Technical Papers
Jun 3, 2024

Analysis of the Mechanical and Mathematical Properties of the Tensors of Coupled Thermoelastic Isotropic Laminates by the Polar Method

Publication: Journal of Engineering Mechanics
Volume 150, Issue 8

Abstract

We consider in this paper the general properties of laminates designed to be isotropic in extension and in bending and with a coupling between the in- and out-of-plane responses. In particular, we analyze the mathematical properties of the tensors describing the elastic and thermal behavior and the mechanical consequences of these properties. The polar formalism for planar tensors is used in this study. By this approach, it is easy to put in light some interesting, qualitative, mechanical, and mathematical facts concerning coupled isotropic laminates and to appreciate the fundamental differences, from the mathematical and mechanical point of view, between hybrid laminates, i.e., composed by layers of different materials, and laminates made of identical plies.

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No data, models, or code were generated or used during the study.

References

Benvenuto, E. 1991. Vol. 2 of An introduction to the history of structural mechanics. Berlin: Springer.
Dugas, R. 1950. Histoire de la mécanique. Neuchâtel, Switzerland: Editions du Griffon.
Fukunaga, H. 1990. “On isotropic laminate configurations.” J. Compos. Mater. 24 (5): 519–535. https://doi.org/10.1177/002199839002400504.
Gay, D. 2014. Composite materials design and applications—Third edition. Boca Raton, FL: CRC Press.
Grédiac, M. 1999. “A procedure for designing laminated plates with required stiffness properties. Application to thin quasi-isotropic quasi-homogeneous uncoupled laminates.” J. Compos. Mater. 33 (20): 1939–1956. https://doi.org/10.1177/002199839903302005.
Jones, R. M. 1999. Mechanics of composite materials. 2nd ed. Philadelphia: Taylor & Francis.
Love, A. E. H. 1944. A treatise on the mathematical theory of elasticity. Cambridge, UK: Cambridge University Press.
Paradies, R. 1996. “Designing quasi-isotropic laminates with respect to bending.” Compos. Sci. Technol. 56 (4): 461–472. https://doi.org/10.1016/0266-3538(96)00006-1.
Pressley, A. 2010. Elementary differential geometry. Berlin: Springer.
Stackgold, I. 1950. “The Cauchy relations in a molecular theory of elasticity.” Q. Appl. Math. 8 (2): 169–186.
Thomson, W. 1856. “Elements of a mathematical theory of elasticity.” Philos. Trans. R. Soc. 146 (Dec): 481–498. https://doi.org/10.1098/rstl.1856.0022.
Thomson, W. 1878. “Mathematical theory of elasticity.” Encyclopedia Britannica 7: 819–825.
Todhunter, I., and K. Pearson. 1886. History of the theory of elasticity, vol. 1. Cambridge, UK: Cambridge University Press.
Toponogov, V. A. 2006. Differential geometry of curves and surfaces—A concise guide. Boston: Birkhäuser.
Tsai, S. W., and T. Hahn. 1980. Introduction to composite materials. Stamford, CT: Technomic.
Vannucci, P. 2013. “General theory of coupled thermally stable anisotropic laminates.” J. Elast. 113 (Oct): 147–166. https://doi.org/10.1007/s10659-012-9415-0.
Vannucci, P. 2018. Anisotropic elasticity. Berlin: Springer.
Vannucci, P. 2023. “On the mechanical and mathematical properties of the stiffness and compliance coupling tensors of composite anisotropic laminates.” J. Compos. Mater. 57 (26): 4197–4214. https://doi.org/10.1177/00219983231206600.
Vannucci, P. 2024. “On the thermoelastic coupling of anisotropic laminates.” Arch. Appl. Mech. 94 (Mar): 1121–1149. https://doi.org/10.1007/s00419-024-02572-y.
Vannucci, P., and G. Verchery. 2002. “A new method for generating fully isotropic laminates.” Compos. Struct. 58 (1): 75–82. https://doi.org/10.1016/S0263-8223(02)00038-7.
Vasiliev, V. V., and E. V. Morozov. 2001. Mechanics and analysis of composite materials. New York: Elsevier.
Verchery, G. 1982. “Les invariants des tenseurs d’ordre 4 du type de l’élasticité.” In Proc., Colloque Euromech 115 (Villard-de-Lans, 1979): Comportement mécanique des matériaux anisotropes, 93–104. Paris, Editions du CNRS.
Werren, F., and C. B. Norris. 1953. Mechanical properties of a laminate designed to be isotropic. Madison, WI: US Forest Products Laboratory.
Wu, K. M. 1979. Isotropic composite plates. Warren, MI: General Motors Research Laboratories.
Wu, K. M., and B. L. Avery. 1992. “Fully isotropic laminates and quasi-homogeneous laminates.” J. Compos. Mater. 26 (14): 2107–2117. https://doi.org/10.1177/002199839202601406.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 150Issue 8August 2024

History

Received: Sep 30, 2023
Accepted: Apr 17, 2024
Published online: Jun 3, 2024
Published in print: Aug 1, 2024
Discussion open until: Nov 3, 2024

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Full Professor of Mechanics, Laboratoire de Mathématiques de Versailles, Université de Versailles et Saint Quentin, UMR8100, Versailles 78000, France. ORCID: https://orcid.org/0000-0002-3891-2043. Email: [email protected]

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