The theory of structural models of longitudinal shear for orthotropic UD composites is developed. Alternative simplifying hypotheses for symmetric composites are formulated. General formulas for the shear moduli of kinematically and statically consistent models are obtained. It is proved that they give the lower and upper bounds of the exact value and lie within the Reuss–Voigt interval. The rule of boundary duality is formulated. New formulas for the special cases of binary composites are obtained. A comparison between the bounds found and the Hashin–Hill bounds is made for a transtropic material in the space of two variables (fiber volume fraction and the relative stiffness). The results are ambiguous: both lower and upper bounds intersect.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 48, No. 3, pp. 381-400, May-June, 2012.
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Fedorov, V.A. Structural models of the longitudinal shear of UD composites with a symmetric structure. Mech Compos Mater 48, 259–272 (2012). https://doi.org/10.1007/s11029-012-9273-7
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DOI: https://doi.org/10.1007/s11029-012-9273-7