Summary
It is shown that the necessary parameters for an invariant description of the elastic behaviour of a transversely isotropic medium in terms of the spectral decomposition of its compliance tensor are the four eigenvalues of it and a dimensionless parameter, appropriately defined, the eigenangle ω. A study of the variational bounds imposed by thermodynamic restrictions on the values of the eigenangle ω is presented. It is further proposed that the eigenangle ω can be successfully used as a single parameter characterizing qualitatively both elasticity and toughness of transversely isotropic media.
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References
Thomson, W.: Elements of a mathematical theory of elasticity. Phil. Trans. Royal Soc.A 155, 481–498 (1956).
Rychlewski, J.: On Hooke's law. PMM48 (3), 303–314 (1984).
Olszak, W., Urbanowski, W.: The plastic potential and the generalized distortion energy in the theory of nonhomogeneous anisotropic elastic-plastic bodies. Arch. Mekh. Stos.8, 671–694 (1956).
Theocaris, P. S., Philippidis, T. P.: Spectral decomposition of compliance and stiffness fourthrank tensors suitable for orthotropic materials. ZAMM70 (10), Art. 8892 (1990).
Walpole, L. J.: Fourth-rank tensors of the thirty-two crystal classes: multiplication tables. Proc. Royal Soc.A 391, 149–179 (1984).
Walpole, L. J.: Elastic behaviour of composite materials: theoretical foundations. In: Advances in applied mechanics, vol. 21, pp. 169–242. New York: Academic Press 1981.
Lakes, R.: Foam structures with a negative Poisson's ratio. Science235, 1038–1040 (1987).
Huntington, H. B.: The elastic constants of crystals. New York: Academic Press 1958.
Knight, M.: Three-dimensional elastic moduli of graphite/epoxy composites. J. Comp. Mater.16 (3), 153–159 (1982).
Gieske, J. H., Allred, R. E.: Elastic constants of B-Al composites by ultrasonic velocity measurements. Exp. Mech.14, 158–165 (1974).
Smith, R. E.: Ultrasonic elastic constants of carbon fiber and their composites. J. Appl. Phys.43 (6), 2555–2561 (1972).
Blessing, G. V., Elban, W. L.: Aluminum matrix composite elasticity measured ultrasonically. J. Appl. Mech.48, 965–966 (1981).
Read, D. T., Ledbetter, H. M.: Elastic properties of a boron—aluminum composite at low temperatures. J. App. Phys.48 (7), 2827–2831 (1977).
Blakslee, O. L., Proctor, D. G., Seldin, E. J., Spence, G. B., Weng, T.: Elastic constants of compression-annealed pyrolytic graphite. J. Appl. Phys.41 (8), 3373–3382 (1970).
Lekhnitskii, S. G.: Anisotropic plates. Gordon and Breach 1968.
Theocaris, P. S., Philippidis, T. P.: Stress distribution in orthotropic plates with coupled elastic properties. Acta Mech.80, 95–111 (1989).
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Theocaris, P.S., Philippidis, T.P. Variational bounds on the eigenangle ω of transversely isotropic materials. Acta Mechanica 85, 13–26 (1990). https://doi.org/10.1007/BF01213539
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DOI: https://doi.org/10.1007/BF01213539