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.
Since its founding years, the ISD worked at the forefront of developments in finite element analysis research. Today, this heritage manifests itself in ongoing research efforts regarding the basis of this highly successful method.
This research includes spring cell lattices as substitutes for continua as well as investigating the application of the FE² method for the Theory of Porous Media (TPM²), where an iterative finite element problem is solved.
Recently, model order reduction techniques have become a flourishing field as well, where classical techniques as well as newly developed machine learning algorithms aim towards reducing the simulation cost of highly complex system.
Environmental engineering 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.
From single lobuli to the whole organ, biomechanical research is trying to bridge vastly different behaviour on several scales. One such project implores the effects of pharmaceuticals and flow constrictions on detoxification and fatty liver syndrome. This work is done in cooperation with the Medical University of Jena.
Further interest is in mechanical properties of articular cartilage and its dependency on fiber distribution and alignment.
Within the field of uncertainty quantification, there are several methods of taking natural scattering and lack of data in numerical calculations into account. If both are considered in combination, one speaks of polymorphic uncertainty quantification (PUQ). Using the Theory of Porous Media (TPM), geotechnical problems are captured numerically and their reliability quantified by PUQ methods from the field of probabilistic, possibilistic as well as fuzzy methods.
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.
Mathematical models are the classical tool to describe and predict fluid and solid mechanics in porous materials. These models are typically strongly coupled differential equations of several primary variables. Hence, solving them might be of high computational complexity.
Model reduction aims to develop new techniques for reducing the models' complexity and, consequently, increasing their computational efficiency. It is based on utilizing natural properties of the porous medium to reduce the number of primary variables or the dimensionality of the models.