567 citations · 1.7k across the 25 of their papers we have counts for
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Quadratic invariants of elastic moduli
Andrew N. Norris
A quadratic invariant is defined as a quadratic form in the elements of a tensor that remains invariant under a group of coordinate transformations. It is proved that there are 7 q…
Euler-Rodrigues and Cayley formulas for rotation of elasticity tensors
Andrew N. Norris
It is fairly well known that rotation in three dimensions can be expressed as a quadratic in a skew symmetric matrix via the Euler-Rodrigues formula. A generalized Euler-Rodrigues…
The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry
Maher Moakher, Andrew N. Norris
The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic…
Pure shear axes and elastic strain energy
Andrew N. Norris
It is well known that a state of pure shear has distinct sets of basis vectors or coordinate systems: the principal axes, in which the stress is diagonal, and pure shear bases, in…
Poisson's ratio in cubic materials
Andrew N. Norris
Expressions are given for the maximum and minimum values of Poisson's ratio for materials with cubic symmetry. Values less than -1 occur if and only if the maximum shear modulu…
Impedance of a sphere oscillating in an elastic medium with and without slip
Andrew N. Norris
The dynamic impedance of a sphere oscillating in an elastic medium is considered. Oestreicher's formula for the impedance of a sphere bonded to the surrounding medium can be expres…