Mechanical Properties of Solids

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Elasticity is the property of a body by which it tends to regain its original shape and size when the deforming force is removed. For example, a spring regains its shape after being stretched.

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An elastic body regains its original shape and size after removal of deforming force (e.g., steel spring). A plastic body does not regain its original shape and remains deformed (e.g., lump of putty).

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Stress is the internal restoring force per unit area of cross-section of a deformed body. Stress = Force / Area. Its SI unit is Nm⁻² or Pascal (Pa).

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Longitudinal stress occurs when deforming forces act along the length of a body. Two types: (1) Tensile stress – when the body is stretched, (2) Compressive stress – when the body is compressed.

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Shearing stress occurs when deforming forces act tangentially to the surface, changing the shape without changing volume. Example: Pushing the top of a book sideways while the bottom is fixed.

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Strain is the ratio of change in dimension to the original dimension (e.g., ΔL/L). Since it is a ratio of two similar quantities (length/length), it has no units and is dimensionless.

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Volume strain is the ratio of change in volume to the original volume: Volume strain = ΔV / V. It occurs under uniform pressure without change in shape.

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Shearing strain is the angle θ (in radians) through which a line perpendicular to the fixed plane is turned due to tangential force. For small angles, θ ≈ Δx / y, where Δx is displacement and y is hei…