Effective second-order elastic constants of a strained crystal using the finite strain elasticity theory

The finite strain elasticity theory of Murnaghan has been used to derive the expressions for the effective second-order elastic constants of tetragonal, trigonal, orthorhombic, monoclinic, and triclinic crystals in their strained state in terms of the second- and third-order elastic constants of the respective crystals in their natural state. These expressions are employed to obtain the pressure derivatives of the effective second-order elastic constants of some trigonal and tetragonal crystals for which experimental second- and third-order elastic constant data are available.