Materials engineering formula sheet
| Formula | Equation | Symbols | Conditions |
|---|---|---|---|
| Stress & Strain | |||
| Poisson's Ratio | ν = -ε_transverse / (ε_axial) | ν Poisson's Ratio; εₜ Transverse Strain; εₐ Axial Strain | Small strains; typical values depend on material |
| Shear Modulus | G = E / (2(1+ν)) | G Shear Modulus (Pa); E Young's Modulus (Pa); ν Poisson's Ratio | Isotropic, linear elastic material |
| Bulk Modulus | K = E / (3(1-2ν)) | K Bulk Modulus (Pa); E Young's Modulus (Pa); ν Poisson's Ratio | Isotropic, linear elastic material |
| True Stress | σ_t = σ_e(1 + ε_e) | σₜ True Stress (Pa); σₑ Engineering Stress (Pa); εₑ Engineering Strain | Uniform deformation before necking; constant volume assumption |
| Stress Concentration 1 | σ_max = K_t σ_nom | σₘₐₓ Maximum Stress (Pa); Kₜ Stress Concentration Factor; σₙₒₘ Nominal Stress (Pa) | not defined |
| True Strain | ε_t = ln(1 + ε_e) | εₜ True Strain; εₑ Engineering Strain | Uniform deformation before necking |
| Failure Theories | |||
| Von Mises Stress | σ_v = √(σ₁² - σ₁σ₂ + σ₂²) | σᵥ Von Mises Stress (Pa); σ₁ Principal Stress 1 (Pa); σ₂ Principal Stress 2 (Pa) | Plane stress condition (σ₃ = 0) |
| Tresca Criterion (Max Shear Stress) | τ_max = (σ₁ - σ₃) / 2 | τₘₐₓ Maximum Shear Stress (Pa); σ₁ Max Principal Stress (Pa); σ₃ Min Principal Stress (Pa) | For ductile materials; σ₁ ≥ σ₂ ≥ σ₃ |
Equations are rendered from the library's own typeset source with no term reordered, dropped or simplified. Symbol legends and validity conditions are the library's; an equation is a model, not a guarantee — confirm its assumptions hold before you rely on a result.
- The formula library records no validity conditions for this entry. An absent condition line is not a statement that the formula is unconditional — check the source before applying it outside the obvious case.
Reference values are provided for study and quick reference. Verify against current standards and manufacturer data before safety-critical design.