Axial Deformation

In the linear portion of the stress-strain diagram, the tress is proportional to strain and is given by
 

$\sigma = E \varepsilon$

 

since $\sigma = P / A$ and $\varepsilon = \delta / L$, then $\dfrac{P}{A} = E \dfrac{\delta}{L}$
 

$\delta = \dfrac{PL}{AE} = \dfrac{\sigma L}{E}$

To use this formula, the load must be axial, the bar must have a uniform cross-sectional area, and the stress must not exceed the proportional limit.
 

Stress-strain Diagram

Simple Strain

Also known as unit deformation, strain is the ratio of the change in length caused by the applied force, to the original length.
 

Simple strain

 

$\varepsilon = \dfrac{\delta}{L}$

where δ is the deformation and L is the original length, thus ε is dimensionless.