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Journal Club Theme of Nov. 1 2008: Mechanical behaviour of rubber-like materials

ErwanVerron's picture

Rubber-like material is the generic term to define quasi-linear solid polymers. It encompasses elastomers (natural such as Natural Rubber (NR), and synthetic such as Styrene Butadiene Rubber (SBR), but also other large strain elastic materials such as heat-softened thermoplastics (especially for blow-molding simulation) , but also for biological materials such as muscles, tendons, blood vessel (see for example this book).

The key point to understand their behaviour is the nature of elasticity involved in these materials: the elasticity is mainly entropic. Then it is classically referred to as “Entropic elasticity” and “Rubber elasticity ” and the constitutive equations are derived from the general framework of large strain hyperelasticity (usually these materials are considered homogeneous, isotropic, incompressible and elastic). Nevertheless, the mechanical response of these materials and especially Natural Rubber is highly more complicated: they exhibit stress-softening, long-term viscoelasticity, initial or induced anisotropy, hysteresis, volume change, ...

This Journal Club will be divided into two parts:


Part 1: review of classical results

This first part focuses on the classical constitutive equations used for these materials. I propose you a short review of the complex behaviour of Natural Rubber and some bibliographical references for modelling in the attached file Rubber_stateoftheart_journalclub.pdf and also a quantitative comparison and ranking of 20 hyperelastic models previously posted in Imechanica (link).

Considering these studies, we can discuss about the relevance of the constitutive equations, and about what should be expected from them in design.


Part 2: hot topics

In this second part, I choose to highlight three topics which could be investigated by mechanicians.

The first one is an engineering problem: the prediction of fatigue life of elastomers. It is of major importance in automotive industry for example, because actual simulation tools satisfactorily predict stress and strain histories of rubber parts under service loading conditions, but the use of these results to estimate the fatigue life of components remains a critical issue. The following paper proposes a complete review of this problem, highlighting the two main approaches: the fatigue crack propagation problem (considered for tyres) and the fatigue crack nucleation problem (considered for anti-vibration systems such as engine and exhaust mounts).

Mars, W.V., Fatemi, A., A literature survey on fatigue analysis approaches for rubber. Int. J. Fatigue, 24, 949–961, 2002.


The second topic concerns crack propagation and more especially its physical nature. Even if fracture mechanics was successfully applied to rubber-like materials, some special phenomena are not well-understood. I propose you to discuss a recent paper in which authors conducted experiments in order to explain the transition from a straight to a wavy crack and to characterize the corresponding instability.

Deegan, R.D., Petersan, P., Marder, M., and Swinney, H.L., Oscillating fracture paths in rubber, Phys. Rev. Lett., 88, 14304, 2002. Number of papers about this subject can be found at link .


The third topic is devoted to Natural Rubber and especially to the phenomenon of strain-induced crystallization. More precisely, the two following papers give the results of real-time measurement of crystallization and melting during uniaxial loading cycles. Experiments were conducted using WAXS measurement. The hysteretic response of NR is directly related to this phenomenon and both authors propose physical theories to explain it. I believe that this strain-induced phase transformation problem can lead to interesting constitutive equations.

Toki, S., Fujimaki, T., and Okuyama, M., Strain-induced crystallization of natural rubber as detected real-time by wide-angle X-ray diffraction technique, Polymer, 41, 5423-5429, 2000.

Trabelsi, S., Albouy, P.-A., and Rault, J., Crystallization and melting processes in vulcanized stretched Natural Rubber, Macromolecules, 36, 7624 - 7639, 2003.

PDF icon Rubber_stateoftheart_journalclub.pdf452.75 KB
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Zhigang Suo's picture

Dear Erwan:  Thank you so much for this very, very informative post.  I have read your pdf file, which consists of a collection of experimentally determined stress-strain curves, and a compilation of the literature on the mechanical behavior of elastomers.  I'm urging my students to study your review. 

My group has been studying the emerging application of elastomers as electromechanical transducers. Here are two recent reviews of this application:

In this application, rupture and fatigue are both of great concern.  Also of great challenge is to model nonlinear deformation under combined mechanical and electrical loads.  Your theme of the jClub will be of great value to us.   

Zhigang Suo's picture

I should have also listed two other sources of helpful information on dielectric elastomers:

Jung W. Hong's picture

The dielectric elastomer might be also very useful for energy harvesting circuits since it does not have fatigure cracks.


ErwanVerron's picture

Thanks for these comments.

It seems that dielectric elastomers and their applications are a new important field of research. Once the physical principles being established and some applications developped, I am sure that engineering investigations will be (or already are) necessary: design tools, fatigue life, maybe fracture mechanics, ... 

For all these problems, there already exists a large bibliography devoted to rubber mechanics: number of problems have been investigated in the past (since the mid 50s). Moreover, more complex studies are in progress (homogeneization techniques, thermo-mechanical modelling) in the community of rubber researchers. Similarly, but I am not sure it is relevant to these applications, number of works have been published on the problem of large deformation of membranes (for rubber, for molding).

Obviously, both communities should work together and bridges have to be build between researchers in these fields.

MichelleLOyen's picture

You make an excellent point about the importance of, but relative lack of current understanding, considerations of fracture mechanics in soft, extensible materials.  I first became interested in this problem in the context of injury but there are many areas in which a better understanding of fracture processes, both qualitatively and quantitatively, would be useful in both medicine and engineering.  We sometimes find a useful paper in the textiles industry, since many soft tissues resemble fabrics with strong covalent bonds along the fiber but weak interactions between the fiber.  In that context we're interested in how the failure of individual fibrils or even individual covalent bonds could relate to failure of the tissue at a macroscopic scale.  Thanks for the link to papers on this interesting subject.

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