Which one is more difficult to compress, steel or rubber?

Updated: Aug 1, 2021

Let's first understand what is compressibility. It is an ability of the material to resist volume change caused by the surrounding pressure . For example, a gas has much less resistance toward volume change as compared to the solid material. i.e., gas is much more compressible than a solid material. The compressibility of a material is generally characterized by its bulk modulus, i.e., a high bulk modulus solid material is hard to compress than a low bulk modulus solid material.

So the next question arises is that where rubber or rubber like materials stand in relation to steel from the bulk modulus point of view. Following table shows the approximate bulk modulus (K) for common materials.

Materials Bulk Modulus in GPa

Diamond 443

Alumina 62 ± 14

Steel 160

Limestone 65

Granite 50

Glass 35 to 55

Graphite 34

Sodium chloride 24.42

Shale 10

Chalk 9

Rubber 1.5 to 2

Sandstone 0.7

So clearly rubber has a bulk modulus fully two orders of magnitude lower than that of steel. Practically, steel is much more difficult to compress than rubber.

But what about Poisson's ratio consideration? In solid mechanics the PR of steel is taken as 0.3, which suggest high compressibility of steel as compared to a rubber whose PR is usually reported near 0.5. It sounds totally non-intuitive.

It is very important to understand that the concept of compressibility/incompressibility is based on the comparison with other deformations (say shear deformation). The shear strain in steel is of the same order as volumetric strain, whereas shear strain in a rubber is of several orders of magnitude higher than the volumetric strain. At molecular scale level, a rubber is a network of polymer chains. Rubber is generally crosslinked by some suitable crosslinking agents like sufur or peroxide to improve the elasticity of rubbery materials. In this process chains are interconnected by the covalent bonds. These covalent bonds give rise to solid-like behavior of the rubber. In absence of these crosslinks, rubber becomes a polymer melt or liquid.

"rubber acts as an elastic solid globally, but acts as a liquid locally"

Rubber has a high ratio of bulk modulus (K) to shear modulus (G). This ratio is also often referred to as the compressibility ratio (K/G). so rubber's typical deformations are dominated by the shear deformation. Assuming it to be totally incompressible usually introduces little error. A high K/G ratio does not necessarily mean high bulk modulus K value. The compressibility consideration becomes crucial in application where the material is placed in a highly confined environment like O-ring or grove.

Poisson’s ratio,μ= ( (3K/G) -2))/((6K/G) +2))

Relationship between compressibility ratio and Poisson's ratio. S. Pal and K. Naskar- Machine Learning Model Predict Stress-Strain Plot for Marlow Hyperelastic Material Design, Materials Today Communication, https://doi.org/10.1016/j.mtcomm.2021.102213

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