Yieldkriterier

Yieldkriterier, or yield criteria, are constitutive rules used in plasticity theory to determine when a material transitions from elastic to plastic behavior under load. They define a yield surface in stress space; when the stress state lies inside the surface, the material responds elastically, and when the surface is reached, plastic deformation begins and is governed by a flow rule. The yield surface may evolve through hardening mechanisms as plastic deformation accumulates.

Common yield criteria include: von Mises (J2) criterion, which yields when the deviatoric part of the stress reaches a critical value and is widely used for metals with isotropic hardening; Tresca criterion, based on maximum shear stress, historically important and simpler but sometimes less accurate for certain materials. Mohr-Coulomb is widely used in geotechnical engineering for soils and rocks and depends on cohesion and internal friction, producing a non-smooth yield surface. Drucker-Prager provides a smooth approximation to Mohr-Coulomb and is popular in finite element modeling of soils and porous materials. There are also anisotropic criteria, such as Hill-type models and more advanced formulations like Yld2000, which account for direction-dependent yielding in some metals.

Hardening laws describe how the yield surface evolves with plastic deformation. Isotropic hardening translates the surface outward, while kinematic hardening translates it in stress space; many models combine both. Yield criteria are typically coupled with a flow rule and a hardening law to predict plastic flow, residual stresses, and material failure under complex loading.

Applications of yield criteria span metal forming, structural analysis, automotive and aerospace components, and geotechnical engineering. The choice of criterion depends on material behavior, pressure sensitivity, temperature, and strain rate, and is calibrated from mechanical tests.