The concept of norm

The comparison of magnitudes of the norms can give valuable information about the origin of the physical property under examination. Since the norm is invariant in the material, the norm of a Cartesian tensor may be used as the most suitable representing and comparing the overall effect of a certain property of anisotropic materials of the same or different symmetry or the same material with different phases based on the crystallographic level (Spencer, 1983; Srinivasan, 1998; Tu, 1968; Nye, 1959; Voigt, 1889; Radwan, 1991; Ikeda, 1990). The larger the norm value, the more effective the property is. Generalizing the
concept of the modulus of a vector, a norm of a Cartesian tensor is defined as the square

root of the contracted product over all the indices with itself (Srinivasan, 1998; Tu, 1968;

Radwan, 1991). Since the constructed basis in this method is orthonormal and C.., is in ‘ ijkm

the space spanned by that orthonormal basis, the norm for the elastic stiffness, for example, is given by:

N = llCll = {Cijj (24)

Updated: October 10, 2015 — 5:59 am