What is the Difference Between Modulus of Elasticity and Modulus of Rigidity?
🆚 Go to Comparative Table 🆚The modulus of elasticity and modulus of rigidity are both elastic moduli that describe a material's resistance to deformation. However, they differ in the type of deformation they describe and the conditions under which they are applicable.
- Modulus of Elasticity (E): This property helps in calculating the deformations of an object when the deforming force is applied parallel to the surface. It is relevant for axial loading and is only valid for elastic deformations. The modulus of elasticity is also known as Young's modulus and can be used to explain how a material resists transverse deformations under small deformations.
- Modulus of Rigidity (G): Also known as the shear modulus, this property helps in calculating the deformation of an object when the deforming force is applied at right angles to the surface. It is relevant for shear stress and is valid for both elastic and non-elastic deformations. The modulus of rigidity is used to measure the rigidity of a body and is the ratio of shear stress to shear strain.
The relationship between the modulus of elasticity and modulus of rigidity can be expressed as:
$$E = 2G(1 + \mu)$$
where E is the modulus of elasticity, G is the modulus of rigidity, and μ is the Poisson's ratio. The SI unit for both modulus of elasticity and modulus of rigidity is Pascal (Pa), which is equivalent to 1 N/m².
Comparative Table: Modulus of Elasticity vs Modulus of Rigidity
The modulus of elasticity and the modulus of rigidity, also known as the shear modulus, are both elastic properties of a material. However, they describe different types of deformation and stress. Here is a table highlighting the differences between the two:
| Property | Modulus of Elasticity | Modulus of Rigidity (Shear Modulus) |
|---|---|---|
| Description | The modulus of elasticity is the property of a material that indicates the resistance to deformation when a force is applied, such as in the case of linear stress (tensile or compressive) | The modulus of rigidity, also known as the shear modulus, is the property of a material that indicates the resistance to deformation when a shear force is applied, such as in the case of shear stress |
| Formula | $$E = \frac{\sigma}{\epsilon}$$ (where $$\sigma$$ is stress and $$\epsilon$$ is strain) | $$G = \frac{\tau}{\gamma}$$ (where $$\tau$$ is shear stress and $$\gamma$$ is shear strain) |
| Units | Pascals (Pa) | Pascals (Pa) |
| Relationship | $$E = 2G(1 + \mu)$$ (where $$E$$ is the modulus of elasticity and $$G$$ is the modulus of rigidity) and the ratio of Poisson's (Heaviside's) ratio to the bulk modulus (K) is given by $$\mu = \frac{K - 1}{K}$$. | N/A |
In summary, the modulus of elasticity relates to axial loading, while the modulus of rigidity relates to shear stress.
- Elastic Modulus vs Young’s Modulus
- Plasticity vs elasticity
- Young Modulus vs Tensile Strength
- Bulk Modulus vs Young Modulus
- Elastic vs Inelastic
- Elastic vs Plastic Deformation
- Isothermal vs Adiabatic Elasticity
- Rigidity vs Spasticity
- Elastic vs Inelastic Collision
- Elasticity of Demand vs Elasticity of Supply
- Viscoelastic vs Viscoplastic
- Elasticity of Demand vs Price Elasticity of Demand
- Ductility vs Malleability
- Spring Constant vs Stiffness Factor
- Deformation vs Strain
- Tensile Strength vs Yield Strength
- Elastic vs Perfectly Elastic Collision
- Gravitational Potential Energy vs Elastic Potential Energy
- Ductility vs Brittleness