Abstract
The antiplane elastic deformation of a homogeneous isotropic prestretched cylindrical body is studied in a nonlinear formulation in actual–state variables under incompressibility conditions, the absence of volume forces, and under constant lateral loading along the generatrix. The boundary–value problem of axial displacement is obtained in Cartesian and complex variables and sufficient ellipticity conditions for this problem are indicated in terms of the elastic potential. The similarity to a plane vortex–free gas flow is established. The problem is solved for Mooney and Rivlin—Sonders materials simulating strong elastic deformations of rubber–like materials. Axisymmetric solutions are considered.
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REFERENCES
Yu. N. Rabotnov, Mechanics of a Deformable Solid [in Russian], Nauka, Moscow (1988).
A. I. Lur'e, Nonlinear Theory of Elasticity [in Russian], Nauka, Moscow (1980).
Z. N. Litvinova, “Mechanism of fracture of a nonlinearly elastic cracked body in antiplane deformation,” Dokl. Akad. Nauk SSSR, 272, No. 6, 1344-1347 (1983).
J. K. Knowles, “On finite anti-plane shear for incompressible elastic materials,” J. Austral. Math. Soc., Ser. B, 19, Part 4, 400-415 (1976).
F. D. Murnaghan, “Finite deformations of an elastic solid,” Am. J. Math., 59, No. 2, 235-260 (1939).
L. I. Sedov, Introduction to Continuum Mechanics [in Russian], Fizmatgiz, Moscow (1962).
I. G. Petrovskii, Lectures on Partial Differential Equations [in Russian], Fizmatgiz, Moscow (1961).
V. D. Bondar', “Finite plane deformations of an incompressible elastic material,” Prikl. Mekh. Tekh. Fiz., No. 2, 155-164 (1990).
S. I. Pai, Introduction to the Theory of Compressible Flow, Van Nostrand, New York (1960).
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York (1961).
M. L. Smolyanskii, Tables of Indefinite Integrals [in Russian], Fizmatgiz, Moscow (1963).
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Bondar', V.D. Nonlinear Antiplane Deformation of an Elastic Body. Journal of Applied Mechanics and Technical Physics 42, 337–344 (2001). https://doi.org/10.1023/A:1018848524294
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DOI: https://doi.org/10.1023/A:1018848524294