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Third-order elastic coefficients (TOECs) have been measured experimentallyand tabulated with pretty good accuracy since the middle of the previouscentury. In the classical acoustic measurement method the recalculation ofinstantaneous stiffness change onto TOECs is based on the use of Green strain.In recent calculations performed by means of atomistic and quantum methods manydifferent strain measures are employed. In result, quite different sets ofTOECs can be obtained for the same material. In this paper, it is shown howdramatically the coefficients obtained depend on the choice of strain measure.The known formulas for calculation of the second derivative of a tensor-valuedfunction of tensor variable are corrected. The formulas are essential for thecorrect analytic calculation of the tangent stiffness matrix in finite elementmethod, among others.

Third-order elastic coefficients and logarithmic strain in constitutive and finite element modelling of anisotropic elasticity