Elasticity and Inelasticity of Rubber

  • R. W. Ogden
Part of the International Centre for Mechanical Sciences book series (CISM, volume 452)


In this chapter we focus on the isothermal phenomenological theory of the elasticity and inelasticity of rubber. First, we describe experimental results that characterize the elastic behaviour of rubber, in particular of vulcanized natural rubber. This is followed by illustrations of how the behaviour departs from the purely elastic; we examine stress softening associated with the Mullins effect, and the different degrees of stress softening for different rubbers are highlighted. Other inelastic effects such as hysteretic stress-strain cycling following pre-conditioning of the material (to remove the Mullins effect) are also described.

With this background established we then begin the process of mathematical modelling of these behaviours. We describe the theory of elasticity necessary for the modelling of the elastic behaviour, and for simple homogeneous deformations we illustrate the good agreement between theory and experiment. We then move on from elasticity and discuss the modelling of stress softening and the Mullins effect. For this purpose the (quasi-static) theory of pseudo-elasticity is used since this represents a relatively simple extension of the well-established theory of elasticity and is able to capture the Mullins effect both qualitatively and quantitatively. The theory is described and then used to fit some basic data on the Mullins effect.

Finally, we examine briefly the effects of time and rate dependence and associated with viscoelastic behaviour, and some outstanding problems in the modelling of the inelastic behaviour of rubber are discussed with particular reference to viscoelasticity.


Natural Rubber Deformation Gradient Residual Strain Pure Shear Nominal Stress 
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Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

  • R. W. Ogden
    • 1
  1. 1.Department of MathematicsUniversity of GlasgowGlasgowUK

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