VonMisesKriterium

The von Mises criterion, often referred to as the von Mises yield criterion or the maximum distortion energy criterion, is a foundational concept in metal plasticity. It predicts yielding of ductile materials under complex loading by comparing the state of stress to a single scalar yield measure.

Mathematically, the criterion uses the deviatoric part of the stress tensor. The von Mises equivalent stress is defined as sigma_vm = sqrt(3 J2), where J2 is the second invariant of the deviatoric stress: J2 = 1/2 s_ij s_ij, and s_ij = sigma_ij - (1/3) sigma_kk delta_ij. Yield is assumed to occur when sigma_vm reaches the uniaxial yield stress sigma_y. A key feature is that hydrostatic (pressure) stress does not influence yielding in this model, since only the distortional (deviatoric) component enters the criterion.

Applications and usage: the von Mises criterion is widely used in finite element analysis and the design of ductile metals due to its relative simplicity and good empirical correlation with many metals under multiaxial loading. It is commonly paired with isotropic or kinematic hardening models to represent material strengthening with plastic deformation.

Limitations: while effective for many metals, the criterion is not universal. It may not accurately predict yielding for materials with significant anisotropy, strong strain-rate sensitivity, or notable pressure dependence (such as some polymers or soils). In such cases, alternative or modified criteria (e.g., Hill’s criterion for anisotropy or Drucker–Prager for pressure-sensitive materials) may be more appropriate. The von Mises criterion remains a standard reference in plasticity theory and engineering practice.