extension-over-length-defines-strain - Elasticity and Nonlinear Dynamics Step by Step

Normal strain is the extension per unit original length, epsilon = delta-L / L, a dimensionless measure of how much a bar stretches relative to its size. It is the deformation that stress produces in a linear elastic material. The ratio is exact only for the stated extension and length under uniform axial loading; real materials add calibration, geometry, temperature, loading history, and uncertainty.

Axial strain is an exact dimensionless deformation ratio. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Axial strain starts with two length markers

The original length and extension are checked separately before the dimensionless ratio is accepted.

L_0=8\ \text{m}\qquad \Delta L=2\ \text{m}

Larger extension makes larger strain

Hold the original length fixed. The strain column is just the extension divided by that length.

\begin{array}{c|c|c}L_0&\Delta L&\epsilon\\8\ \text{m}&1\ \text{m}&\frac{1}{8}\\8\ \text{m}&2\ \text{m}&\frac{1}{4}\\8\ \text{m}&4\ \text{m}&\frac{1}{2}\\\end{array}

Axial strain is extension divided by original length

The strain is a dimensionless checked ratio, not a percent written in prose.

\epsilon=\frac{\Delta L}{L_0}=\frac{2\ \text{m}}{8\ \text{m}}=\frac{1}{4}