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