Elastic Moduli

Step 1: Understanding Stress-Strain Curve
The stress-strain curve describes how a material deforms under applied stress.
In the elastic region, the material returns to its original shape after the stress is removed.
Step 2: Elastic Modulus
The slope of the stress-strain curve in the elastic deformation region is known as the elastic modulus, which measures the material's stiffness.
It is calculated as the ratio of stress to strain: Where:
is the elastic modulus,
is the stress,
is the strain.

Step 3: Conclusion
Thus, the slope of the stress-strain curve in the elastic region is the elastic modulus.

Step 1: Understanding Hooke’s Law
Hooke's law states that the strain produced in a material is directly proportional to the applied stress within the elastic limit.
Mathematically, it is given by: Where:
is the stress,
is the Young's Modulus (a constant for the material),
is the strain.

Step 2: Other Laws for Comparison
Bernoulli’s law deals with the conservation of energy in flowing fluids.
Poisson’s law relates to the ratio of lateral strain to longitudinal strain when a material is stretched.

Step 3: Conclusion
Thus, Hooke’s law describes the relationship between stress and strain within the elastic limit.