The relationships between the elastic moduli and compliances of transversely
isotropic and orthotropic materials, which correspond to different appealing sets of
linearly independent fourth-order base tensors used to cast the elastic moduli and
compliances tensors, are derived by performing explicit inversions of the involved
fourth-order tensors. The deduced sets of elastic constants are related to
each other and to common engineering constants expressed in the Voigt
notation with respect to the coordinate axes aligned along the directions
orthogonal to the planes of material symmetry. The results are applied to a
transversely isotropic monocrystalline zinc and an orthotropic human femural
bone.
Keywords
algebra of tensors, elastic constants, human femur,
orthotropic materials, transverse isotropy, zinc