### Main Difference

The main difference between modulus of elasticity and modulus of rigidity is that modulus of elasticity is effective only for elastic deformations, whereas modulus of rigidity is effective for both non-elastic and elastic deformations.

### Modulus of Elasticity vs. Modulus of Rigidity

Modulus of elasticity is defined for forces normal to the surface, while the modulus of rigidity is defined for forces acting the surface parallel laterally to it. The deformation is linear for the modulus of elasticity, whereas the deformation is a circular one for the modulus of rigidity. Modulus of elasticity is effective only for elastic deformations, whereas modulus of rigidity is effective for both non-elastic and elastic deformations. The object in the deforming force either gets shortened or lengthened where the modulus of elasticity is calculated; on the other hand, one of the surfaces of the object becomes displaced concerning another surface where the modulus of rigidity is calculated. The modulus of elasticity is always larger than the modulus of rigidity, and the exceptions of this rule are “auxetic” materials that have negative Poisson’s ratios, but these materials are present less common.

### Comparison Chart

 Modulus of Elasticity Modulus of Rigidity Modulus of elasticity is mainly used to figure out the distortion of a solid substance when a bending force acts at normal to a surface of the solid. Modulus of rigidity normally helps to estimate the distortions of an object when a deforming force acts parallel to the surface of an object. Direction of Forces Forces which are normal to the surface Forces acting the surface parallel laterally to it Deformation The deformation is linear The deformation is a circular one Effectiveness Effective only for elastic deformations Effective for both non-elastic and elastic deformations Change in Shape The object in the deforming force either gets shortened or lengthened One of the exteriors of the object becomes displaced concerning another surface Relative Size Larger than the modulus of rigidity Smaller than the modulus of elasticity

### What is the Modulus of Elasticity?

Modulus of elasticity or commonly known as young’s modulus is a figure that defines the ratio of stress to strain in a particular object or in solid substance that is deformed by a deforming force which is normal to the surface of an object. The stress is defined as a solid which is the distorting force per unit area. For example, an item becomes extended due to the result of a tensile force acts on it. Thus, the deforming force is at normal to the surface of the object, so the stress is sometimes called normal stress. The strain is generally defined as the fractional change in the length of the object. Presume that the body has length x˳ before the distorting force acts on it, and when the body gets extended by length ∆x in the deforming force. Stress and strain are considered as dimensionless quantities. Modulus of elasticity means the object tends to deform elastically when an external force is applied. The stiffer material usually has higher elastic modulus. Modulus of elasticity is active only for elastic distortions, and the object under the deforming force either becomes shortened or lengthened in the calculation of the modulus of elasticity. The modulus of elasticity is always larger than the modulus of rigidity, and the exceptions of this rule are “auxetic” materials that have negative Poisson’s ratios, but these materials are present less common.

### What is the Modulus of Rigidity?

Modulus of rigidity or sometimes known as shear modulus is a figure that generally provides the shear stress which takes action on a solid per unit area. Therefore, modulus of rigidity helps to guess the distortions of a body when a deforming force performs equivalent to the face of an object causing one of the faces of the object to become displaced concerning another surface. The modulus of rigidity considered to have the percentage between shear stress and shear strain. The equation of shear stress contains the same method as for the equation of the normal stress, but there is an observable difference is in the way the force acts. The unit of shear stress in Newton per meter squared or normally known as Pascal. Not only solids have shear stress, but fluids can also have a shear stress. The shear strain is considered as the proportion of relative displacement between the faces to the separation between the faces. The modulus of elasticity is always larger than the modulus of rigidity, and the exceptions of this rule are “auxetic” materials that have negative Poisson’s ratios, but these materials are present less common.

### Key Differences

1. The forces of modulus of elasticity are normal to the surface, while the forces of modulus of rigidity are acting the surface parallel laterally to it.
2. The distortion is linear for the modulus of elasticity, whereas the deformation is a circular one for the modulus of rigidity.
3. Modulus of elasticity is effective only for elastic deformations, whereas modulus of rigidity is effective for both non-elastic and elastic deformations.
4. The object in the deforming force either gets shortened or lengthened where the modulus of elasticity is intended; on the other hand, one of the surfaces of the object becomes displaced concerning another surface where the modulus of rigidity is calculated.
5. The modulus of elasticity is always larger than the modulus of rigidity, and the exceptions of this rule are “auxetic” materials that have negative Poisson’s ratios, but these materials are present less common.

### Conclusion

Above discussion concludes that the modulus of elasticity is effective only for elastic deformations and the object under the deforming force either gets shortened or lengthened, whereas modulus of rigidity is effective for both non-elastic and elastic deformations, but one of the surfaces of the object becomes displaced concerning another surface. 