Spectral decomposition of the compliance fourth-rank tensor for orthotropic materials |
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Authors: | P S Theocaris D P Sokolis |
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Institution: | (1) National Academy of Athens, P.O. Box 77230 G-175 10 Athens, Greece, GR |
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Abstract: | Summary The compliance tensor related to orthotropic media is spectrally decomposed and its characteristic values are determined.
Further, its idempotent tensors are estimated, giving rise to energy orthogonal states of stress and strain, thus decomposing
the elastic potential in discrete elements. It is proven that the essential parameters, required for a complete characterisation
of the elastic properties of an orthotropic medium, are the six eigenvalues of the compliance tensor, together with a set
of three dimensionless parameters, the eigenangles θ, ϕ and ω. In addition, the intervals of variation of these eigenangles
with respect to different values of the elastic constants are presented. Furthermore, bounds on Poisson's ratios are obtained
by imposing the thermodynamical constraint on the eigenvalues to be strictly positive, as specified from the positive-definite
character of the elastic potential. Finally, the conditions are investigated under which a family of orthotropic media behaves
like a transversely isotropic or an isotropic one.
Received 5 January 1999; accepted for publication 22 June 1999 |
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Keywords: | Spectral decomposition compliance tensor orthotropic medium Euler angles elastic strain energy Poisson's ratios quasi-isotropic medium |
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