Poisson's Ratio

Theory

ν = −ε_lateral/ε_axial. For isotropic materials ν ranges 0 (cork) to ~0.5 (rubber, incompressible). Most metals: 0.25-0.35; PLA ~0.36; PETG ~0.40. ν = 0.5 is perfectly incompressible. Auxetic materials have ν < 0. Thermodynamic stability requires −1 < ν < 0.5.

Application

ν matters in multi-axial stress states: biaxial shell loading, constrained thermal expansion, and press-fit tolerances. FEA requires ν alongside E. Ignoring ν in thermal analysis of printed enclosures can introduce 10-20% error in predicted thermal stress.

Common mistakes

Bulk-material ν is often incorrectly assumed for FDM parts. ν cannot be measured from a simple tensile test without lateral displacement data. ν > 0.5 is physically impossible for passive materials.

Related terms: Strain, Young's Modulus, Stress, Anisotropy