# Why Rubber is incompressible?

Dear All,

Why rubber and like soft materials are incompressible? I do not want any
explanation in formula like, volumetric strain is zero or poissons
ratio is 0.5 etc. Physically whats happening when we apply compressive
load? For example take a gas, when you compress, the density will
change. Is there any of the properties are changing?

Thank you,

Muthu Kumar M

### Re: Why is rubber incompressible

The answer to your question is quite involved and difficult to provide
without the help of statistical mechanics and thermodynamics, all of
which require some formulae.   The basic idea is that entropic effects
dominate in rubber-like materials relative to internal energy and that
causes the volume change during deformation to be quite small under certain circumtances. A similar question is "why is water incompressible?"

Your question can be rephrased as "why is the equilibrium volumetric strain zero in rubber-like materials at small strains?"  The first step in exploring this question is to find some experimental data that proves that statement.  Do you have any?  In fact, rubber can be compressed significantly if you apply a sufficiently high hydrostatic pressure.

To understand the physics of rubbers, the best place to start is

The physics of rubber elasticity by  L. R. G. Treloar.

A nice paper that addresses part of the subject is

Simple presentation of network theory of rubber, with a discussion of other theories by Hubert M. James, Eugene Guth

Journal of Polymer Science, Volume 4, Issue 2, pages 153–182, April 1949.

-- Biswajit

### Re: Why is rubber incompressible

Dear Biswajit,

I am not afraid of mathematics, my point is that people may use the formula from the solid mechanics and conclude with that. I do not want that point of view as I mentioned in my question. You are most welcome with mathematics to explain. In your answer, "why is the equilibrium volumetric strain zero in rubber-like materials at small strains?"  Is it only for small strains? I don’t think so. During my masters, I worked on hydrogel (above 90% of water) material which is highly nonlinear elastic (hyperelastic). With my experimental results I confirmed the incompressibility.

Muthu Kumar M

### Hydrogels == rubbers? or Why is rubber incompressible?

I think Zhigang, Grant, and Ajit's answers to your other post are the easiest to understand.  However, there are several questions that require some thought to resolve.  For instance, if we consider a cubic RVE with polymer chains along the edges and cross-links/hard segments at the nodes, we should be easily able to change the volume by applying hydrostatic tension/compression.  We don't see that volume change in uniaxial or biaxial tests because both tests involve more shear distortion than volumetric distortion (and a lot of relaxation).

Most of the polymer chain physics based models of elastomer elasticity start with the assumption  of incompressibility. The second paper that I listed does not and is worth reading.

For hydrogels, if the rate of loading is slow enough, you may get water-like behavior even at large strains ( I'm not very familiar with hydrogels).  That's not true of some of the elastomers (e.g. estane+plasticizers) I've looked at where the relaxation time is quite large and significant volume changes can be observed at large strains.

-- Biswajit

### Compressibility and incompressibility of hydrogels

People interersted in this discussion should also look at another thread of the same topic, also initiated by Muthu Kumar.

In recent years, we have studied hydrogels extensively, both theoretically and experimentnally.  We have mostly worked on a particular type of hydrogels:  a network of polymers swollen with water.  Fig. 1 in the following paper will make the discussion easier.

The polymer chains are crosslinked with covalent bonds, while water molecules and polymers interact with weak bonds.  Consequently, a hydrogel has the attributes of both a solid and a liquid.  The network of polymers provides elasticity, and weak bonds allow water molecules to migrate.

As illustrated in Fig. 1 in the above paper, the hydrogel may both change shape and volume. For the polymer chains to deform, water molecules in the gel must change neighbors, a process that is thermally activated, of the same kind as that in a liquid. Fig. 1 sketches two modes of deformation. The first mode results from local rearrangement of molecules, allowing the gel to change shape but not volume. This mode of deformation occurs over a time scale that is independent of the size of the sample. The local rearrangement is of the same kind as rearranging polymer chains during large deformation of a dry elastomer, a process that gives rise to viscoelasticity. The second mode results from long-range migration of water molecules, allowing the gel to change both shape and volume. This mode of deformation occurs over a time scale that becomes long when the sample is large.

In the following paper, we give an interpretation of Poisson's ratio in a gel, when the gel is compressed for a long time, and water molecules have enough time to migrate out.

See the discussion of Fig. 2.

You may also wish to look at the following paper, where a hydrogle is tested with indentation and uniaxial compression.