Elasticity
3.0 Strain
3.0 Strain
The ratio of the change in configuration (i.e. shape, length or volume) to the original configuration of the body is known as strain. $$Strain = \frac{{Change\ in\ Configuration}}{{Original\ Configuration}}$$ Strain, being the ratio of two like quantities, has no unit and dimension.
Types of Strain:
1. Longitudinal Strain
This type of strain is produced when the deforming force causes a change in length of the body.
It is defined as the ratio of the change in length to the original length of the body.
Consider a wire of length $L$. When the wire is stretched by a force $F$, then let the change in length of the wire is $\Delta L$.
Therefore, $$\begin{equation} \begin{aligned} Longitudinal\ Strain = \frac{{Change\ in\ length}}{{Original\ Length}} \\ or \\ Longitudinal\ Strain = \frac{{\Delta L}}{L} \\\end{aligned} \end{equation} $$
2. Volume Strain
This type of strain is produced when the deforming force produces a change in volume of the body as shown in Fig. E. 6.
It is defined as the ratio of the change in volume to the original volume of the body.
Consider a body of volume $V$. When the body is compressed uniformly by a force $F$, then let the change in volume is $\Delta V$.
$$\begin{equation} \begin{aligned} VolumeStrain = \frac{{Change\ in\ Volume}}{{Original\ Volume}} \\ Volume\ Strain = \frac{{\Delta L}}{L} \\\end{aligned} \end{equation} $$
3. Shear Strain
This type of strain is produced when the deforming force causes a change in the shape of the body as shown in Fig. E. 7.
It is defined as the angle ($\phi $) through which a face originally perpendicular to the fixed face is turned as shown in the figure.
$$Shear\ Strain = tan\phi = \frac{{\Delta x}}{x}$$
Since $tan\phi \approx \phi $ as $\phi$ is very small. So, $$\phi = \frac{{\Delta x}}{x}$$
