Abstract
Concepts of the gradient mechanics of composites are formulated and analytical relationships proposed for the description of fields in composites. Constitutive equations are derived for fibrous composites, and the influence exerted by gradient effects on the physicomechanical characteristics and failure of materials is demonstrated in an example of problems involving longitudinal shear. Thermodynamic potentials plotted with allowance for gradient effects are presented.
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References
G. A. Vanin, “Gradient theory of the shear of multilevel composites,” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 120–127 (1995).
W. Miller, Symmetry and Separation of Variables [Russian translation], Mir, Moscow (1981).
N. Watson, Theory of Bessel Functions. Part 1 [Russian translation], Inostrennaya Literatura, Moscow (1949).
N. V. MacLaughlan, Theory and Application of Mathieu Functions [Russian translation], Inostrennaya Literatura, Moscow (1953).
G. P. Cherepanov, Brittle Fracture Mechanics [in Russian], Nauka, Moscow (1974).
G. Sih and G. Libowitz, “Mathematical Theory of brittle failure,” in: Failure [Russian translation], Vol. 2, Mir, Moscow (1975), pp. 83–203.
G. Pluvinash, Mechanics of Elastoplastic Failure [Russian translation], Mir, Moscow (1993).
G. A. Vanin, Micromechanics of Composite Materials [in Russian], Naukova Dumka, Kiev (1985).
Yu. I. Sirotin and M. P. Shaskol'skaya, Fundamentals of Crystal Physics [in Russian], Nauka, Moscow (1975).
I. I. Gol'denblat, Nonlinear Problems of Elasticity Theory [in Russian], Nauka, Moscow (1969).
Additional information
A. A. Blagonravov Machine-Science Institute, Russian Academy of Sciences, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 3–20, January–February, 1996.
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Vanin, G.A. Gradient mechanics and thermodynamics of multilevel composites 1. Longitudinal shear and related problems. Mech Compos Mater 32, 1–13 (1996). https://doi.org/10.1007/BF02254642
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DOI: https://doi.org/10.1007/BF02254642