# Is Young's modulus a measure of stiffness or elasticity?

Young's modulus seems like a modulus of stiffness. It tells us how difficult is it (how much stress is required) to produce longitudinal strain in a solid. It does not tell anything about how an object will react when the deforming force is removed.

How can one on the basis of young's modulus decide that steel is more elastic than a rubber band?

• Stiffness is more related to bending and deflection.
– user137289
Dec 31 '19 at 15:25
• @Pieter Yes, but in, as you say, "common language", stiff is the opposite of "elastic". Jan 2 '20 at 22:44
• @BobD That is not the only opposite. As common-language antonyms, Merriam-Webster also gives brittle, crumbly, flakey, friable. And I might also choose words like ductile, malleable, pliable, plastic, or viscous.
– user137289
Jan 2 '20 at 23:41
• May 26 '20 at 4:45

In physics elasticity is defined as the ability of a material to resist a distorting influence and return to its original size and shape when the distorting influence is removed (source Wikipedia).

Young’s Modulus is the ratio of applied stress to resulting strain in the linear elastic region of behavior. Therefore, they greater Young’s modulus the stiffer a material is, that is, the greater the materials ability to resist a distorting influence (applied stress). For this reason, given the above general definition of elasticity, Young’s modulus is also called the modulus of elasticity.

Due to the highly overall non linear behavior of rubber I believe Young’s modulus for rubber is usually quoted forces small loads. The values for rubber are much lower than steel meaning that rubber is much less able to resist a distorting influence than steel as would obviously be expected.

Given the above definitions of elasticity and Young’s modulus we would conclude that the “elasticity” of rubber is less than steel. It is admittedly counter intuitive because on the one hand we think of rubber bands as being highly elastic in the sense that they’re easy to stretch. But on the other hand if they’re easier to stretch that means they’re less able to resist distortion, which is consistent with the physics definition of elasticity and Young’s modulus.

Hope this helps.

• Wikipedia is not a good source. That "definition" does not define anything.
– user137289
Dec 31 '19 at 13:26
• @Pieter Forty years experience writing product safety standards taught me that agreeing on definitions can be a futile exercise. After 10 years as IEEE working group chairman for surge protective devices and we still couldn’t get agreement on how to define the damn things. Wiki definition aside we still have something called the modulus of elasticity, even though the greater the value the stiffer the material. Probably should be called modulus of stiffness. But it isn’t. Dec 31 '19 at 13:59
• The difference between “common language” usage of term elasticity and the definition of modulus of elasticity is probably the motivation behind the OP’s question. I don’t disagree with your answer. My answer was only intended to acknowledge the difference. We don’t need definitions to know it is easier to stretch rubber than steel. Dec 31 '19 at 13:59
• Stiffness in materials science is more related to bending and shear forces, so that is not a good alternative. If I was in the mood, I might try to change that article in Wikipedia. Or delete it it altogether, because elasticity does not have that meaning in physics.
– user137289
Dec 31 '19 at 14:05
• @ArunArora For what it's worth, at least in my opinion, the motivation for your question was logical so I am up voting it. If in terms of "common language" as Pieter says, stiff is the opposite of elastic, one would think that a greater "modulus of elasticity" would mean less "stiff", as opposed to more "stiff". So, from a "common language" perspective it seems Young's modulus should be called the modulus of stiffness. Jan 2 '20 at 22:41

It is not true that steel is more elastic than rubber. Not in common language.

Yes, steel has a larger modulus of elasticity, Young's modulus, the ratio of stress to strain $$Y=\varepsilon/\sigma$$. This is in the region of elastic response as long as the deformation $$\sigma=\Delta \ell/\ell$$ increases linearly with stress $$\varepsilon =F/A$$. The response is assumed to be immediate (fast, but slower than the speed of sound). For metals, this is on the order of 100 GPa, similar values for iron and for steel - it takes a lot of force to make a small elastic compression or elongation.

Steel also has a larger elastic limit of stress, a steel rod can support very large tensile loads without permanent changes in its length.

This does not say anything about the range of deformations that are reversible. For steel etc the elastic strain limit is usually on the order of $$10^{-3}$$. For rubber the range of elastic stretching is much larger. That is why rubber is elastic in ordinary language.

Compressibility is a word that has similar meanings in physics and in the common language. In physics, it is the reciprocal of the bulk modulus which is closely related to Young's modulus. In common language, compressibility is similar to elasticity.