Mechanical Properties

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Mechanical Properties — Key Facts Stress = F/A (force per unit area); Strain = ΔL/L (change per unit length); both dimensionless Young’s Modulus E = Stress/Strain; Hooke’s Law: Stress ∝ Strain within elastic limit Types: Young’s (tension/compression), Bulk (uniform pressure), Shear (parallel force) Elastic potential energy: U = ½ × stress × strain × volume = ½(FΔL/A) ⚡ Exam tip: Deformation is reversible within elastic limit, permanent after plastic deformation

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Mechanical Properties — NEET/JEE Study Guide Stress-strain curve: proportional limit → elastic limit → yield point → ultimate strength → fracture Hooke’s Law: stress = E × strain; E_steel ≈ 2×10¹¹ Pa, E_rubber ≈ 10⁹ Pa Poisson’s ratio σ = -lateral strain/axial strain; for rubber σ can be ~0.5; for cork σ ≈ 0 (almost incompressible) Elastic aftereffect: slight delay in recovering original shape after removing load

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Mechanical Properties — Comprehensive Notes Derivation: E from interatomic potential U(r) = A/r¹² - B/r⁶; Hooke’s law emerges near equilibrium Bulk modulus: K = -V(ΔP/ΔV); compressibility = 1/K; for water K ≈ 2×10⁹ Pa (very incompressible) Shear modulus: G = F/A / (Δx/L) = τ/γ; relates to E via G = E/(2(1+σ)) Elastic constants relation: E = 2G(1+σ) = 3K(1-2σ); only 2 of 3 are independent Stress concentration: cracks or sharp corners increase local stress by factor 3-5; explains fracture origin Ductile vs brittle: ductile (steel, aluminium) - large plastic region; brittle (glass, ceramics) - fracture at yield

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