Combining isogeometric analysis (IGA), finite element methods (FEM) and embedded mesh (EM) coupling for contact problems

• Applicant: Professor Dr.-Ing. Alexander Popp
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 446494172

Contact processes and the physical phenomena typically associated with them (e.g. friction, wear) are still among the greatest challenges in modelling and numerical simulation in civil engineering based on finite element methods (FEM). The seemingly indissoluble link between FEM mesh generation in the volume of the bodies involved and on the contact surfaces with regard to usable discretization techniques, element sizes and element shapes is a particular obstacle. While at the discrete contact boundaries, especially in the case of curved surface geometries, a high continuity of the shape functions and fine boundary layer meshes prove to be advantageous, there is a strong desire for structured, ideally even Cartesian hexahedral grids and a flexible reusability of well-established finite element technology, for example to avoid locking, inside the volume. This research project is dedicated to the complete resolution of this dilemma by developing a novel discretization method for general nonlinear 3D contact problems based on a combination of FEM, isogeometric analysis (IGA) and so-called embedded mesh coupling methods. The new approach consists of the following core building blocks: the contact surfaces of the bodies involved are taken exactly from the CAD geometry model using isogeometric approaches with non-uniform rational B-splines (NURBS) and fulfill inherently high continuity properties (at least C1-continuity). A regular hexahedral grid is generated inside the domain, independent of the processes at the contact boundaries, which guarantees complete flexibility in the choice of element technology (e.g. classical C0-continuous FEM or again NURBS) and an optimal element shape (3D voxel) at least in the undeformed initial configuration. In order to connect these two parts, a surface-oriented boundary layer mesh is first generated from the discrete NURBS contact surface by extrusion. The project focuses on two new techniques to consistently couple IGA surface mesh and volume mesh. Since these two meshes overlap, most classical methods cannot be used without further ado due to their violation of discrete stability conditions. Instead, suitable embedded mesh coupling methods based on mortar / Lagrange multiplier methods as well as Nitsche methods will be developed. In contrast to currently available approaches, such as FEM smoothing methods, complete 3D NURBS meshing or NURBS enrichment methods, the resulting contact formulation will for the first time combine all the advantages of independent and in each case according to local requirements optimally generated boundary layer meshes and volume meshes for contact problems.

• DFG Programme: Research Grants