Differentiable structure of the set of coaxial stress–strain tensors | Zendy

Clotet Josep | Zendy; Magret M. Dolors | Zendy; Peña Marta | Zendy

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Differentiable structure of the set of coaxial stress–strain tensors

Author(s) -

Clotet Josep,

Magret M. Dolors,

Peña Marta

Publication year - 2008

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.1108

Subject(s) - differentiable function , mathematics , pure mathematics , dimension (graph theory) , equivalence (formal languages) , action (physics) , space (punctuation) , coaxial , mathematical analysis , physics , linguistics , philosophy , quantum mechanics , electrical engineering , engineering

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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