The von Mises criterion is a theoretical approach used in engineering and materials science to predict the yielding of ductile materials under complex loading conditions. It states that yielding occurs when the distortion energy in a material reaches a critical level, which can be determined from uniaxial stress tests. This criterion helps engineers design structures that can withstand various forces without failing. In practical terms, the von Mises criterion simplifies the analysis of stress states by allowing the combination of different types of stresses, such as tensile and shear stresses, into a single equivalent stress. This makes it easier to assess whether a material will yield under specific loading scenarios.