Name: Strain and Elastic Modulus
Uploaded: 2023-04-30T11:03:42
Description: Learn by watching this video about Strain and Elastic Modulus at JoVE.com

The amount of deformation experienced by an object under stress, divided by its initial dimensions, is called strain. Strain is a dimensionless quantity.
If the deformation due to the applied force results in an increase in the length of an object, it is called tensile strain. Whereas, if the&#160;length decreases due to stress, it is called compressive strain.
The change in the volume of an object due to the applied force in all directions is known as bulk strain. If the direction of the force is parallel to the object&#39;s plane, it undergoes deformation along that plane, and this is known as shear strain.
For small deformations, the elastic modulus is defined as the ratio of the stress exerted on the object to the resultant strain.
Young&#39;s modulus is the ratio of tensile stress to tensile strain. The ratio of volumetric stress to volumetric strain is known as bulk modulus, whereas the ratio of shear stress to shear strain corresponds to shear modulus.

strain and elastic modulus

The quantity that describes the deformation of a body under stress is known as strain. Strain is given as a fractional change in either length, volume, or geometry under tensile, volume (also known as bulk), or shear stress, respectively, and is a dimensionless quantity. The strain experienced by a body under tensile or compressive stress is called tensile or compressive strain, respectively. In contrast, the strain experienced under bulk stress and shear stress is known as volume and shear strain, respectively. The greater the stress, the greater the strain; however, the relationship between strain and stress is not necessarily linear.
Only when the stress acting on a body is sufficiently low is the deformation caused by it directly proportional to the stress value. The proportionality constant in this relation is called the elastic modulus. As strain is dimensionless, the physical unit of elastic modulus is the same as stress (pascal). When a body is characterized by a large value of elastic modulus, the effect of stress is small. On the other hand, a small elastic modulus means that stress produces large strain and a noticeable deformation. For example, stress applied on a rubber band produces a larger strain (deformation) than the same stress applied on a steel band with the same dimensions, because the elastic modulus for rubber is two orders of magnitude smaller than the elastic modulus for steel. The elastic modulus for tensile stress is called the Young&#39;s modulus; for bulk stress, it is called the bulk modulus; and for shear stress, it is called the shear modulus.
Table 1. Approximate Elastic Moduli for Selected Materials
<table style="margin-left: auto; margin-right: auto;">
	<tbody style="border: 1px solid black;">
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Material</td>
			<td style="color: black; border: 1px solid black; text-align: center;">Young&#39;s modulus 
			(1010 Pa)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">Bulk modulus 
			(1010 Pa)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">Shear modulus 
			(1010 Pa)</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Aluminum</td>
			<td style="color: black; border: 1px solid black; text-align: center;">7.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">7.5</td>
			<td style="color: black; border: 1px solid black; text-align: center;">2.5</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Bone (tension)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.8</td>
			<td style="color: black; border: 1px solid black; text-align: center;">8.0</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Brass</td>
			<td style="color: black; border: 1px solid black; text-align: center;">9.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">6.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">3.5</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Brick</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.5</td>
			<td style="color: black; border: 1px solid black; text-align: center;"></td>
			<td style="color: black; border: 1px solid black; text-align: center;"></td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Copper</td>
			<td style="color: black; border: 1px solid black; text-align: center;">11.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">14.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">4.4</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Crown glass</td>
			<td style="color: black; border: 1px solid black; text-align: center;">6.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">5.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">2.5</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Granite</td>
			<td style="color: black; border: 1px solid black; text-align: center;">4.5</td>
			<td style="color: black; border: 1px solid black; text-align: center;">4.5</td>
			<td style="color: black; border: 1px solid black; text-align: center;">2.0</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Hardwood</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.5</td>
			<td style="color: black; border: 1px solid black; text-align: center;"></td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.0</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Iron</td>
			<td style="color: black; border: 1px solid black; text-align: center;">21.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">16.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">7.7</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Lead</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.6</td>
			<td style="color: black; border: 1px solid black; text-align: center;">4.1</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.6</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Marble</td>
			<td style="color: black; border: 1px solid black; text-align: center;">6.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">7.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">2.0</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Nickel</td>
			<td style="color: black; border: 1px solid black; text-align: center;">21.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">17.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">7.8</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Polystyrene</td>
			<td style="color: black; border: 1px solid black; text-align: center;">3.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;"></td>
			<td style="color: black; border: 1px solid black; text-align: center;"></td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Silk</td>
			<td style="color: black; border: 1px solid black; text-align: center;">6.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;"></td>
			<td style="color: black; border: 1px solid black; text-align: center;"></td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Steel</td>
			<td style="color: black; border: 1px solid black; text-align: center;">20.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">16.0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">7.5</td>
		</tr>
	</tbody>
</table>
This text is adapted from <a href="https://openstax.org/books/university-physics-volume-1/pages/12-3-stress-strain-and-elastic-modulus">Openstax, University Physics Volume 1, Section 12.3: Stress, Strain, and Elastic Modulus.</a>

Learn by watching this video about Strain and Elastic Modulus at JoVE.com

Strain and Elastic Modulus

The quantity that describes the deformation of a body under stress is known as strain. Strain is given as a fractional change in either length, volume, or ...