Abstract
The fourth-order coupling parameters of lattice theory are related to the set of nonlinear elastic constants of fourth and lower order. The invariance properties of a lattice are used to derive the relationships. Explicit relations are illustrated for a cubic lattice. For a face-centered-cubic lattice, the assumption of central forces for fourth-order coupling parameters leads to approximate relations between fourth-order elastic constants. Dependent on the character and extent of the lattice lower-order coupling parameters, different sets of approximate relations between fourth-order constants are found to be available for use in the determination of those constants from experimental data.
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