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  • 1
    Electronic Resource
    Electronic Resource
    Spectral decomposition of the compliance fourth-rank tensor for orthotropic materials (2000)
    Springer
    Archive of applied mechanics 70 (2000), S. 289-306 
    Details
    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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  • 2
    Electronic Resource
    Electronic Resource
    Sorting out the elastic anisotropy of transversely isotropic materials (2000)
    Springer
    Acta mechanica 143 (2000), S. 129-140 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary By means of the spectral decomposition of the complianceS and stiffnessC tensors for transversely isotropic materials, the elastic loading eigenstates of these anisotropic materials are defined in a simple and efficient manner. It was shown that the necessary parameters for an invariant description of the elastic behavior of transversely isotropic materials are the four eigenvalues, complemented by the eigenangle ω. However, restrictions are imposed on the variational bounds of this parameter, based on the classical thermodynamical requirement for positive definite strain energy density. It is the purpose of this paper to study the influence of the imposed thermodynamic restrictions, along the spectrum of variation of the eigenangle ω, on the type and properties of the corresponding elastic bodies, and describe the limits imposed by the respective values of ω on the elastic properties of anisotropic materials. Based on this study, transversely isotropic media are categorized systematically into four classes, depending on the value of their eigenangle ω, which is sufficient for a monoparametric qualitative characterization of both their elastic properties and their respective toughness.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01170943
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    Paper (German National Licenses)
    Fulltext
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