# Strain

Started by Lauren Hartle, Fall 2011.

Defined along one dimension of a material, strain can be either normal or shear. Normal strain is the ratio of the length change along that dimension to the length along that dimension.

$\epsilon = \frac{\Delta L}{L}$

And what about shear strain?


The engineering, or cauchy strain uses the pre-deformation length in this measure, while the true strain uses the length of the material at the time the strain is measured (this length changes as the material is deformed). Shear strain along a particular axis measures the angular displacement when the material is deformed perpendicular to this axis. For small displacements, it can be approximated as, where the indices indicate the axis of deformation and the axis of interest:

$\gamma_{ij} = \frac {1}{2} \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_i}{\partial x_j} \right)$

By geometry, one can deduce that $\gamma_{ij} = \gamma_{ji}$. Figure 1 illustrates 2-D normal (top diagrams) and shear strain (bottom diagrams) in x and y.

Having mention "engineering" strain and others, what is in the diagram? And are other diagrams useful?