Location of Repository

Euler-Rodrigues and Cayley formulas for rotation of elasticity tensors

By A. N. Norris, Dedicated Professor and Michael Hayes

Abstract

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 polynomial of degree 2n in a skew symmetric generating matrix is derived for the rotation matrix of tensors of order n. The Euler-Rodrigues formula for rigid body rotation is recovered by n = 1. A Cayley form of the n th order rotation tensor is also derived. The representations simplify if there exists some underlying symmetry, as is the case for elasticity tensors such as strain and the fourth order tensor of elastic moduli. A new formula is presented for the transformation of elastic moduli under rotation: as a 21-vector with a rotation matrix given by a polynomial of degree 8. Explicit spectral representations are constructed from three vectors: the axis of rotation and two orthogonal bivectors. The tensor rotation formulae are related to Cartan decomposition of elastic moduli and projection onto hexagonal symmetry.

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.310.7583
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://arxiv.org/pdf/cond-mat/... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.