The quadrilateral parametric contact element based on the moving friction cone formulation

Contact between bodies is most commonly analyzed using quadrilateral contact elements that are based on 8-node brick (hexahedral) continuum finite elements. As a quadrilateral contact surface, in comparison to a triangular contact surface (tetrahedral continuum elements), is not necessarily flat, or it deforms as deformable body deforms, contact formulation turns to be a complex problem. Recent developments in contact routines based on the Moving Friction Cone (MFC) approach for flat triangular contact elements enabled significant simplifi-cations in the element formulation, what is used herein. The MFC formulation of contact is based on the single gap vector, instead of two vectors (slip and stick one). The curved contact surface is defined in a parametric form, thus enabling fi-nite deformations and a Lagrangian definition of contact.