Why is stress proportional to strain in Hooke's law?

[koolraj09]

Hi guys.
Hooke's Law is stated as: Stress is proportional to strain within elastic limit (or load proportional to deformation).
But I can't really figure out why this happens. I mean what is the cause of this proportionality?

 

[Mapes]

I'm not sure whether you're interested in the math reason or the physical reason. Math reason: every generalized "displacement" (e.g., distance or strain) is proportional to generalized "force" (e.g., load or stress) for small displacements, as can be shown by a Taylor series expansion,

$$f(x_0+\Delta x)\approx f(x_0)+f^\prime(x_0)\Delta x$$

where the first term is zero because $x_0$ is the equilibrium position.

Physical reason: pulling on something stretches atomic bonds* and induces a restoring force so that the atoms can go back to their equilibrium spacing.

*Or straightens polymer chains, in elastomers, where the restoring force is entropic. (This is a more advanced topic.)

 

[electromax]

Physical reason: pulling on something stretches atomic bonds* and induces a restoring force so that the atoms can go back to their equilibrium spacing.

*Or straightens polymer chains, in elastomers, where the restoring force is entropic. (This is a more advanced topic.)

I think he were looking for this answer! Great explanation.