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A two-scale homogenisation approach for fluid saturated porous media

T. Ricken, F. Bartel


Thinking about the description of biomaterials, e.g. human tissue, plants or sponges, we always have to take into account a global design composed of various substructures with different characteristics on a lower level. Examples of such substructures are pores which can be saturated with fluids or gases, fibres with different orientations or cells which can be influenced by chemical reactions. For the theoretical description of the behaviour enhanced continuum mechanical models give promising approaches. Unfortunately, up to now it has not been possible to simulate a biological system with only one design model, due to the high complexity. So it is necessary to think about techniques which simplify the model but still consider the essential characteristics.

Currently we are researching on a two-scale homogenisation approach for fluid saturated porous media with a reduced two-phase material model, which covers the behaviour of large poro-elastic deformation.


Industry: ThyssenKrupp Steel Europe

Multiphase and multiscale description for steel solidification processes

T. Ricken, L. Moj


During hot metalworking processes (e.g. casting), semi-finished steel undergo high thermo-mechanical loadings cycles. Large deformations combined with high heating and cooling rates causes considerable structural changes, which have a significant impact on the mechanical properties of the steel. The project aims the development of a robust numerical model that covers the entire temperature range from room to melting temperature.

A two-scale model for the solidification and the process simulation using micro and macro scale is proposed, where both scales contain solid and liquid physical states of the steel. The macro scale is described with help of theory of porous media (TPM) for dynamic processes. This theory simplifies the description of occurring phases, where local distribution is neglected. Furthermore, a strong thermal coupling was achieved. We use finite plasticity superimposed by a creep law for the solid phase.

The calculation of solidification was shifted to the micro-scale. Here, a Ginzburg-Landau type free energy function including a double-well potential with two local minima for completely solid and liquid phases is used.

We use a finite element and a finite difference method for the macro- and the micro-scale. The microscopic boundary value problem is solved on each gauss point.


DFG project no. RI 1202/6-1

Polymorphic uncertainty quantification for stability analysis of fluid saturated soil and earth structures

T. Ricken, C. Henning


Nowadays, numerical simulations enable the description of mechanical problems in many application fields, e.g. in soil or solid mechanics. During the process of physical and computational modeling, a lot of theoretical model approaches and geometrical approximations are sources of errors and uncertainties. In order to get access to a risk assessment these uncertainties and errors must be captured and quantified. For this aim a new priority program SPP 1886 has been installed by the DFG which focuses on the so called polymorphic uncertainty quantification. In cooperation with the ‘chair of mathematical statistics with applications in biometrics’ we enhance the deterministic structural analysis through two promising approaches of analytical and stochastic sensitivity analysis to capture impacts of the different uncertainties on computational results. Additionally the sensitivities of uncertainties will be compared and rated to develop more efficient methods and tools for the sizing of earth structures in the long-run.




Environmental Mechanics

DFG project no. RI 1202/3-1,2

Multiphase modeling of bacterial methane oxidation in landfill cover layers

T. Ricken, A. Thom


Under aerobic conditions methanotrophic bacteria are able to convert methane (CH4) into carbon dioxide (CO2) and water. This exothermic reaction leads to a significant reduction of the climate impact. Over a period of 100 years, the global warming potential of methane is 25 times higher than that of carbon dioxide. 
Since methanotrophic bacteria are situated within the landfill cover layer and therefore can convert the harmful methane emissions arising from the degradation of organic waste to the less harmful carbon dioxide, the biological oxidation of methane can be considered as a method of passive aftercare for landfills to reduce climate-impact. The application of methanotrophic treatment is limited by the low forecast ability of the biological processes in the landfill cover. These dynamic processes are influenced by a variety of environmental factors. For a full scale implementation a model with high reliability is needed to simulate the behavior of methanotrophic layers on a landfill site.


A. Sindern, T. Ricken, J. Bluhm, R. Widmann, M. Denecke, T. Gehrke
A coupled multi-component approach for bacterial methane oxidation in landfill cover layers
submitted for publication in PAMM, 2014

T. Ricken, A. Sindern, J. Bluhm, R. Widmann, M. Denecke,  T. Gehrke, T. C. Schmidt
Concentration driven phase transitions in multiphase porous media with application to methane oxidation in landfill cover layers
ZAMM - Journal of Applied Mathematics and Mechanics 94 (7), 609 – 622, doi:10.1002/zamm.201200198, 2014.

A. Sindern, T. Ricken, J. Bluhm, R. Widmann, M. Denecke
Bacterial methane oxidation in landfill cover layers – a coupled FE multiphase description
Proc. Appl. Math. Mech., 13(1):193-194, 2013


EU, H2020 -MSCA-ITN-2014, 643087 "REMIDIATE - Improved decision-making in contaminated land site investigation and risk assessment"

Simulation, prediction and optimization of remediation activities in contaminated sites

T. Ricken, S. M. Seyedpour


Over the past few decades, soil and subsequently ground water contamination have raised growing concern as factors threatening the life of humans and other organisms as well as agricultural production sustainability. These concerns are, on the one hand, due to the increasing contaminated sites and their spreading throughout the world, and, on the other hand, due to the complicated environmental conditions governing these sites. According to reports, in Europe alone, there are more than 3,000,000 polluted sites, eight percent of which are classified as “highly polluted” and in urgent need of being cleaned up (EPA).

The purpose of this project is to simulate the remediation process in contaminated site in frame work of theory of porous media. In this frame work we can simulate all remediation techniques. The theory of porous media provides a comprehensive and excellent framework for modeling multiphasic porous body consisting of immiscible solid skeleton saturated by fluids and missible concentrations in solid and fluid.





Scale bridging multiscale and multiphase FE-simulation of the human liver

T. Ricken, D. Werner


The liver is the central metabolic organ in the human body. The main tasks of the liver are production of proteins, secretion of hormones, removal of waste products and storage as well as depletion of high energy substances. The functionality of the liver is mainly influenced by the perfusion of the smallest repetitive sub elements, the so called lobules. A dysfunctional micro perfusion is mainly caused by diseases of the liver, such as steatosis, cirrhosis or tumor growth.

For the simulation of the functionality and perfusion of the liver we are aiming for a multiphasic, continuum mechanical formulation of the liver, taking the macro scale (organ level), meso scale (liver lobule) and micro scale (metabolism in the hepatocytes) into account. Since the structure of the liver can be described as a porous, fluid saturated solid, use of the Theory of Porous Media (TPM) for modelling the micro perfusion is made. The origin of the TPM lays in the mechanical description of fluid filled soils, formulated in the early 19th century by Terzaghi.


Modeling and simulation of articular cartilage

T. Ricken, D. Albrecht


Articular cartilage is part of the connective tissue of humans and animals. As the only type of connective tissue does it not dispose on an important part of cells. It’s a multi-phase material consisting of fluids, electrolytes and solid parts. The parts can be split in proteoglycans und collagen fibers. The proteoglycans compose the extracellular matrix (ECM), which generates the shape of the tissue und with it the shape of the articular cartilage. The Function of the ECM is the fixation of the collagen fibers in the tissue. In articular cartilage are most of the collagen fibers from type II (~95%). The ECM is streamed by the second phase, the fluid. The fluid consists of tissue water resinated with electrolytes. The volume fraction of the fluid phase, depending on the creature, is in between 30% to 50% of the mass fraction. This is much more as all other connective tissue. The collagen fibers also include fluid. This fluid is fixed in the fibers and cannot squeezed out without damage the fiber, this fluid has only an indirect influence on the stiffness of the collagen fibers. This observation led to the mechanical properties of the articular cartilage. It is a porous material with incompressible, transverse-isotropic material behavior for the fluid as well as the solid. This means the distribution and orientation of the fibers is the central point for the permeability as well as the deformation of the solid fraction.