Summary
The problem of a cylindrical mixture of a nonlinearly elastic solid and an ideal fluid subjected to combined finite axial extension and torsion is considered. In previous work, a ‘universal relation’ has been presented by assuming a small angle of twist. In this work, the general problem for the finite deformation of the swollen cylinder is discussed in the context of Mixture Theory. Computational results for the variation of the radial and tangential stretch ratios and the distribution of the fluid in the swollen deformed state are presented. The results demonstrate that the swollen volume of a cylinder reduces with twisting when the axial stretch ratio is held constant. Computational results for the reduction in the swollen volume predict the same qualitative and quantitative trends as observed in experimental results.
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References
Gandhi, M. V., Rajagopal, K. R., Wineman, A. S.: A universal relation in torsion for a mixture of solid and fluid. Journal of Elasticity15 (2), 155–166 (1985).
Atkin, R. J., Craine, R. E.: Continuum theories of mixtures: basic theory and historica development. Q. J. Mech. Appl. Math.29 (2), 209–244 (1976).
Bowen, R. M.: Continuum physics (Eringen, A. C., ed.), Vol.3. New York: Academic Press 1975.
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. Engng. Sci.9, 871–889 (1981).
Rajagopal, K. R., Wineman, A. S., Gandhi, M. V.: On boundary conditions for a certain class of problems in mixture theory. Int. J. Engng. Sci.24 (8), 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. Engng. Sci.25 (11/12), 1441–1457 (1987).
Gandhi, M. V., Usman, M.: Exact solutions for the uniaxial extension of a mixture slab. Archives of Mechanics40 (2), 271–282 (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 a the 24th Annual Technical Meeting of the Society of Engng. Sci., Salt Lake City, Utah, September 1987.
Treloar, L. R. G.: Swelling of a rubber cylinder in torsion: part 1. Theory. Polymer13, 195–202 (1972).
Green, A. E., Naghdi, P. M.: On basic equations for mixtures. Q. J. Mech. Appl. Math.22 (4), 427–438 (1969).
Mills, N.: Incompressible mixtures of Newtonian fluids. Int. J. Engng. Sci.4, 97–112 (1966).
Treloar, L. R. G.: The physics of rubber elasticity, 3rd ed. London: Oxford University 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).
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. Engng. Sci. In press, (1989).
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Gandhi, M.V., Usman, M., Wineman, A.S. et al. Combined extension and torsion of a swollen cylinder within the context of mixture theory. Acta Mechanica 79, 81–95 (1989). https://doi.org/10.1007/BF01181481
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DOI: https://doi.org/10.1007/BF01181481