Mechanical Properties of SolidsMind Map

When a deforming force is applied to a solid, the solid develops internal restoring forces that oppose deformation. Stress is defined as restoring force per unit area. It may be tensile, compressive, hydraulic or shear depending on the way force acts. Strain is the relative change in shape or size caused by stress. Longitudinal strain measures change in length, volumetric strain measures change in volume and shear strain measures change in shape. For small deformations, stress is proportional to strain, giving the stress-strain relationship. If deformation disappears after removing the force, it is elastic deformation. If a permanent change remains, it is plastic deformation.

Hooke's law states that stress is directly proportional to strain within the proportional limit. This simple law allows us to define elastic moduli, which measure stiffness of a material. Young's modulus describes resistance to change in length, bulk modulus describes resistance to change in volume and shear modulus describes resistance to change in shape. These constants are material properties and have the same unit as stress because strain is dimensionless. Elastic constants are related through Poisson's ratio for isotropic materials. When a body is elastically deformed, work done by external force is stored as elastic potential energy. Elastic energy density equals the area under the stress-strain graph in the linear region.

The stress-strain curve shows how a material responds as stress is gradually increased. Initially, the graph is a straight line and Hooke's law is obeyed up to the proportional limit. The elastic limit is the maximum stress up to which the material completely regains its original shape on unloading. Beyond this, plastic deformation begins. The yield point marks the stage where strain increases greatly with little increase in stress. Ultimate stress is the maximum stress the material can bear. After this, necking or weakening may occur, and the specimen finally breaks at the breaking point. Ductile materials show large plastic deformation, while brittle materials break with little strain.

Elasticity is essential in designing safe buildings, bridges, cranes, cables, springs and machines. Materials in engineering structures must withstand stress without exceeding elastic or breaking limits. A safety factor is used so that working stress remains much smaller than breaking stress. Suspension bridges use steel cables because steel has high Young's modulus, high tensile strength and reliable elastic behaviour. Elasticity also appears in daily life through springs, rubber bands, vehicle suspension, mattresses, shock absorbers and sports equipment. Practical NEET applications often test why certain materials are chosen, how safe load is calculated and how extension changes with length, area and Young's modulus.