• Individual production for precast concrete parts

• Controllable metamaterials and smart structures

• Multi-scale algorithms and simulation for the patient-specific optimization of endovascular interventions in cerebral aneurysms

• Multi-scale modelling of thermomechanical frictional contact for complex problems in engineering

• Algebraic multigrid methods for preconditioning of block systems

• Highly efficient and parallel scalable mortar methods for contact and multi-field problems

• Use of eigenfrequencies for the identification of cracks

• Combination of Isogeometric Analysis, Finite Element Methods, and Embedded Mesh Coupling Methods for contact problems​

• Combination of data- and physics-based methods for hybrid digital twins

• Mixed-dimensional models for fiber/fluid interaction

• Mixed-dimensional coupling in solid mechanics

• Optimal control problems governed by elliptic variational inequalities

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).

Prof. Dr.-Ing. Alexander Popp, Dr.-Ing. Ivo Steinbrecher

Czech Academy of Sciences in Prague

University of West Bohemia in Pilsen

This project investigates metamaterial properties of locally periodic structures constituted by conventional and smart materials. Smart materials distinguish themselves from standard passive metamaterials by controllability through electroactive components and time-space alternating geometrical layouts.

Controllable and adaptive structures equipped with embedded actuators and sensors connected to electric circuits provide a higher level of multi-functionality such as the capability of vibration and wave propagation control, shape morphing, or modifying stiffness in space and time.

The research work is embedded into an international consortium and will be conducted in close collaboration with scientific partners at the Czech Academy of Sciences in Prague (Czech Republic) and at the University of West Bohemia in Pilsen (Czech Republic).

Prof. Dr.-Ing. Alexander Popp,  Dr.-Ing. Sebastian Brandstäter, Moritz Frey M.Sc.

Prof. Dr.-Ing. Alexander Popp, Dr.-Ing. Matthias Mayr, Martin Frank M.Sc.

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. Applications of thermomechanical contact include screw connections under temperature loading and shrink fitting. 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, which is an acronym for MUSAM-IMCS Rough Contact cOde. MIRCO is being actively developed and is open-source. It can be utilized as a contact constitutive law in other FEM software packages by using it as a library and is available for access on GitHub.

Dr.-Ing. Matthias Mayr, Max Firmbach M.Sc.

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.

The project focuses on the approximate calculation of eigenvalues of various differential operators on areas with cracks using isogeometric analysis. Methods are to be developed that allow the simulated eigenvalues to represent as accurately as possible the eigenfrequencies of test objects with cracks that can be measured in practice, and also to show corresponding convergence results. Subsequently, these natural frequencies shall be used to identify the crack, i.e., to determine the shape of the crack. This inverse problem is to be solved with a neural network, for the training of which we need simulation data of as high quality as possible in order to be able to guarantee a meaningful application in practice.

Prof. Dr. Thomas Apel, Philipp Zilk M.Sc.

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 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, since the two regions pose different requirements on continuity, element type, mesh orientation and mesh refinement. 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. For doing this, appropriate mortar / Lagrange multiplier formulations as well as Nitsche's method will be investigated.

In this project, methods for hybrid digital twins of critical infrastructure are investigated and developed. The main focus is the combination of physics-based modeling using Finite Element Methods (FEM) and data-based modeling with machine learning techniques.

The first application case are steel-reinforced concrete bridges. On the physics-based modeling side, a mixed-dimensional FEM model for steel-reinforced concrete components is developed. Complementary, variants of neural networks are investigated. Both are combined to improve the material model with measurement data and obtain a reduced order model of the physical system. 

Still, attention is paid to generality and application independence of the methods, so that the developed techniques can also be used by the project partners. New algorithms are implemented in the form of an in-house software solution. An associated hardware platform for high performance computing is provided at the Data Science & Computing Lab.

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.