression. The effective higher-order elastic constants are expressed in terms of pressure-independent actual higher-order elastic constants. Explicit expressions are given for the expansion coefficients of the effective second-, third-, and fourth-order elastic constants with respect to volume strain and pressure, up to terms involving the actual fifth-order elastic constants.