In designing structural elements and machine parts using ductile materials, it is crucial to ensure that these components withstand applied stresses without yielding. Yielding is initially determined through a tensile test, which evaluates the material's response to uniaxial stress. However, tensile stress is insufficient when components face biaxial or plane stress conditions This condition requires advanced criteria to predict failure.

The Maximum Shearing Stress Criterion, also known as the Tresca Criterion, assesses component safety under various stress states by comparing the maximum shearing stress within the material to that at the yield point in a uniaxial tensile test. Shearing stress, which is significant in the yielding of ductile materials, is visualized through Tresca's hexagon in stress space. This graphical representation forms a boundary condition: stresses within the hexagon indicate safety, while those outside suggest potential yielding.

Alternatively, the Maximum Distortion Energy Criterion, known as the Von Mises criterion, is based on the distortion energy theory. This criterion states that yielding occurs from the energy stored due to distortion. A component is considered safe if the distortion energy per unit volume from applied stresses is less than that at the yield point. The Von Mises stress, derived from principal stresses, quantifies this energy, aiding in evaluating material behavior under complex stress states.