A) Linear Stress-Strain Curve

Materials that follow Hooke's Law exhibit a linear stress-strain curve. This means that when a tensile or compressive force is applied to the material, it deforms proportionally to the amount of force applied. The stress (force per unit area) is directly proportional to the strain (change in length per unit length) within the elastic limit of the material. This linear relationship is described by Hooke's Law, which states that the stress is equal to the elastic modulus multiplied by the strain.

b) Curve-Linear Stress-Strain Curve

Some materials may exhibit a curve-linear stress-strain curve. This means that the relationship between stress and strain is not strictly linear but follows a curve initially and then becomes linear. This behavior can occur in materials that have a yield point, where the stress required to cause further deformation suddenly decreases. Beyond the yield point, the stress-strain relationship becomes linear and follows Hooke's Law.

c) Parabolic Stress-Strain Curve

Parabolic stress-strain curves are typically observed in brittle materials, such as ceramics. These materials do not exhibit a linear relationship between stress and strain. Instead, the stress-strain curve initially rises rapidly until it reaches the maximum stress (also known as the ultimate stress) that the material can withstand before failure. After reaching the maximum stress, the curve drops rapidly as the material fractures. The parabolic shape of the curve reflects the brittle nature of these materials and their sudden failure without much plastic deformation.