Von Mises Stress⚠ unverified
Mechanical / Stress Analysis · Von Mises equivalent stress (2D state)
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| sigma_x | σx | Pa | 100000000.0 | Normal stress x |
| sigma_y | σy | Pa | 50000000.0 | Normal stress y |
| tau_xy | τxy | Pa | 30000000.0 | Shear stress |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| sv | σv | Pa | Von Mises stress |
The science & history
Understanding the Parameters
- Six stress components — full symmetric stress tensor in Cartesian form.
- $\sigma_{\mathrm{vm}}$ — always ≥ 0; reduces to $|\sigma|$ in uniaxial tension; pure hydrostatic stress gives $\sigma_{\mathrm{vm}} = 0$ (no distortional energy).
Derivation (Approaching a Proof)
Von Mises (distortional energy) criterion: yield when the second invariant of the deviatoric stress reaches the uniaxial yield value. Expressing that invariant in components yields the formula above. Equivalent form: $\sigma_{\mathrm{vm}} = \sqrt{3J_2}$.
History
Maxwell–Huber–Hencky–von Mises yield criterion is the default ductile metal yield model in design and FEA.
Related Concepts: Factor of Safety, Shear Stress, Hookes Law Strain Stress, Strain Energy Density
Notes: Registry calculator materials-von-mises-stress (unverified). Elastic stress components as
inputs (not a plasticity solver).