Quadratic invariants of elastic moduli

Details Quadratic invariants of elastic moduli Quadratic invariants of elastic moduli

2006-12-19

arxiv.org/abs/cond-mat/0612506v5

Quart. J. Mech. Appl. Math. 60, 367-389, 2007.

Physics

Condensed Matter

Materials Science

20 pages

Scientific paper

10.1093/qjmam/hbm007

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 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 (1987) and Ahmad (2002).

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