1. Concept Overview
When a material is stretched, compressed, twisted, or sheared due to an applied force, its shape or size changes slightly. This change is measured using a quantity called strain. It tells us how much a material has deformed compared to its original dimensions.
Strain has no units because it is simply a ratio of change in length, shape, or volume to the original value.
2. Definition
3. Key Ideas Explained
3.1. Strain is a Measure of Deformation
Strain tells us how much a material deforms when stress acts on it. Even if the deformation is very small, strain helps quantify it precisely. Since both the change and original dimensions have the same units, their ratio is unitless.
3.2. Types of Strain
3.2.1. Longitudinal Strain
This occurs when the length of a material changes due to stretching or compression.
The formula is:
\( \text{Longitudinal strain} = \dfrac{\Delta L}{L} \)
Example: A wire becomes slightly longer when a weight hangs from it.
3.2.2. Shear Strain
This occurs when the shape of the material changes due to a force acting parallel to one of its faces.
It is the angular displacement produced and is written as:
\( \text{Shear strain} = \tan \theta \approx \theta \) for small angles
Example: A stack of papers shifting layer by layer when pushed sideways.
3.2.3. Volumetric Strain
This occurs when the overall volume of a material changes due to pressure applied from all directions.
The formula is:
\( \text{Volumetric strain} = \dfrac{\Delta V}{V} \)
Example: A deep-sea container compressed slightly by water pressure.
3.3. Strain Depends on Original Dimensions
Two objects may experience the same change in length, but their strains can be different because the original sizes are different. A small change in a short object creates large strain, whereas the same change in a long object produces small strain.
3.4. Strain Does Not Tell How Strong a Material Is
Strain only tells us how much a material deforms. It does not indicate the internal forces (that is stress). A soft material may show large strain under small force, while a hard material shows tiny strain even under large forces.
4. Relation Between Stress and Strain
Stress produces strain. In the elastic region of a material, strain is directly proportional to stress. This connection is expressed by Hooke’s Law, which states that:
\( \text{Stress} \propto \text{Strain} \)
This relationship is fundamental to elasticity and is used to define elastic moduli such as Young’s modulus, bulk modulus, and shear modulus.
5. Examples to Build Intuition
5.1. Stretching a Rope
When you pull a rope tightly, it becomes slightly longer. The ratio of the increase in length to its original length is the strain produced in the rope.
5.2. Pushing a Soft Eraser
Pressing an eraser shortens it. The fractional decrease in length is compressive strain. Since erasers are soft, the strain is easily noticeable.
5.3. Shearing a Stack of Cards
If you push the top card of a stack sideways, the layers underneath shift. The angle through which the layers tilt represents shear strain.