A-level Physics/Forces and Motion/Deformation of solids

Hooke's law
$$F = {k\;x}$$

This applies to an object's deformation only before the elastic limit; from then on it deforms plastically and no longer follows this law. it states that, extension is directly proportional to the applied force.

Spring Constant
$$k = \frac{1}{gradient}$$

$$k = \frac{F}{x}$$

The gradient refers to the gradient of a Tension-Extension graph. The standard units of k are N m−1

Strain
$$Strain = \frac{Extension}{Original\; length}$$

Because this is a division of two measurements of length, Strain has no units and remains a ratio.

It can also be represented as $$Strain = \frac{ Change in  length } {Original\; length}$$

Stress
$$Stress = \frac{Force}{CrossSectional\; Area}$$

The units for Stress are N m−2, otherwise known as Pascals (Pa)

The Young's modulus
$$Young \; modulus = \frac{Stress}{Strain}$$

Strain energy
$$Strain \; energy = \frac{1}{2}Fx$$

However, due to Hooke's Law, it can be calculated in another form, y=mx+c;

$$Strain \; energy = \frac{1}{2}2jx = \frac{1}{2}kx^2 $$

Elastic limit
the maximum extent to which a solid may be stretched without permanent alteration of size or shape.

Plastic limit
When the stress is sufficient to permanently deform the metal, it is called plastic deformation.