Abstract
It is often declared in the literature that the seven classical invariants used to characterize the strain energy of a compressible orthotropic elastic solid are independent. In this paper, we show that only six of the seven classical invariants are independent, and a syzygy exists between the classical invariants. Consequently, all other sets of seven invariants, proposed in the literature, that are uniquely related to the set of classical invariants, have only six independent invariants.
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Spencer, A.J.M.: Constitutive theory for strongly anisotropic solids. In: Spencer, A.J.M. (ed.) Continuum Theory of the Mechanics of Fiber Reinforced Composites. CISM Courses and Lectures, vol. 282, pp. 1–32. Springer, Wien (1984)
Holzapfel, G.A., Ogden, R.W.: Constitutive modeling of passive myocardium: a structurally based framework of material characterization. Philos. Trans. R. Soc. A 367, 3445–3475 (2009)
Merodio, J., Ogden, R.W.: The influence of the invariant I8 on the stress-deformation and ellipticity characteristics of doubly fiber-reinforced non-linearly elastic solids. Int. J. Non-Linear Mech. 41, 556–563 (2006)
Shariff, M.H.B.M.: Physical invariants for nonlinear orthotropic solids. Int. J. Solids Struct. 48, 1906–1914 (2011)
Rubin, M.B., Jabareen, M.: Physically based invariants for nonlinear elastic orthotropic solids. J. Elast. 90, 1–18 (2008)
Spencer, A.J.M.: Theory of invariants. In: Eringen, A.C. (ed.) Continuum Physics I (Part III). Academic Press, New York (1971)
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Shariff, M.H.B.M. Nonlinear Orthotropic Elasticity: Only Six Invariants are Independent. J Elast 110, 237–241 (2013). https://doi.org/10.1007/s10659-012-9389-y
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DOI: https://doi.org/10.1007/s10659-012-9389-y