Hooke's law

${\displaystyle F={k\;x}}$

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

${\displaystyle k={\frac {1}{gradient}}}$

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

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

Strain

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

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

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

Stress

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

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

The Young's modulus

${\displaystyle Young\;modulus={\frac {Stress}{Strain}}}$

Strain energy

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

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

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

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.