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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on May 4, 2007
The Quarterly Journal of Mechanics and Applied Mathematics 2007 60(3):367-389; doi:10.1093/qjmam/hbm007
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Q. Jl Mech. Appl. Math, Vol. 60. No. 3 © The author 2007. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Quadratic invariants of elastic moduli

Andrew N. Norris{dagger}

( Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854-8058, USA )

{dagger} < norris{at}rutgers.edu>

Received 23 December 2006. Revise 8 March 2007.
  Abstract

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 seven quadratic invariants of the 21-element elastic modulus tensor under SO(3) and 35 under SO(2). This answers some open questions raised by Ting and Ahmad in this journal.


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