Deformation and stability of compressible rubber O-rings

ADINA (2008) Structures-modeling and theory guide 3.8, pp. 339–341

Ali, A., Housseini, M., & Sahari, B. B. (2010). A review of constitutive models for rubber-like materials. American Joyrnal of Engineering and Applied Science, 3(1), 232–239.

ANSYS, Inc. (2004) Theory Reference, ANSYS 9.0

Arruda, E. M., & Boyce, M. C. (1993). A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. Journal of the Mechanics and Physics of Solids, 41(2), 389–412.

Atluri, S. N., & Cazzani, A. (1995). Rotations in computational solid mechanics. Archives of Computational Methods in Engineering, 2(1), 49–138.

Benham, C. J. (1983). Geometry and mechanics of DNA superhelicity. Biopolymers, 22, 2477–2495.

Bonet, J., & Wood, R. D. (1997). Nonlinear mechanics for finite element analysis. Cambridge: Cambridge University Press.

Cassenti, B., & Staroselsky, A. (2000). Strength and Stability of Rubber O-Ring Seals. In K. Grassie, E. Teuchkholl, G. Wegner, J. Hauser, & H. Hanselka (Eds.), Functional Materials, 13. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA. doi: 10.1002/3527607420.ch56 .

Chadwick, P., & Ogden, R. W. (1971). On the definition of elastic moduli. Archive for Rational Mechanics and Analysis, 44, 41–53.

Destrade, M., Gilchrist, M. D., Motherway, J., & Murphy, J. G. (2012). Slight compressibility and sensitivity to changes in Poisson’s ratio. International Journal for Numerical Methods in Engineering, 90(4), 403–411.

Dolbow, J., & Belytschko, T. (1999). Volumetric locking in the element free Galerkin method. International Journal for Numerical Methods in Engineering, 46(6), 925–942.

Duffet, G., & Reddy, B. D. (1986). The solution of multi-parameter system of equations with application to problems in nonlinear elasticity. Computer Methods in Applied Mechanics and Engineering, 59, 179–213.

Gent, A. N. (2005). Elastic instabilities in rubber. International Journal of Non-Linear Mechanics, 40(2–3), 165–175.

Gent, A. N., Suh, J. B., & Kelly, S. G., III. (2007). Mechanics of rubber shear springs. International Journal of Non-Linear Mechanics, 42, 241–249.

Ghaemi, H., Behdinan, K., & Spence, A. (2006). On the development of compressible pseudo-strain energy density function for elastomers Part 1. Theory and experiment. Journal of Materials Processing Technology, 178, 307–316.

Goriely, A. (2006). Twisted rings and the rediscoveries of Michell’s instability. Journal of Elasticity, 84, 281–299.

Gurvich, M., & Fleischman, T. S. (2003). A simple approach to characterize finite compressibility of elastomers. Rubber Chemistry and Technology, 76, 912–922.

Kamiński, M., & Lauke, B. (2013). Parameter Sensitivity and Probabilistic Analysis of the Elastic Homogenized Properties for Rubber Filled Polymers. CMES, 93(6), 411–440.

MARC (2005) MARC reference Library: Volume A User Information, MARC Analysis Research Corporation

Ogden, R. W. (1972). Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society of London A, 326, 565–584.

Pantuso, D., & Bathe, K.-J. (1997). On the stability of mixed finite elements in large strain analysis of incompressible solids. Finite Elements in Analysis and Design, 28, 83–104.

Reed, K. W., & Atluri, S. N. (1983) On the generalization of certain rate-type constitutive equations for very large strains. In C. S. Desai, & R. H. Gallagher (Eds.), Constitutive laws for engineering materials, theory and application (pp. 71–75). College of Engineering, Department of Civil Engineering Mechanics, University of Arizona, Tucson

Reese, S., & Wriggers, P. (1995). A finite element method for stability problems in finite elasticity. International Journal for Numerical Methods in Engineering, 38, 1171–1200.

Ritcher, B. (2016). http://www.o-ring-prueflabor.de/en/home/ .

Simo, J. C., & Taylor, R. L. (1991). Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms. Computer Methods in Applied Mechanics and Engineering, 85, 273–310.

Sussman, T., & Bathe, K.-J. (1987). A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Computers & Structures, 26, 357–409.

Tabiei, A., & Khambati, S. (2015). A 3-D visco-hyperelastic constitutive model for rubber with damage for finite element simulation. CMES, 105(1), 25–45.

Treloar, L. R. G. (1975). The Physics of Rubber Elasticity. Oxford: Clarendon Press.

Zéhil, G.-P., & Gavin, H. P. (2013). Unified constitutive modeling of rubber-like materials under diverse loading conditions. International Journal of Engineering Science, 62, 90–105.