Artigo Revisado por pares

On isotropic tensors

1973; Cambridge University Press; Volume: 73; Issue: 1 Linguagem: Inglês

10.1017/s0305004100047587

ISSN

1469-8064

Autores

Harold Jeffreys,

Tópico(s)

Elasticity and Material Modeling

Resumo

1. An isotropic tensor is one the values of whose components are unaltered by any rotation of rectangular axes (with metric σ i ( dx i ) 2 ). Those up to order 4 in 2 and 3 dimensions have many applications. The results suggest a general theorem for tensors of order m in n dimensions, that any isotropic tensor can be expressed as a linear combination of products of δ and є tensors, where δ ij = 1 if i = j and 0 otherwise, and is 0 if any two of the i 1 to i n are equal, 1 if i 1 … i n is an even permutation of 1, 2, 3, …, n , and – 1 if it is an odd permutation.

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