The strain tensor itself can be defined to reflect distortion in any way that results in invariance under total rotation, but the most common definition with regard to which elastic tensors are usually expressed defines strain as the symmetric part of the gradient of displacement with all nonlinear terms suppressed: ε ε i j = 1 2 ( ∂ ∂ i u j + ∂ ∂ j u i ) where u i is the displacement at a point in the i -th direction and ∂ ∂ j is the partial derivative in the j -th direction. Note that: ε ε j j = ∂ ∂ j u j where no summation is intended. Although full Einstein notation sums over raised and lowered pairs of indices, the values of elastic and strain tensor components are usually expressed with all indices lowered. Thus beware (as here) that in some contexts a repeated index does not imply a sum overvalues of that index ( j in this case), but merely a single component of a tensor.