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An attempt has been made to calculate the isotropic third-order elastic constants of a polycrystalline solid in terms of the single-crystal constants using the methods employed by Voigt and Reuss in the second-order case. The application of these calculations to a variety of different materials shows that the discrepancy between the two methods is much greater than in the case of second-order constants.
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Hamilton et al. (1968) studied this question.
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