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Differentiable structure of the set of coaxial stress–strain tensors

✍ Scribed by Josep Clotet; M. Dolors Magret; Marta Peña

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
131 KB
Volume
32
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

In order to study stress–strain tensors, we consider their representations as pairs of symmetric 3 × 3‐matrices and the space of such pairs of matrices partitioned into equivalence classes corresponding to change of bases. We see that these equivalence classes are differentiable submanifolds; in fact, orbits under the action of a Lie group. We compute their dimension and obtain miniversal deformations. Finally, we prove that the space of coaxial stress–strain tensors is a finite union of differentiable submanifolds. Copyright © 2008 John Wiley & Sons, Ltd.

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