For structural steel, Poisson’s ratio typically ranges from 0.25–0.3.
It ensures predictable deformation under loads and is used in stress–strain and deflection calculations.

A rigid body doesn’t deform under any amount of applied force, meaning strain = 0.
This is an idealization used in theoretical mechanics but doesn’t exist in real materials

Bulk modulus (K) = Volumetric stress / Volumetric strain.
It determines how compressible a material is. Higher K = lower compressibility.
Important for materials used under hydrostatic or internal pressure, like cylinders and vessels.

An elastic body returns to its original shape after load removal and follows Hooke’s law (stress ∝ strain).
Such materials are predictable and widely used in engineering analysis.

The correct relation is E = 2G(1 + ν).
It shows how shear and tensile properties are connected for isotropic materials — essential for analyzing both bending and torsional stresses.

Due to Poisson’s effect, when a material is stretched longitudinally, it contracts laterally.
The extent of this contraction depends on Poisson’s ratio (ν).

Typical Young’s Modulus values:

• Rubber ≈ 0.01 GPa

• Aluminum ≈ 70 GPa

• Steel ≈ 200 GPa ✅
  Hence, steel is the stiffest material among the listed — ideal for load-bearing components.

In the linear (elastic) region, the slope of the stress-strain curve represents the Elastic Modulus (E).
It defines the stiffness of materials — steeper slope = stiffer material.

Using relation E = 2G(1 + ν):
200 = 2G(1 + 0.3) → G = 76.9 GPa ≈ 80 GPa.
This shows how elastic constants are interdependent and crucial for determining shaft rigidity and deformation.

According to Hooke’s Law, strain ∝ stress within the elastic limit.
Beyond this limit, the material undergoes permanent deformation. This concept is fundamental in designing springs and load-bearing structures to stay within safe stress limits.

Bulk modulus (K) = Hydrostatic stress / Volumetric strain.
It measures the resistance to uniform compression — important in pressure vessels, hydraulic components, and submarines.

Elasticity means the ability to return to original shape after deformation.
Materials with high Young’s modulus (like steel) are more elastic because they deform less under the same load compared to soft materials like rubber.

A Poisson’s ratio > 0.5 violates the law of conservation of volume — physically impossible.
Most metals have values between 0.25 and 0.35, while rubber approaches 0.5.

For isotropic materials, E = 9KG / (3K + G).
This formula links the three primary elastic constants, helping engineers calculate missing properties for structural analysis.

Modulus of rigidity (G) represents a material’s resistance to shear deformation.
For steel, G ≈ 80 GPa.
It’s crucial for torsional design in shafts and couplings.

Since Young’s modulus is stress divided by strain (dimensionless), its unit is the same as stress = N/m² or Pascal (Pa).
It indicates the magnitude of stress needed for a given strain.

Young’s modulus (E) = Stress / Strain in the same direction.
It measures stiffness or the ability to resist deformation.
Typical values:

• Steel ≈ 200 GPa

• Aluminum ≈ 70 GPa
  Used in tensile and bending calculations.

For incompressible materials like rubber, the volume remains constant even under load, giving ν = 0.5.
It means any elongation in one direction causes equal contraction in the other two — used for rubber seals and elastomeric materials.

Poisson’s ratio (ν) = (Lateral strain) / (Longitudinal strain).
When a material is stretched in one direction, it contracts in the perpendicular direction. Most engineering materials (like steel) have ν ≈ 0.3. It helps in calculating deformation in multi-axial loading systems.

Hooke’s Law states that stress is directly proportional to strain within the elastic limit — i.e., stress ∝ strain or σ = E × ε. Beyond this point, permanent deformation begins. It’s the base for linear elasticity used in structures, beams, and mechanical design.