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Three moduli of elasticity quantify resistance to different types of deformation.

Young's Modulus (Y) measures resistance to longitudinal deformation: Y = $\frac{F/A}{(Delta L/L)}$ = $\frac{FL}{A*Delta L}$. It applies to solids only. Steel has Y = 200 GPa (very stiff); rubber has Y = 0.01 GPa (very compliant). Y is the slope of the linear region of the stress-strain curve. A wire acts as a spring with constant k = $\frac{YA}{L}$.

Shear Modulus or Modulus of Rigidity (G or eta) measures resistance to shape deformation: G = $\frac{F/A}{theta}$. It applies to solids only. Fluids have G = 0 (they flow under shear). For most metals, G is roughly Y/2.5. Shear modulus governs torsional rigidity.

Bulk Modulus (B or K) measures resistance to volume change: B = -Delta P * V/Delta V. The negative sign ensures B > 0. It applies to all states of matter — the only modulus defined for liquids and gases. For an ideal gas: $B_{isothermal}$ = P and $B_{adiabatic}$ = gamma*P. Compressibility k = 1/B is its reciprocal.

All three moduli have the same SI unit (Pa) and dimensional formula [M $L^{-1}$ $T^{-2}$]. For a perfectly rigid body, all three approach infinity. For a perfectly plastic body, all three are zero. The three moduli are not independent — for isotropic materials, any two (along with Poisson's ratio) determine the third.