Elastic Limit: The elastic limit is the maximum amount of force a material can handle before it loses its ability to return to its original shape. Below this limit, the material behaves elastically, but beyond it, it undergoes permanent deformation.
Stress: Stress refers to the internal force per unit area that develops within a material when it's subjected to an external force. It's what causes the material to resist deformation.
Strain: Strain is the relative change in shape or size of a material when it's subjected to stress. It's measured by the ratio of the change in length or volume to the original length or volume of the material.
Hooke's Law: Hooke's Law states that, within the elastic limit, the stress applied to a material is directly proportional to the strain it experiences. This means that if you double the stress, you'll double the strain. The constant of proportionality, represented by E, is known as the elastic constant or modulus of elasticity. Its value varies for different materials and its unit is the pascal ().
There are three types of elastic constants.
(i) Young's modulus of elasticity (): This is the ratio of longitudinal stress to longitudinal strain. Longitudinal stress is the force applied per unit area in the direction of the force, while longitudinal strain is the change in length per unit length of the material. Mathematically, it's expressed as:
(ii) Bulk modulus of elasticity (): This is the ratio of volume stress to volume strain. Volume stress is the force applied per unit area to compress or expand the material uniformly, while volume strain is the change in volume per unit volume of the material. Mathematically, it's expressed as:
(iii) Rigidity modulus (): Also known as shear modulus, this is the ratio of tangential (or shear) stress to shear strain. Shear stress is the force applied parallel to the surface of the material, while shear strain is the change in shape due to this force. Mathematically, it's expressed as:
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