The Tresca Criterion is a yield criterion used in material science and engineering to predict the failure of materials under complex loading conditions. It is based on the maximum shear stress theory, stating that yielding occurs when the maximum shear stress in a material reaches a critical value. This criterion is particularly useful for ductile materials, such as metals, where shear failure is a common mode of failure. In mathematical terms, the Tresca Criterion can be expressed as the difference between the maximum and minimum principal stresses. It is often represented graphically in a stress space, where the failure envelope forms a hexagonal shape. This helps engineers and designers assess the safety and performance of structures and components under various loading scenarios.