Criterion for the strong ellipticity of the equations of motion of an anisotropic linear-elastic material

Two methods of verifying the strong ellipticity of the equations of motion (the SE-condition) for an arbitrary anisotropic linear-elastic material are proposed. A mechanical interpretation of a number of the corollaries of the SE-condition is given. Effective sufficient criteria for the realizabilit...

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Bibliographic Details
Published in:Journal of applied mathematics and mechanics 2016-01, Vol.80 (6), p.485-509
Main Authors: Zubov, L.M., Rudev, A.N.
Format: Article
Language:English
Subjects:
Criteria
Elastic anisotropy
Ellipticity
Equations of motion
Equilibrium
Equilibrium equations
Materials elasticity
Mathematical analysis
Realizability
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Summary:Two methods of verifying the strong ellipticity of the equations of motion (the SE-condition) for an arbitrary anisotropic linear-elastic material are proposed. A mechanical interpretation of a number of the corollaries of the SE-condition is given. Effective sufficient criteria for the realizability of the SE-condition and the weak version of it, the so-called Hadamard inequality, are found for materials of the monoclinic and 6-constant hexagonal systems. The case of a two-dimensional space is considered. Finite sets of elementary inequalities that are equivalent to the SE-condition and the Hadamard inequality are presented for materials of a 7-constant tetragonal system as well as a simple sufficient criterion for the ellipticity of the equilibrium equations of a uniform medium. Numerical examples are analysed and a comparison of the different methods of verifying the SE-condition is presented.
ISSN:0021-8928
0021-8928
1873-4855
DOI:10.1016/j.jappmathmech.2017.06.007