On some aspects for contact with rigid surfaces: Surface-to-rigid surface and curves-to-rigid surface algorithms

Special algorithms allowing a simplified description of contact between deformable body and rigid surfaces are developed based on the geometrically exact covariant description of contact. A special attention is given to various geometric combinations where the contact can be represented as (a) contact between surfaces and (b) contact between a curve and a surface. For contact between surfaces, leading to the Segment-To-Analytical Surface (STAS) approach, two algorithms can be distinguished based on the selection of a coordinate system for the Closest Point Projection (CPP) procedure: (a) Rigid Surface is a “Slave” surface and (b) Rigid Surface is a “Master” surface. A special combination of both contact kinematics for the surface-to-surface and for the curve-to-curve approaches is employed for the contact between a curve and a surface leading to the Curve-To-Rigid Surface (CTRS) approach. The last algorithm is verified with the well known Euler formula for the rope-cylinder interaction as well as with a new derived generalization into a 3D spiral rope on a cylinder. The developed algorithms can be straightforwardly implemented within an iso-geometric approach as well as within the conventional finite elements where rigid surfaces are given by CAD patches. Any type of elements can be employed for the contacting deformable surface/curve because the algorithms are formulated in a covariant form.