Question

Define stress, strain and elasticity.

Short answer

Stress is force per unit area. Strain is the deformation due to stress. Elasticity is a material's ability to return to its original shape after being deformed.

Step-by-step solution

Define Stress

Stress is defined as the internal resistance offered by a material to an external force. It is measured as force per unit area. The formula for stress is: \[\text{Stress} (\tau) = \frac{\text{Force} (F)}{\text{Area} (A)}\]

Define Strain

Strain is the measure of the deformation of the material due to the applied stress. It is the ratio of change in dimension to the original dimension, given by: \[\text{Strain} (\text{ϵ}) = \frac{\text{Change in Length} (\text{ΔL})}{\text{Original Length} (\text{L})}\]

Define Elasticity

Elasticity is the property of a material to return to its original shape and size after the removal of the applied force that caused the deformation. Elasticity is quantified by the modulus of elasticity, also known as Young's modulus, which is the ratio of stress to strain: \[\text{Young's Modulus} (E) = \frac{\text{Stress} (\tau)}{\text{Strain} (\text{ϵ})}\]

Key concepts

Stress

Stress refers to the internal resistance that a material offers to an applied external force. It's essentially how the material fights back against being deformed. When you push, pull, twist, or compress a material, it tries to regain its shape and resists the force applied.
Stress is calculated using the formula:
\[\text{Stress} (\tau) = \frac{\text{Force} (F)}{\text{Area} (A)}\]
This means that stress is the force applied divided by the area over which the force is distributed. Imagine squishing a sponge by pushing down on it with your hand. The harder you push (increased force) or the smaller the area of your hand, the greater the stress on the sponge.

Strain

Strain is a measure of how much a material deforms due to the applied stress. It's a way to quantify how much the shape of the material has changed. It's crucial to understand that strain is dimensionless—it's a ratio and doesn't have units.
The formula for strain is:
\[\text{Strain} (\epsilon) = \frac{\text{Change in Length} (\Delta L)}{\text{Original Length} (L)}\]
Suppose you pull on a rubber band. The change in length (\(\Delta L\)) divided by its original length (\(L\)) gives you the strain. If the rubber band was 10 cm long and stretched to 12 cm, the strain would be 0.2 or 20%.

Elasticity

Elasticity is the property of a material that allows it to return to its original shape and size after the deforming force is removed. Think of it as the material's memory of its original form. If a material is elastic, it will bounce back to its original shape once you stop applying a force.
For example, when you stretch a rubber band and then let go, it snaps back to its initial shape. That's elasticity in action. This property is important in materials that need to endure deformations but return to their original state, such as springs.

Young's Modulus

Young's Modulus, also known as the modulus of elasticity, is a measure of the stiffness of a material. It tells you how much a material will deform under a given load and is calculated using the ratio of stress to strain.
Here's the formula:
\[\text{Young's Modulus} (E) = \frac{\text{Stress} (\tau)}{\text{Strain} (\epsilon)}\]
A material with a high Young's modulus is very stiff, meaning it doesn't deform much under stress. Metals like steel have high moduli, making them robust and less flexible. On the other hand, materials like rubber have low Young's moduli, meaning they stretch and bend easily.