Contact Analysis

Contact analysis models the interaction between deformable or rigid bodies that can come into and out of contact during loading. The problem is inherently nonlinear because the contact area, boundary conditions, and load paths change as bodies deform. Contact formulations enforce the impenetrability constraint (bodies cannot pass through each other) and may include friction to resist tangential sliding. Common formulations include the penalty method, Lagrange multipliers, augmented Lagrange, and MPC (multi-point constraint) methods. Contact detection algorithms determine when and where surfaces interact, while contact types define the interface behavior: bonded (no separation or sliding), frictionless (free sliding), rough (no sliding), or frictional (Coulomb friction). Surface-to-surface contact is generally preferred over node-to-surface for accuracy, especially with mismatched meshes. Symmetric contact treats both surfaces equally, while asymmetric contact designates one as target and one as contactor. Small sliding assumes relative motion is small compared to element size, while finite sliding handles large relative motions. Hertzian contact theory provides analytical solutions for curved surfaces in contact, predicting elliptical or circular contact areas and pressure distributions.