Mechanical Properties of Solids
Solids are rigid—they resist being pushed, pulled, twisted, or stretched. Yet no material is perfectly rigid.
Start with the simplest version: this lesson is about Mechanical Properties of Solids. If you can explain the core idea to a friend using everyday language, examples, and one clear reason why it matters, you have moved from memorising to understanding.
Solids are rigid—they resist being pushed, pulled, twisted, or stretched. Yet no material is perfectly rigid. Apply enough force to a steel beam, and it bends. Even mountains deform under their own weight over geological timescales. Understanding how solids respond to forces reveals why materials fail, how engineers design structures, and what determines material strength. This chapter explores stress, strain, and elasticity.
Stress: Force Per Unit Area
Stress σ = F/A, with SI unit pascal (1 Pa = 1 N/m²). Three types: tensile (pulling), compressive (squeezing), and shear (sliding parallel to a surface).
Strain: Fractional Deformation
Strain is the dimensionless ratio of deformation to the original size. Longitudinal strain ε = ΔL/L. Volumetric strain = ΔV/V (used with bulk modulus). Shear strain = Δx/L (lateral shift / height).
Hooke's Law
Within the elastic limit, stress is proportional to strain: σ = E ε. The constant E is the elastic modulus. For tensile/compressive stress E is called Young's modulus, Y.
Elastic Moduli
Young's modulus Y = (F/A) / (ΔL/L) — resistance to length change. Bulk modulus B = −P / (ΔV/V) — resistance to volume change under uniform pressure (negative sign because volume decreases when pressure increases). Shear modulus G (or η) = (F/A) / (Δx/L) — resistance to shape change.
Stress–Strain Curve
Region OA is linear (proportional limit). A→B is the elastic region (no permanent deformation). B is the yield point; beyond B the material deforms plastically (region B→D). D is the ultimate tensile strength; beyond D the material fractures at E. The area under the elastic part is the elastic potential energy per unit volume = ½ σ ε.
Poisson's Ratio
When a wire is stretched longitudinally, it contracts laterally. Poisson's ratio σ_p = (lateral strain)/(longitudinal strain) is between 0 and 0.5 for most materials.
Elastic Potential Energy
Energy stored per unit volume in a stretched wire = ½ × stress × strain = ½ Y ε² = (1/2) σ²/Y. Total energy U = ½ × F × ΔL.
Engineering Applications
Bridge cables use steel for high Y. Pressure vessels need high B. Reinforced concrete pairs concrete (strong in compression) with steel (strong in tension). Cantilever beams sag by δ = WL³/(3YI) — depth (which sets the second moment I) matters more than width.
Socratic Questions
- Why does stress depend on the area over which force is applied, not just the force? Give two practical examples.
- A rubber band and a steel wire are stretched by the same fractional amount. Which experiences greater stress, and why?
- What happens at the molecular level when a material crosses its yield point and begins to deform plastically?
- Why can't all materials be made infinitely stiff (high Young's modulus)? What trade-offs are involved?
- Glass and rubber respond very differently to the same tensile stress. How do their stress–strain curves differ, and why?