Gain expertise in calculating the intense, localized pressures that arise when elastic bodies are pressed together. Move beyond surface analysis to focus on the critical subsurface zone where maximum shear stresses occur. Master the methodology for applying established criteria, such as the maximum shear stress (Tresca) and maximum distortion energy (von Mises) theories, to accurately predict yielding and subsurface shear failure in ductile materials. Understand the profound difference between the maximum compressive stresses occurring at the contact surface and the often more critical shear stresses found in the material's interior. This knowledge is essential for the reliable design and evaluation of rolling elements, gear systems, and heavy bearings under extreme pressure.