# Derive relationship between elastic constants of silicon

### Eamcet Online Study Material - Physics - Elasticity - cesenahotel.info

discuss about the difference between Young's modulus, Modulus of rigidity and. Bulk modulus. The SI unit of Youngs modulus is N/mm2. SI unit · pascal. Derivations from other quantities. G = τ / γ. Shear strain. In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is defined as the ratio of shear stress to the shear strain: The derived SI unit of shear modulus is the pascal (Pa), although it is usually expressed in. Young's modulus or Young modulus is a mechanical property that measures the stiffness of a solid material. It defines the relationship between stress (force per unit area) and strain In SI base units, Pa = kg m−1 s−2 . The Young's modulus of a material can be used to calculate the force it exerts under specific strain.

Stress is proportional to strain provided the strain does not exceed the elastic limit. Modulus of elasticity depends on the nature of the material and the past treatment it has gone through. The modulus of elasticity of a body is the magnitude of stress to be applied to produce unit strain.

Three kinds of strain: When an external force is applied to a rod along its length the fractional change in its length is called longitudinal strain. If l is the original length and Dl the longitudinal extension.

When simultaneous compression and extension in mutually perpendicular directions take place in a bodythe change of shape it undergoes is called shearing strain.

**Relation between bulk modulus and young modulus (relation between E and K)**

Within the elastic limit of a bodythe ratio between the longitudinal stress and the longitudinal strain is called the Young's modulus of elasticity. Within the elastic limit of a bodythe ratio of tangential stress to the shearing strain is called rigidity modulus of elasticity. It is defined as the ratio of stress to volumetric strain. The reciprocal of the bulk modulus is called compressibility.

### Shear modulus - Wikipedia

It is the maximum stress that a material can withstand and beyond the breaking stress, the material breaks. The breaking stress is also called tensile strength.

The breaking stress of a material is constant. The state of temporary loss of elastic nature of a body due to continuous strain is called elastic fatigue.

Any real material will eventually fail and break when stretched over a very large distance or with a very large force; however all solid materials exhibit nearly Hookean behavior for small enough strains or stresses. If the range over which Hooke's law is valid is large enough compared to the typical stress that one expects to apply to the material, the material is said to be linear. Otherwise if the typical stress one would apply is outside the linear range the material is said to be non-linear.

Steelcarbon fiber and glass among others are usually considered linear materials, while other materials such as rubber and soils are non-linear. However, this is not an absolute classification: For example, as the linear theory implies reversibilityit would be absurd to use the linear theory to describe the failure of a steel bridge under a high load; although steel is a linear material for most applications, it is not in such a case of catastrophic failure. In solid mechanicsthe slope of the stress—strain curve at any point is called the tangent modulus.

## Young's modulus

It can be experimentally determined from the slope of a stress—strain curve created during tensile tests conducted on a sample of the material. Directional materials[ edit ] Young's modulus is not always the same in all orientations of a material.

Most metals and ceramics, along with many other materials, are isotropicand their mechanical properties are the same in all orientations. However, metals and ceramics can be treated with certain impurities, and metals can be mechanically worked to make their grain structures directional. These materials then become anisotropicand Young's modulus will change depending on the direction of the force vector.