Modulus of Rigidity

Introduction

Modulus of rigidity is a material’s elastic shear stiffness, usually indicated by the letter G, or sometimes by S, and can be seen as the ratio of the shear stress to shear strain. Shear modulus is the same thing as modulus of rigidity. Shear stress is a component of stress that is parallel to the cross-section of material. The shear force causes it. On the other hand, the strain in a body occurs when particles are moved relative to a reference length. The strains belong to either the normal or shear category. Normal strains are perpendicular to the element’s face and shear strains are parallel. Let us now briefly discuss the modulus of rigidity                                                                                              .

Body

A rigid body model shows an item that doesn’t deform when external forces are applied. This type of model is extremely helpful for assessing mechanical systems. Physical characteristics of the material used to create an item determine how stiff that item may be. When squashing pressure is applied to a tennis ball, its rubber becomes elastic; however, plastic ping-pong balls become brittle. Ping-pong balls and tennis balls can, however, bounce very well in other situations as rigid bodies. The application of a force can cause a change in shape as a result of deformation, even under relatively modest stress. In physics, stress and strain describe forces on objects that are undergoing deformation.

• Stress: A force per unit area is defined as stress. The three types of stresses are: 

1. Tensile stress: The tensile stress of an object refers to its resistance to a force capable of tearing it apart.
2. Compressive stress: This occurs when compression is caused by forces.
3. Bulk stress: Bulk stress results from pressing an item in all directions.

• Strain: Stress causes an object or medium to deform. Strain is a measure of this deformation. Whenever a length, volume, or shape changes, that is called strain. The three types of strains are: 

1. Tensile strain: It is produced by tensile stress.
2. Bulk strain: This is generated by shear stress. 
3. Shear strain: The strain caused by shear stress.

Due to the existence of three different strain types–longitudinal, shearing, and volumetric, there are three basic types of moduli. These are as follows:

• Young’s modulus: A material’s Young’s modulus, also known as its modulus of elasticity, is what determines how well a material can resist compression and elongation relative to its length. In the world of linear elastic solids, this is a measure of their mechanical properties. A Young’s modulus characterizes the relationship between strain and stress. Solid objects deform when pressure is applied to them. Elastic objects regain their original shape quickly when pressure is released.
• Bulk modulus: Bulk elastic properties of a material are used to determine how much compression material will undergo in the presence of external pressure. It is imperative to determine and record the pressure-change ratio concerning fractional volume compression. It is based on the ratio between the pressure applied and the corresponding relative reduction in material volume.
• Shear modulus: In the event of a shear force causing lateral deformation, the modulus of rigidity is the elastic coefficient. Body rigidity is measured by this. Shear modulus formula = shear stress/shear strain.

Let’s learn more about the modulus of rigidity.

Define modulus of rigidity 

An important measure of a solid’s mechanical properties is its shear modulus of elasticity. There are several measurements of stiffness that occur in the generalized Hooke’s law, such as the shear modulus. Different situations lead to different types of stress and strain. The strain and stress are generally proportional to small deformations, and this is called Hooke’s Law. Once elastic materials are stretched, molecules and atoms become deformed until stress is applied. The body returns to its original state once the stress is removed. 

When forces are applied parallel to a solid surface, while they are simultaneously applied to the other, the shear modulus measures the degree of deformation caused. Different materials respond differently to stress or strain when tested in various directions, such as wood, paper, and pretty much all single crystals.

Pressure waves and shear waves are the two kinds of waves that can occur in a homogeneous and isotropic solid. Shear modulus controls the velocity of shear waves. Additionally, with increasing temperature, metals tend to lose their shear modulus. Increasing pressure seems to increase the shear modulus as well. In many metals, vacancy formation energy, melting temperature, and shear modulus are correlated. Many models are available for predicting a metal’s shear modulus.

Modulus of rigidity formula 

G= Txy/ Yxy= (F/A) / (Δx/l)= Fl/AΔx

Here, Txy= F/A is the shear stress;

An object experiences force F;

An area where a force is exerted is A;

Shear strain is Yxy= Δx/l;

Transverse displacement is represented by Δx.

The initial length of material is l

It is a particular form of Hooke’s law of elasticity.

Conclusion:

Generally, rigidity refers to a solid’s ability to change its shape. It follows that a force applied externally on a solid material will not change its shape. There is a strong attraction between the particles, as seen by the close packing of particles. Rigidity modulus is important because it gives us an indication of the extent of deformation that will occur based on how much stress is applied. Torsion tests measure a material’s modulus of rigidity. Using Young’s modulus, you can determine whether a material is resistant to elastic deformation. Stiff materials have a high Young’s modulus and change shape very slightly under elastic load. Young’s modulus of an elastic material is low, and it changes its shape easily.