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

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Abstract
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.