New relations between elastic constants of different orders under central force interactions

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Abstract
The analysis of contributions to elastic constants is made consistent by introducing a first order term into the contribution to the elastic free energy density. The precise relation between Fuchs elastic constants and Brugger elastic constants is made explicit. New relations between elastic constants of different orders are revealed for central force interactions by extending the method that generates the Cauchy relation. The reduction in computation that these produce is illustrated by reference to the electrostatic contributions to the first, second and third order elastic constants of cubic metals.

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