extension-over-length-defines-strain - Elasticity: Stress, Strain, and Material Response Step by Step

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}