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The constitutive tensor of linear elasticity: Its decompositions, Cauchy relations, null Lagrangians, and wave propagation
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10.1063/1.4801859
/content/aip/journal/jmp/54/4/10.1063/1.4801859
http://aip.metastore.ingenta.com/content/aip/journal/jmp/54/4/10.1063/1.4801859
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

A tensor T ijkl of rank 4 in three-dimensional (3d) space has 34 = 81 independent components. The 3 dimensions of our image represent this 81d space. The plane depicts the 21-dimensional subspace of all possible elasticity (or stiffness) tensors. This space is span by its irreducible pieces, the 15d space of the totally symmetric elasticity S (a straight line) and the 6d space of the difference (also depicted, we are sad to say, as a straight line). Oblique to is the 21d space of the reducible M-tensor and the 6d space of the reducible N-tensor. The “plane” is the only place where elasticities (stiffnesses) are at home. The spaces and N represent only elasticities, provided the Cauchy relations are fulfilled. Then, A = N = 0 and and cut in the 15d space of S. Notice that the spaces M and C are intersecting exactly on S.

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/content/aip/journal/jmp/54/4/10.1063/1.4801859
2013-04-29
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The constitutive tensor of linear elasticity: Its decompositions, Cauchy relations, null Lagrangians, and wave propagation
http://aip.metastore.ingenta.com/content/aip/journal/jmp/54/4/10.1063/1.4801859
10.1063/1.4801859
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