Algorithmic aspects in large deformation contact analysis using ‘Solid-Shell’ elements

A special application for the so-called ‘Solid-Shell’ elements are sheet metal forming problems with high stretching and large local contact pressure where standard 2D-shells fail to converge respectively do not give reasonable results. To describe such kind of problems besides a full 3D continuum discretization appropriate contact formulations are necessary to introduce the contact condition of the metal sheets against the rigid tools. In this contribution a velocity description is taken for formulation of contact conditions. A penalty as well as an augmented Lagrangian approach for frictionless contact is used as a first step in our developments. Special attention is paid to different numerical integration schemes of the contact integral and tangent matrices. As a result a series of different contact elements including various cases as “node-to-surface”, “segment-to-segment” and “analytical rigid surface-to-segment” is considered under the unified description. For selected numerical examples the influence of the order of the quadrature formulae in a subdomain integration approach as well as the order of finite element interpolation used in the computations is discussed. The algorithms appear also to work well for friction type problems, which will be tested in a following paper.