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Complete Set of Bounds for the Technical Moduli in 3D Anisotropic Elasticity

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Abstract

The paper addresses the problem of finding the necessary and sufficient conditions to be satisfied by the engineering moduli of an anisotropic material for the elastic energy to be positive for each state of strain or stress. The problem is solved first in the most general case of a triclinic material and then each possible case of elastic syngony is treated as a special case. The method of analysis is based upon a rather forgotten theorem of linear algebra and, in the most general case, the calculations, too much involved, are carried out using a formal computation code. New, specific bounds, concerning some of the technical constants, are also found.

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Acknowledgements

I would like to sincerely thank the anonymous reviewer who pointed out to me that the theorem used in this article is originally due to J. J. Sylvester.

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  1. LMV - Laboratoire de Mathématiques de Versailles, UMR8100, Université de Versailles et Saint Quentin, 45, Avenue des Etats-Unis, Versailles, 78035, France

    Paolo Vannucci

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  1. Paolo Vannucci
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Correspondence to Paolo Vannucci.

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Vannucci, P. Complete Set of Bounds for the Technical Moduli in 3D Anisotropic Elasticity. J Elast 156, 549–569 (2024). https://doi.org/10.1007/s10659-024-10062-z

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