Completed Projects

2026

2025

In the last years, contact formulations have mostly been developed using the classical Finite Element Method (FEM). However, a typical finite element mesh cannot provide a continuous normal vector field due to the C⁰ continuity at element intersections. A common solution is to refine the mesh at the contact boundary, which leads to an unnecessary extension of the refined elements into the domain volume. To achieve a higher-order continuity on the contact boundary, contract formulations using Isogeometric Analysis (IGA) have been proposed more recently. These typically use NURBS shape functions for the geometry description as well as the approximation of the solution field. However, the NURBS elements again reach into the domain volume, where their higher-order continuity do not necessarily offer more advantages (due to the reduced regularity of contact problems) but rather cause additional computational costs. 

In this project, we propose a separation of the meshing process for the contact boundary region and for the internal volume of the involved bodies. For the discretization of the contact boundary region, a boundary layer of NURBS elements is defined, which can be refined locally at desired areas without influencing the mesh size within the internal volume. On the other hand, the volume domain is discretized using classical hexahedral finite elements on Cartesian grids in the reference configuration. This results in two independent, yet overlapping meshes, which are consistently coupled to each other using an Embedded Mesh (EM) approach. Within this project, appropriate mortar/Lagrange multiplier formulations will be investigated. Moreover, the goal is to develop a general workflow to simplify the model creation of complex contact problems.

This project aims to develop an efficient two-scale numerical scheme integrating implicit finite element (FEM) computations at the macro-scale and the boundary element method (BEM) at the micro-scale for the accurate solution of frictional and thermomechanical contact problems with microscopic interface roughness. The whole range of frictional regimes, from full stick over stick-slip transitions to full sliding, will be handled as well as any complex loading path. The two-scale model will be compared with a fully resolved 3D FEM model using high-performance computing (HPC) techniques. Frictional contact problems are relevant in many engineering and physics research areas. In mechanical engineering, they arise in configurations such as wheel-rail contact, bearings, brakes or wheel-asphalt contact. Friction is also of interest for the interaction between soil and pile foundations in civil and geotechnical engineering applications, and in biomechanics the relative motion in hip-joint prostheses leads to abrasive wear. In all these scenarios, the interface between bodies in contact is not microscopically flat, but its roughness presents multi-scale features that influence the deformation and the stress states in the material.

The project includes the development of a micro-scale BEM software named MIRCO (hosted on GitHub), which is an acronym for MUSAM-IMCS Rough Contact cOde. MIRCO is being actively developed and is open-source. It can be utilized as an independent rough surface contact solver or as a a library in other FEM software packages.

Bayerisches Verbundforschungsprogramm (BayVFP)

Max Bögl

FIT AG

Institut und Labor für Konstruktiven Ingenieurbau, UniBw München

Within the scope of the joint project "Individuelle Fließfertigung für Betonfertigteile" (IFB), a continuous digital process chain between planning and manufacturing of reinforced concrete components is being created. At the same time, modular manufacturing solutions are being developed using robotics and 3D printing.

The main contribution of IMCS is the optimization of steel-reinforcements in non-standard reinforced concrete components. Conventional calculation methods result in a conservative dimensioning of such components and thus in a non-optimal use of resources. The approach developed at IMCS is based on state-of-the-art mixed-dimensional interaction methods to simulate the composite reinforced concrete as detailed and efficient as possible. This allows the application of shape optimization algorithms for the steel-reinforcements.

The research and development work is carried out in close cooperation with strong partners from the Bavarian construction industry (Max Bögl), additive manufacturing (FIT AG) and research (Institut und Labor für Konstruktiven Ingenieurbau, UniBw München).

Dr.-Ing. Ivo Steinbrecher

In this PhD project, we will advance the coupling of multi-physics problems using mortar finite element methods with a particular focus on the application in nonlinear contact mechanics. Due to the intrinsically nonlinear nature of the introduced constraints at the contact boundary, significantly increased requirements arise for, among other things, contact search algorithms, nonlinear solvers, optimal preconditioning of linear systems of equations, a fully consistent linearization of the problem for implicit time integration, and Mortar-specific operations such as the computation of the mesh intersection at the contact surface within each Newton iteration.

High-fidelity finite element simulations of contact problems potentially require several million degrees of freedom, but demand more computational effort than comparable problems from pure solid mechanics due to the issues mentioned above. Thus, the implementation in a parallel software framework is inevitable. The first step of the PhD project is the development of a highly parallel scalable framework in a MPI-based distributed memory environment, an independently distributed volume and mortar discretization, and an optimal load balancing on the physical processor cores. The implementation is carried out in the multi-physics framework 4C, which is jointly developed in cooperation with the TU Munich and the Helmholtz Zentrum Hereon.

In various engineering and biomechanical applications, the integration of slender fibers with three-dimensional bodies significantly enhances the mechanical properties of the overall structure. In this project, novel coupling methods are developed for such problems, where the fibers are explicitly modelled using one-dimensional (1D) beam theories, resulting in a very accurate and efficient numerical formulation. State-of-the-art finite element methods (FEM) are used for the 3D solids. Such approaches are also referred to as mixed-dimensional coupling, as the underlying differential equations are defined on domains with different dimensions. A key advantage of these mixed-dimensional methods is the simplicity of model generation, as the 1D fibers and 3D bodies can be discretized independently of each other. Over the course of this project, coupling methods for embedded fibers in volumes (1D-3D) and fibers connected or in contact with surfaces (1D-2D) based on Mortar/Lagrange multiplier methods have already been successfully developed.

The project deals with optimal control of variational inequalities. A priori error estimates for finite element discretizations of optimal control problems for elliptic variational inequalities and different regularization strategies are considered. Further information can be found here.

Prof. Dr. Thomas Apel, Christof Haubner M.Sc.

Prof. Dr. Thomas Apel, Volker Kempf M.Sc.

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