In physics and materials science, stiffness refers to the resistance of a material to deformation when subjected to an applied force. It is a fundamental property that characterises how much a material will deform under an applied load.
For instance, a metal ruler, which is stiff and resists bending, and a rubber band, which is less stiff and flexible, easily deforms under applied force.
Stiffness is typically described in terms of Hooke’s Law, which relates stress and strain in elastic materials.
Hooke’s Law is expressed mathematically as:
Stress=Young’s Modulus×Strain
Where:
- Stress (σ) is the force applied per unit area.
- Young’s Modulus (E) is a material property known as the modulus of elasticity or elastic modulus. It is a measure of the stiffness of the material.
- Strain (ε) is the relative deformation or change in size of the material.
In simple terms, Hooke’s Law states that the stress applied to a material is directly proportional to the strain it undergoes, as long as the material remains within its elastic limit (meaning it returns to its original shape after the load is removed). The slope of the stress-strain curve, represented by Young’s Modulus, is a measure of the material’s stiffness.
Daily Life Examples of Stiffness
- Clothing Fabric:
- Stiffer fabrics like denim are used for jeans because they hold their shape well and provide durability.
- Softer, more flexible fabrics like cotton jersey are used for comfortable T-shirts.
- Footwear:
- Shoes made of leather or other stiff materials provide support and maintain their shape, offering stability to the foot.
- In contrast, athletic shoes often have flexible soles to allow for better movement.
- Furniture:
- Wooden chairs and tables are made from stiff materials to provide structural support and maintain their form under the weight of a person or objects.
- Sofas or mattresses use materials with a combination of stiffness and flexibility for comfort and support.
- Automobiles:
- Car bodies are designed to be stiff to withstand forces during movement, ensuring structural integrity and safety.
- Suspension systems use a combination of stiff and flexible components to provide a balance between stability and comfort.
- Smartphones and Electronics:
- The outer casings of electronic devices are often made of stiff materials like metal or high-strength polymers to protect the internal components from damage.
- Flexible materials, like in the hinges of foldable smartphones, allow for movement without breaking.
- Construction Materials:
- Stiff materials like steel and concrete are used in building structures to provide strength and stability.
- Flexible materials, such as certain types of rubber or elastomers, are used in seals and joints to accommodate movements and vibrations.
- Sports Equipment:
- Stiff materials are used in the frames of bicycles, tennis rackets, and golf clubs to provide rigidity for efficient energy transfer during use.
- Flexible materials are incorporated into items like running shoes to absorb impact forces and enhance comfort.
- Cookware:
- Stiff materials like cast iron or stainless steel are used for pots and pans to withstand high temperatures and provide durability.
- Flexible materials like silicone are used in spatulas and baking molds for easy handling and removal of cooked items.
Solved Numerical Problem of Stiffness
Suppose we have a steel rod with a length of 2 meters and a cross-sectional area of 0.0004 m20.0004m2. The rod is subjected to a force of 5000 Newtons, resulting in a deformation (strain) of 0.002. Calculate the stiffness (Young’s Modulus) of the steel rod.
Solution:
Given data:
- Length of the steel rod (L): 2 meters
- Cross-sectional area (A): 0.0004 m2
- Force applied (F): 5000 Newtons
- Strain (ε): 0.002
Stress(σ)=Force (F)/Area(A)
σ = 5000N/0.0004 m2
Young modulus = E = σ/ε
σ=5000N/0.0004 m2
=12,500,000 N/m2
E = 12,500,000 N/m / 0.002
= 6,250,000,000N/m2
The stiffness (Young’s Modulus) of the steel rod is 6,250,000,000 N/m2.
