Contactmechanica

Contactmechanica, often called contact mechanics in English, is the branch of solid mechanics that studies the deformations, stresses, and contact forces that arise when bodies come into contact. It addresses how normal contact, friction, adhesion, wear, and separation develop from material properties, surface topography, and loading conditions. The field is essential for predicting contact pressures, slip and stick behavior, and the reliability of mechanical interfaces across engineering, tribology, biomechanics, and geophysics.

Analytical foundations include Hertzian contact theory, which describes elastic contact between bodies under frictionless loading, particularly spheres and cylinders. More general formulations arise from Signorini’s unilateral contact concepts, and Mindlin’s work on partial slip and tangential loading. For adhesive interactions, models such as Johnson–Kendall–Roberts (JKR) and Derjaguin–Muller–Toporov (DMT) extend the framework to account for surface energy, with applicability depending on material stiffness and scale.

Numerical methods are widely used for complex geometries and materials. Finite element methods with contact constraints employ techniques such as penalty, Lagrange multipliers, or augmented Lagrangian formulations; boundary element methods are also common for certain problems. Multiscale and statistical approaches address rough surface contact, while specialized models handle friction, wear, and separation phenomena.

Applications include rolling-element bearings, gear interfaces, tire-road contact, and micro- and nano-scale devices (MEMS), as well as biological joints where soft tissues interact with rigid or compliant surfaces. The field remains active as materials, surfaces, and computational capabilities evolve.