ISSN:
1432-0681
Keywords:
Key words Spectral decomposition
;
compliance tensor
;
orthotropic medium
;
Euler angles
;
elastic strain energy
;
Poisson's ratios
;
quasi-isotropic medium
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s004199900066
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