The ISD pursues diverse resarch interests, connecting experts from various fields such as aerospace, civil, and electrical engineering as well as mathematics, physics, and medicine. Support comes through cooperations with research partners, grants from government projects such as the DFG, DAAD and HORIZON2020 or industrial partners such as Thyssen Krupp AG.
Continuum-biomechanical modeling helps to understand the mechanics of living systems as well as and to understand the function of organisms, to predict changes due to alterations and to propose therapies and interventions. Therein, biological tissues can be divided into hard tissues like bone and tooth and soft tissues such as brain, cartilage, liver, skin or blood vessels with different mechanical properties. One of the significant differences is the increased deformability of soft tissues compared to hard tissues. Therefore, applied infinitesimal deformation for industrial materials such as metals cannot be applied for the description of soft tissues and instead finite deformation theories are often used to describe their mechanical behavior. We develop multiphase methods to describe processes in soft tissue like the liver, brain tissue, cartilage or human skin. In addition to the constitutive description of the materials, special properties and behaviors such as the transport of concentrations, growth processes or an osmotic pressure are considered.
- Soft Tissue Modeling
- Multiphase Modeling
- Growth and Remodeling
Physics-based modeling has been the classical tool for describing and predicting the behavior of multiphysical systems. High fidelity simulations of such systems require suitable numerical schemes as well as fine scale spatio-temporal grids.
Within multiphysics, the proper design of such numerical schemes is challenging. Beside stability, even in the asymptotic ranges of the material parameters, accuracy of primal (e.g., displacement) as well as dual quantities (e.g., stresses) are required. Within many engineering applications, accurate dual quantities are even more relevant than the primal ones. Strictly speaking, this requires the incorporation of primal as well as dual quantities into the numerical schemes, enlarging size and complexity of the emerging linear equation systems. In return, this paves the way to construct parameter-robust, adaptive solution strategies, delivering guaranteed accuracy on tailored spatio-temporal grids.
Even with the current advances of computational capabilities, many engineering questions, such as optimization, uncertainty quantification, model-based predictive control or clinical-time constraints require a reduction of computational complexity. Therefore, reconstruction-based techniques, such as equilibration, reduces complexity by calculating sufficiently accurate fluxes based on the primal variables. A direct incorporation into the numerical scheme is therefore not required. A different approach dealing with the same issue is called model-order reduction (MOR).
MOR methods have been developed to reduce computational time complex, multiphysical systems while preserving their important physical features. Most popular MOR methods can be classified into three main categories: 1) knowledge-driven approaches utilizing tools such as asymptotic analysis and homogenization. 2) Projection-based methods extracting the essential dynamical features and projecting the models onto those features. 3) Data-driven approaches applying machine learning methods on simulation or experimental data.
In this group we investigate the applicability of different MOR methods and reconstruction-based techniques on different industrial, medical, and environmental applications. Moreover, novel model-reduction methods, based hybrid reduction and reconstruction techniques, will be developed and tested. Our aim is to achieve the most possible fast predictions, while still maintaining acceptable stability and accuracy levels.
When developing a theoretical model for real world phenomena, one often has to neglect a few circumstances to get towards a suitable representation one can work with easily. In most cases, the assumptions being made deviate from the actual behaviour of the system under consideration.
Uncertainty quantification is the field of determining these systematic errors and statistical evaluation of their influence in numerical simulations.
- Polymorphic Uncertainty Quantification
- Sensitivity Analysis
- Bayesian Models
Experimental mechanics is a branch of engineering mechanics used to solve engineering problems using measurements, and can be defined as the investigation of the mechanical behaviour of an object under load or excitation by conducting experiments. The measured mechanical quantities conventionally associated with experimental mechanics are the following: deformations, which can serve as a basis for the determination of stresses or loads (forces, torques); accelerations, velocities, displacements, angles, etc. In addition to the conventional quantities, any aspect relevant to a given object can be measured or recorded by photographic or video recording, in order to determine more effectively the actual state by experimental methods, while knowledge of this actual state can subsequently facilitate a clearer description, i.e. the mathematical formulation of the phenomenon.
- Test & Measurement: DIC and Thermal camera
- Additive Manufacturing process
- Auxetic Structures
Environmental mechanics ranks highly among the modern and most important topics today. Here, the quantitative influence of bacterial methane oxidization in landfill sites and its mechanical reaction to this stimulus is investigated, as well as remediation activities in soil.
Antarctic sea ice
Extended theory of porous media
Machine Learning combines techniques from linear algebra, statistical learning, and optimization to automatically compute best estimate models for a given problem. While it's not a given that machine-learned models are the best approach to solving every problem, success stories are legion and the results produced are fascinating.
Since domain knowledge isn't directly imposed on algorithms in most cases, unintuitive solutions can be found that human experts sometimes miss.