Summary
In this work, the finite extension and torsion of a swollen elastic cylinder bonded to an inner rigid cylindrical core are investigated in the context of the theory of interacting continua. The boundary value problem is solved numerically in order to determine the variation of the stretch-ratios, the stresses and also the volume fraction of the solid. The results of these investigations not only demonstrate significant gradients in the stretch ratios and severe stress concentrations but also stress reversals under certain conditions. These stress reversals which occur in the neighborhood of the interface of the inner and outer cylinders can have a significant impact on damage studies pertaining to fiber/matrix debonding in fiber-reinforced composites, for example.
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Shi, J. J., Wineman, A. S., Rajagopal, K. R.: Applications of the theory of interacting continua to the diffusion of a fluid through a nonlinear elastic medium. Int. J. Eng. Sci.9, 871–889 (1981).
Gandhi, M. V., Rajagopal, K. R., Wineman, A. S.: A universal relation in torsion for a mixture of Solid and fluid. J. Elasticity15, 155–165 (1985).
Rajagopal, K. R., Wineman, A. S., Gandhi, M. V.: On boundary conditions for a certain class of problems in mixture theory. Int. J. Eng. Sci.24, 1453–1463 (1986).
Gandhi, M. V., Rajagopal, K. R., Wineman, A. S.: Some nonlinear diffusion problems within the context of the theory of interacting continua. Int. J. Eng. Sci.25, 1441–1457 (1987).
Gandhi, M. V., Usman, M.: Equilibrium characterization of fluid-saturated continua and an interpretation of the saturation boundary condition assumption for solid-fluid mixtures. Int. J. Eng. Sci.27, 539–548 (1989).
Gandhi, M. V., Usman, M.: Exact solutions for the uniaxial extension of a mixture slab. Arch. Mech.40, 275–286 (1988).
Gandhi, M. V., Usman, M.: The flexure problem in the context of the theory of interacting continua. SES Paper No. ESP 24.87016, presented at the 24th Annual Technical Meeting of the Society of Engineering Science, Salt Lake City, Utah, September 1987.
Gandhi, M. V., Usman, M.: On the non-homogeneous finite swelling of a non-linearly elastic cylinder with a rigid core. Int. J. Non-linear Mech.24, 251–261 (1989).
Treloar, L. R. G.: Swelling of a rubber cylinder in torsion. Part 1. Theory. Polymer13, 195–202 (1972).
Gandhi, M. V., Usman, M., Wineman, A. S., Rajagopal, K. R.: Combined extension and torsion of a swollen cylinder within the context of mixture theory. Acta Mech.79, 81–95 (1989).
Atkin, R. J., Craine, R. E.: Continuum theories of mixtures: basic theory and historical development. Q. J. Mech. Appl. Math.29, 209–244 (1976).
Bowen, R. M.: Continuum physics (Eringen, A. C., ed.), Vol. 3. New York: Academic Press 1975.
Green, A. E., Naghdi, P. M.: On basic equations for mixtures. Q. J. Mech. Appl. Math.22, 427–438 (1969).
Mills, N.: Incompressible mixtures of Newtonian fluids. Int. J. Eng. Sci.4, 97–112 (1966).
Treloar, L. R. G.: The physics of rubber elasticity. Oxford: Clarendon Press 1975.
Loke, K. M., Dickinson, M., Treloar, L. R. G.: Swelling of a rubber cylinder in torsion. Part 2. Experimental. Polymer13, 203–207 (1972).
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Gandhi, M.V., Kasiviswanathan, S.R. & Usman, M. Finite extension and torsion of a cylindrical solid-fluid mixture featuring a rigid core. Acta Mechanica 103, 177–190 (1994). https://doi.org/10.1007/BF01180225
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DOI: https://doi.org/10.1007/BF01180225