On effective transversely isotropic elasticity tensors based on Frobenius and L2 operator norms

Abstract A generally anisotropic elasticity tensor, which might be obtained from physical measurements, can be approximated by a tensor belonging to a particular material-symmetry class; we refer to such a tensor as the effective tensor. The effective tensor is the closest to the generally anisotropic tensor among the tensors of that symmetry class. The concept of closeness is formalized in the notion of norm. Herein, we compare the effective tensors belonging to the transversely isotropic class and obtained using two different norms: the Frobenius norm and the L2 operator norm. We compare distributions of the effective elasticity parameters and symmetry-axis orientations for both the error-free case and the case of the generally anisotropic tensor subject to errors.