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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.