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On the representation theorem for linear, isotropic tensor functions

โœ Scribed by K. A. Pericak-Spector; Scott J. Spector

Publisher
Springer Netherlands
Year
1995
Tongue
English
Weight
203 KB
Volume
39
Category
Article
ISSN
0374-3535

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โœฆ Synopsis

The well-know representation theorem for the elasticity tensor C of an isotropic body shows that

for all symmetric tensors E, where tr(E) denotes the trace of E and I is the identity tensor. This theorem is actually a special case of a classical result (cf. e.g. [Je 31, Chapter 7]) on linear, tensor-valued mappings that are isotropic, i.e. C[QHQ T] = QC[HjQ T for all tensors H in the domain of C and all orthogonal tensors Q, where Q~ denotes the transpose of Q.

๐Ÿ“œ SIMILAR VOLUMES

The representation theorem for isotropic
The representation theorem for isotropic, linear asymmetric stress-strain relations
โœ Zhong-Heng Guo ๐Ÿ“‚ Article ๐Ÿ“… 1983 ๐Ÿ› Springer Netherlands ๐ŸŒ English โš– 150 KB

asymmetric In 1974, Gurtin [1] gave an elegant proof of the representation theorem for isotropic, linear stress-strain relations, considerably improving the one supplied by the same author in [2]. We cite this theorem literally as follows (notations will be explained subsequently):