iMechanica - rubber - Comments

Paper

ChrisL — Wed, 19 Nov 2008 08:43:48 -0500

Erwan,

I would be very thankful if you could email me this paper chris.ladubec@nrc.ca

Thank you.

Elastomers and fracture

MichelleLOyen — Thu, 06 Nov 2008 11:57:10 -0500

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.

About dielectric elastomers

verron — Tue, 04 Nov 2008 03:42:09 -0500

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.

The dielectric elastomer

Jung W. Hong — Mon, 03 Nov 2008 18:07:05 -0500

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

sources of helpful information on dielectric elastomers

Zhigang Suo — Sun, 02 Nov 2008 06:35:00 -0500

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

Elastomers as electromechancial transducers

Zhigang Suo — Sat, 01 Nov 2008 20:17:00 -0400

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:

Carpi, De Rossi, Kornbluh, Pelrine, Sommer-Larsen, Dielectric elastomers as electromechanical transducers, Elsevier, 2008.
O'Halloran, O'Malley, McHigh, A review on dielectric elsatomer actuators, technology, applications, and challenges. J. Appl. Phys. 104, 071101 (2008).

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.

"I wonder if such

Nimish — Thu, 07 Aug 2008 11:39:43 -0400

"I wonder if such simulations tell me anything useful at all except when the strains are quite small. " - Biswajit

Dr. Banerjee,

My experience is that when the material model (approx. material model) for the elastomer is developed from the modulus obtained from the elastomer hardness, the results are quiet good for comparison purpose. However, in terms of the absolute values, such a material model may result in a considerable different values. E.g. I had compared the peak contact pressure developed by an o-ring at different lubricant pressures using the approx. material model & using the accurate material model developed from the stress-strain data of the elastomer. I found that the percentage increase in the peak contact pressure - due to increased lubricant pressure - obtained by the approx. material model was close to the one obtained from the accurate material model till ~1000 psi. After ~1000 psi, however, results obtained from the two material models could not be correlated.

~ Nimish.

Re: Treloar: The Physics of Rubber Elasticity

Biswajit Banerjee — Wed, 06 Aug 2008 23:22:35 -0400

Thanks Sanjay. The book is not in our company library but I've sent my spies to a nearby university to track it down and get it for me. I'll post my feedback as soon as I get my hands on the book.

Also, I have received a copy of the paper on mapping Shored hardness values to elastic moduli from one of our readers on iMechanica. I am truly grateful for that and will comment on the contents soon.

-- Biswajit

Treloar: The Physics of Rubber Elasticity

Sanjay Govindjee — Wed, 06 Aug 2008 18:34:02 -0400

Have you looked in Treloar's classic monograph The Physics of Rubber Elasticity? It is nicely explained there.

Prof. Dr. Sanjay Govindjee
University of California, Berkeley

It depends

Sanjay Govindjee — Wed, 06 Aug 2008 18:25:30 -0400

Not to sound too fuzzy but it really depends. if you are working exclusively on a certain class of materials then a company with good practices will over time have a knowledge database on the correlations of the fast easy tests to the more involved tests. The correlations will never be perfect but will give you a certain amount of confidence. If this database does not exist then it is your job (over time) to compile it. Otherwise you can not even say that your computations are even meaningful in the small strain regime.

-sanjay

Prof. Dr. Sanjay Govindjee
University of California, Berkeley

More about rubber: Negative thermal expansion?

Biswajit Banerjee — Tue, 05 Aug 2008 20:53:09 -0400

Since I'm now into rubber I won't be able to rest until I've figured out another issue that's been bothering me.

I distinctly recall being told in a materials science class that natural rubber has a negative coefficient of thermal expansion. However, a search of the literature throws up only positive values of the CTE with a few interspersed papers claiming a negative thermal expansion coefficient. There also appears to be a "thermoelastic inversion effect" which separates the positive and negative expansion regimes. A couple of papers on the effect claim that negative CTEs are observed only at strains greater than 10%.

Can anyone clear up this mess for me?

Thanks in advance.

-- Biswajit

Re: Hardness and non-metals

Biswajit Banerjee — Tue, 05 Aug 2008 18:12:50 -0400

Michelle,

As a computational mechanics/numerical modeler of materials, the major stumbling block that I've faced has been the determination of material properties - particularly, but not exclusively, for nonlinear materials. A simulation is arguably as accurate as the inputs that go into it.

One way to get properties is via ab-initio simulations and coarse-graining up in length scales. But the cost of that can be prohibitive and the accuracy depends strongly on whether the "correct" intermolecular potential has been used. The other option is to perform detailed experiments to determine properties. That's also too expensive most of the situations that I've run into in the recent past.

The lowest cost alternative is a hardness-like test which doesn't require expensive equipment and specimen preparation, and skilled operators. But such tests are barely useful when it comes to fitting good materials models.

Does that mean that computational methods of analysis are essentially useless for industrial research projects which are cash poor? Is a back of the envelope hand calculation the best we can do in such situations?

-- Biswajit

Re: The magic of hardness tests

Biswajit Banerjee — Tue, 05 Aug 2008 17:59:51 -0400

Sanjay,

In academia, during the numerical analysis of elastomeric materials, I always assumed that some stress-strain data would be available. I could then fit a model to those data and do my analysis. Academia allows for the time that's needed to do that.

Industrial research has been quite different in some respects. I now have to do numerical simulations of elastomers using data from hardness tests and rheometer traces, of plastics from supplier data on the powdered form, and so on. I wonder if such simulations tell me anything useful at all except when the strains are quite small.

-- Biswajit

"Hardness" and non-metals

MichelleLOyen — Mon, 04 Aug 2008 12:10:59 -0400

The history of the "hardness" test is an interesting one; the quantity (really the mean supported stress under contact) grew to become popular due to the Tabor relation, where in soft metals the hardness under sharp contact could be easily related to the yield stress of a material. Somehow in the intervening years, and especially in the age of nanoindentation, the fallacy has spread that hardness is a material property. It is not, but it is a measure of the total deformation under a given load and as such it does have some usefulness in many contexts outside of its primary association with plastic deformation resistance in soft metals. In fact, since the plastic deformation resistance of something like rubber is very large, but it's measured "hardness" in terms of load divided by inferred contact area is small (since it's elastic modulus is small) the ideas actually diverge if you're not careful. Only in metals is the "measured hardness" a measure of plastic deformation resistance and you could argue that this is its most useful interpretation.

We followed up Sakai's original work on hardness as a series sum of plastic and elastic deformation components, and extended the ideas to soft polymers and rubbers and also biological materials in the following two papers:

Oyen ML and Ko C-C, Examination of Local Variations in Viscous, Elastic, and Plastic Indentation Responses in Healing Bone , Journal of Materials Science: Materials in Medicine, 18 (2007) 623-8.
Oyen ML, Nanoindentation Hardness Measurements of Mineralized Tissues , Journal of Biomechanics, 39 (2006) 2699-702.

In general, the mean supported stress under contact is definitely a useful measure of mechanical properties, in terms of the total resistance to deformation under a given load (and in the case of viscoelastic or poroelastic polymers or tissues, within a given experiemental measurement time-frame) but that's all it is--a quick and dirty engineering test that gives a rough estimate of something that is not actually a material property. I am not surprised that relating it back to a specific property such as elastic modulus is not trivial, nor that nonlinear elasticity would come up in polymeric or biological materials in terms of the interpretation.

Magic? maybe

Sanjay Govindjee — Mon, 04 Aug 2008 02:31:24 -0400

Yep...in many cases yes. But if you know what you are doing, then a bit less so. -sanjay

Prof. Dr. Sanjay Govindjee
University of California, Berkeley