Mechanical Properties of Solids
How solids respond to external forces: the concepts of stress, strain, and elastic moduli, Hooke's law, stress-strain curves, Young's modulus, shear modulus, bulk modulus, Poisson's ratio, elastic potential energy in a stretched wire, and real-world engineering applications of elastic behaviour
Topics
Introduction, Stress, and Strain
How solids respond to forces: the meaning of elasticity and plasticity, the definition of stress as restoring force per unit area, and the three fundamental types of stress and strain (longitudinal, shearing, and hydraulic)
Hooke's Law and the Stress-Strain Curve
The linear relationship between stress and strain for small deformations, the modulus of elasticity, the complete stress-strain curve for a ductile metal showing proportional limit, elastic limit, yield point, plastic deformation, ultimate tensile strength, and fracture, and the special behaviour of elastomers like rubber and biological tissue
Elastic Moduli and Young's Modulus
The concept of elastic modulus as the ratio of stress to strain within the proportional region, Young's modulus for longitudinal deformation, its formula and units, comparison of Young's modulus values across metals, glass, bone and other materials, and fully worked numerical examples involving stress, elongation, and compression
Shear Modulus and Bulk Modulus
The shear modulus (modulus of rigidity) for tangential deformation, the bulk modulus for volumetric deformation under hydraulic pressure, compressibility and its variation across solids, liquids, and gases, comparison of all three elastic moduli side by side, and fully worked numerical examples on shearing displacement and ocean-depth compression
Poisson's Ratio and Elastic Potential Energy
The relationship between lateral and longitudinal strain captured by Poisson's ratio, its physical meaning and typical values for metals and alloys, and the derivation of elastic potential energy stored in a stretched wire along with its expression as energy density
Applications of Elastic Behaviour
How engineers use elastic properties to design crane ropes, load-bearing beams with I-shaped cross-sections, pillars with distributed ends, and why mountains on Earth cannot exceed about 10 km in height due to the shearing stress limit of rocks