A note on the estimation of the third-order elastic constants of quasi-isotropic materials

A simplified scheme is presented for discussing and calculating estimates of the third-order elastic constants of quasi-isotropic material based on single-crystal data. The difference between the Voigt and Reuss averages at the third order is shown to depend solely on the second-order single-crystal anisotropy. Only the two smaller constants are affected in this way. Chang's data for niobium are used to compare the methods.