Universität Stuttgart

Permanent URI for this communityhttps://elib.uni-stuttgart.de/handle/11682/1

Browse

Search Results

Now showing 1 - 10 of 62

Open Access
An extended biphasic description of the inhomogeneous and anisotropic intervertebral disc
(2009) Karajan, Nils; Ehlers, Wolfgang (Prof. Dr.-Ing.)
It is the aim of this contribution to develop a finite element model, which is as simple as possible, but at the same time complex enough to capture many of the occurring tissue properties of the intervertebral disc (IVD). In order to better understand these properties from an engineering point of view, the needed basic anatomical knowledge is briefly reviewed in the beginning of this treatise, thereby addressing the lumbar spine with focus on the IVD and its material properties. In particular, the IVD appears as the largest avascular part of the body and its microstructure leads to an electro-chemically active material with anisotropic, inhomogeneous and strongly dissipative behaviour. In the following main part of this work, the complete continuum-mechanical modelling process is extensively discussed as well as the numerical treatment of the resulting governing equations. Starting from the thermodynamically consistent Theory of Porous Media (TPM), two phases and three components are introduced for the description of IVD tissue. In particular, this is the extracellular matrix (solid skeleton) carrying fixed negative charges which is saturated by a pore fluid consisting of a solvent (liquid) as well as anions and cations of a dissolved salt. Following the idea of superimposed continua, an individual motion function is introduced for each of the constituents, whereas the components of the pore fluid are always expressed relative to the deforming solid skeleton. In order to capture the finite kinematics of the inelastic solid skeleton, its deformation gradient is multiplicatively split into inelastic and elastic parts. Next, the materially independent balance equations are derived from the respective master balances and accustomed to the soft biological tissue under study. In order to keep the resulting set of equations as simple as possible, while still keeping the ability to reproduce osmotic effects, an assumption according to Lanir is made. In this context, the tissue is regarded to be always immediately in electro-chemical equilibrium, which allows to describe the electro-chemically active tissue using only an extended biphasic model. Applying van't Hoff's law finally allows to compute the occurring osmotic pressure as a function of the solid displacement. Moreover, in order to characterise the inhomogeneous anisotropic and viscoelastic solid skeleton as well as the viscous pore fluid, several constitutive equations need to be formulated, thereby depending on a thermodynamically admissible set of process variables. Herein, the endangerment of postulating nonphysical constitutive assumptions is avoided by strictly following the restrictions resulting from the evaluation of the entropy inequality. Finally, the chosen constitutive functions of the solid skeleton are based on Ogden-type strain energy functions, which automatically include several simpler material laws. The viscoelastic contribution is based on a generalised Maxwell model which is dominated by the concept of internal variables with linear evolution equations. Finally, the superimposed dissipative effect of the viscous pore fluid is captured using the famous Darcy filter law. As a last step, the applicability of the derived model is proven with realistic computations of the IVD. Herein, the resulting set of governing partial differential equations is discretised in time and space using the finite difference method and the mixed finite element method, respectively. The theoretically introduced material parameters are determined using experimental data as well as material parameters obtained from a vast collection of related literature sources. Since many parameters appear in a coupled manner, their identification is often only possible via inverse computations. Following this, a numerical sensitivity analysis is carried out yielding an indication for the relevant parameters in experiments concerning a motion segment in a short-duration compression-flexion experiment as well as in long-term loading situations. Subsequently, the efficiency of the implementation is demonstrated by a parallel simulation of a lumbar spine segment carried out on 84 processors simultaneously, thereby exhibiting almost one million degrees of freedom.
Open Access
A microstructurally-based, multi-scale, continuum-mechanical model of skeletal muscle tissue
(2019) Bleiler, Christian; Ponte Castañeda, Pedro; Röhrle, Oliver
Open Access
Permeability estimation of regular porous structures : a benchmark for comparison of methods
(2021) Wagner, Arndt; Eggenweiler, Elissa; Weinhardt, Felix; Trivedi, Zubin; Krach, David; Lohrmann, Christoph; Jain, Kartik; Karadimitriou, Nikolaos; Bringedal, Carina; Voland, Paul; Holm, Christian; Class, Holger; Steeb, Holger; Rybak, Iryna
The intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny-Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions.
Open Access
Modeling the chemoelectromechanical behavior of skeletal muscle using the parallel open-source software library OpenCMISS
(2013) Heidlauf, Thomas; Röhrle, Oliver
An extensible, flexible, multiscale and multiphysics model for non-isometric skeletal muscle behavior is presented. The skeletal muscle chemoelectromechanical model is based on a bottom-up approach modeling the entire excitation-contraction pathway by strongly coupling a detailed biophysical model of a half-sarcomere to the propagation of action potentials along skeletal muscle fibers, and linking cellular parameters to a transversely isotropic continuum-mechanical constitutive equation describing the overall mechanical behavior of skeletal muscle tissue. Since the multiscale model exhibits separable time scales, a special emphasis is placed on employing computationally efficient staggered solution schemes. Further, the implementation builds on the open-source software library OpenCMISS and uses state-ofthe-art parallelization techniques taking advantage of the unique anatomical fiber architecture of skeletal muscles. OpenCMISS utilizes standardized data structures for geometrical aspects (FieldML) and cellular models (CellML). Both standards are designed to allow for a maximum on flexibility, reproducibility, and extensibility. The results demonstrate the model´s capability of simulating different aspects of non-isometric muscle contraction and to efficiently simulate the chemoelectromechanical behavior in complex skeletal muscles such as the tibialis anterior muscle.
Open Access
Coupled deformation and flow processes of partially saturated soil : experiments, model validation and numerical investigations
(2013) Avci, Okan; Ehlers, Wolfgang (Prof. Dr.-Ing.)
The main focus of the presented thesis lies on realistic simulations of initial-boundary-value problems (IBVP) in the field of geomechanics using a partially saturated soil. To reach this goal, the deformation and flow behaviour of the partially saturated soil has been intensively analysed based on the topics of the experimental investigation, the constitutive modelling, the parameter identification and model validation. Due to the coupled deformation and flow process of partially saturated soils, accurate experimental investigations of their mechanical and hydraulic behaviour are very complex and sophisticated. For the modelling of the partially saturated soil in the framework of the Theory of Porous Media (TPM), the principle of phase separation is applied. Based on this principle, the mechanical and hydraulic properties of the soil can be simply experimentally investigated in a decoupled manner. That means the mechanical deformation-dependent properties of the test material GEBA sand are experimentally investigated on dry sand via drained triaxial experiments with homogeneous boundary conditions, whereas the hydraulic behaviour is determined with deformation-free experiments. In the context of the soil modelling, the mutual interactions of the individual phases of the soil are taken into account by additional production terms (physical coupling terms). On the basis of these experiments, all required constitutive equations for the triphasic soil model have been derived thermodynamically consistent within the TPM. A cruical point in the matter of material modelling is the experimental investigation of the test material, because false measurements or faulty experimental equipments produce faulty data sets. Based on faulty results, wrong conclusions and assumptions of the material behaviour would be drawn and, thus, would lead to incorrect constitutive modelling approaches. In this regard, in order to ensure a measurement of triaxial tests as error-free as possible, the employed triaxial test setup is optimised concerning measuring error sources. The yield as well as the failure behaviour of dense sand is investigated by use of drained triaxial experiments. Especially, it could be shown through triaxial stress-path-depending compression tests that the standard model approach to limit the hardening of the yield surface by a fixed failure surface is not correct. The experimental results show that the evolution of the yield surface is limited by a variable failure surface depending on the hydrostatic stress state. The good agreement of the simulations with the experiments shows that the presented model approach with a hydrostatic stress-dependent failure surface is promising for realistic simulations of quasi-static IBVP of cohesionless-frictional materials. Constitutive models for materials with an non-linear elastic and a plastic hardening and softening behaviour are complex and own many material parameters. For the identification of the large number of material parameters on the basis of experimental data, the FE tool PANDAS was coupled with the gradient-based SQP optimisation method. The required sensitivities of the fitted quantities of the non-linear restricted optimisation problem with respect to the optimised material parameters are computed semi-analytically. The validation of the triphasic soil model in regard to the coupled deformation and flow processes is carried out by numerical simulation of different slope failure scenarios at the technical scale. The numerical results showed that the presented TPM soil model is well suited to mimic the physical behaviour of multiphasic materials such as partially saturated sand and is also be able to reliably predict slope failure triggered by varying the hydraulic boundary conditions. Additionally, the triphasic soil model is applied for the simulation of natural slope movement and is tested for its capability to predict possible failure mechanisms. This investigation is carried out by numerical FE analysis of the Heumös hillslope in Ebnit (Austria). The triphasic model is further extended to model internal soil-erosion problems. Concerning this, an erosion phase is introduced, which represents the fluidised grains detached from the soil skeleton by the streaming pore water. The objective of the numerical investigation of erosion problems is focused on the analyses of embankment destabilisations induced by loosing solidity due to the internal erosion. In this regard, several numerical examples are presented and discussed.
Open Access
Weak or strong : on coupled problems in continuum mechanics
(2010) Markert, Bernd; Ehlers, Wolfgang (Prof. Dr.-Ing.)
The present work aims at giving a concise introduction to the vast field of coupled problems, particularly to those of importance in engineering and physics. Therefore, the common terminology and an appropriate classification of coupled equation systems is presented accompanied by some mathematical and computational issues. Attention is focused on volumetrically coupled multi-field formulations arising from the continuum mechanical treatment of multi-physics problems, but also geometrically coupled problems are addressed. Based on actual problems in the areas of poroelastodynamics, continuum biomechanics, and fluid-saturated porous media in general both the theoretical modeling by means of coupled continuum equations as well as the efficient numerical solution in the context of the finite element method (FEM) are presented and discussed in a problem-oriented fashion.
Open Access
Beschreibung und Anwendung eines elastisch-plastischen Materialmodells mit Schädigung für hochporöse Metallschäume
(2002) Droste, Alexander; Ehlers, Wolfgang (Prof. Dr.-Ing.)
Die Nachfrage nach intelligenten Leichtbaukonzepten für alle Sparten der modernen Transportindustrie steigt ständig. Dabei bestimmen Werkstoffe und Werkstofftechnologien in entscheidender Weise die Anwendbarkeit und Wirtschaftlichkeit der Produkte. Primäre Ziele sind die maximale Energie und Rohstoffeinsparung unter zusätzlichen ökologisch und ökonomischen Randbedingungen, beispielsweise niedrige Herstellungskosten, Gewichtsreduktion und Recyclingfähigkeit. Die Forderung nach geringeren Betriebs- und Fertigungskosten, höheren Nutzlasten, verbesserter Umweltverträglichkeit, erhöhter Unfallsicherheit und steigendem Komfort stellen dabei eine nicht immer leicht zu erfüllende Optimierungsaufgabe an die Produkte und an die verwendeten Materialien dar. Aus technischer Sicht werden Formstabilität und Biegesteifigkeit bei gleichzeitiger Dichtereduzierung als eine effektive Lösung dieser Problematik gesehen. Als Ergebnis solcher Forderungen erweitert die Herstellung und Anwendung metallischer Schäume das Spektrum bestehender Materialien wie Wabenstrukturen (Honeycombs) und Kunstoffschäumen, die bereits erfolgreich im großtechnischen Einsatz sind. Insbesondere die Kombination der hohen spezifischen Steifigkeit und der hohen Energiedissipation in 'Crash'-Situationen in Kombination mit einer geringen spezifischen Dichte führen zu einem deutlich erweiterten Eigenschaftsspektrum. Metallische Schäume bieten Vorteile bezüglich Festigkeit, Temperaturbeständigkeit, Umweltverträglichkeit und Wirtschaftlichkeit gegenüber den bestehenden Materialien. Dabei kann speziellen technischen Anforderungen durch neue Verfahren gezielt über den Herstellungsprozeß und das verwendete Matrixmaterial Rechnung getragen werden. In der vorliegenden Arbeit geht es um die numerische Darstellung des Materialverhaltens solcher hochporösen Metallschäume. Hierdurch lassen sich durch numerischen Verfahren Aussagen über das zu erwartende Verhalten eines solchen Materials bei Belastung treffen. Die Herleitung und Anwendung eines finiten Materialmodells mit Schädigung wird vorgestellt.
Open Access
From particle mechanics to micromorphic continua
(Stuttgart : Institut für Mechanik (Bauwesen), Lehrstuhl für Kontinuumsmechanik, Universität Stuttgart, 2019) Bidier, Sami; Ehlers, Wolfgang (Prof. Dr.-Ing Dr. h. c.)
Classical material tests observe the macroscopic behaviour of structures and materials. However, the material response to an external loading always results from the composition and the interaction of the material at different time and length scales. Kinematically extended microcontinuum theories offer one way of incorporating some microstructural effects into a continuum-based modelling strategy. Thereby, the macroscopic motion at a material point is extended by a micromotion that should consider all relevant microscopic deformation mechanisms. The focus of this monograph is on the relation between the mechanics of granular media and one type of microcontinuum theories, the so-called micromorphic approach. Therefore, a homogenisation method that links particle-based information from the microscale with macroscopic quantities of micromorphic character is presented. To verify the established homogenisation methodology, particle-based simulations of material failure in granular materials are used, supplying the necessary microstructural information, which are then processed towards the scale of Representative Elementary Volumes (REV). The idealised model allows for the transition of the continuously formulated averaging formalisms towards discrete forms in which only a ﬁnite number of particles are evaluated for the computation of the stress and strain quantities on the level of an REV.
Open Access
Mehrskalenmodelle in der Festkörpermechanik und Kopplung von Mehrgittermethoden mit Homogenisierungsverfahren
(2005) Bayreuther, Claus; Miehe, Christian (Prof. Dr.-Ing.)
Ziel dieser Arbeit ist die Formulierung von nichtlinearen homogenisierten Ersatzmodellen für mikroheterogene Materialien und die Konstruktion problemabhängiger Transferoperatoren für Mehrgitterverfahren. Beide Themenkomplexe haben eine effiziente Beschreibung heterogener Festkörperstrukturen zum Ziel. Die Simulation von Verbundstrukturen stellt ein sehr komplexes Problem dar, insbesondere wenn die Skalenabhängigkeit des Werkstoffs miteinbezogen wird. Dies gründet darin, daß die Dimension des makroskopischen Randwertproblems und die Abmessungen der Heterogenitäten auf der Mikroskale stark voneinander abweichen können. In diesem Fall ist eine effiziente Modellierung nur durch geeignete Mehrskalenbildung möglich. In dieser Arbeit werden analytische und neu entwickelte numerische Homogenisierungsmodelle für Skalenübergänge aufbereitet. Im Gegensatz zu analytischen Konzepten gestattet die Methode der Finite Elemente universelle Einsatzmöglichkeiten der numerischen Modelle. Die neuen numerischen Ansätze basieren auf diskreten Variationsprinzipien, deren Umsetzung auf der Mikroskale die Lösung eines Randwertproblems mit speziellen Randbedingungen erfordert: (i) lineare oder (ii) periodische Randverschiebungen oder (iii) homogene Randspannungen auf dem Rand einer charakteristischen Mikrostruktur. Die Effizienz der neuen numerischen Ersatzmodelle wird anhand repräsentativer Einheitszellen verifiziert. Bei kleiner Skalenseparation führt die direkte numerische Diskretisierung des Verbundwerkstoffs in der Regel auf großdimensionierte Gleichungssysteme, die den Einsatz schneller Löser, wie Mehrgitterverfahren, bedingen. Bei Mehrgittermethoden liegt die Schwierigkeit in der Konstruktion geeigneter Transferoperatoren. In dieser Arbeit wird dieses Problem durch Einbeziehung der neu entwickelten Homogenisierungstechniken gelöst. Effizienz und Anwendungsgrenzen der neuen Transferoperatoren werden an typischen Modellproblemen im Vergleich zu alternativen Konzepten aufgezeigt.
Open Access
Chemo-electro-mechanical modelling of the neuromuscular system
(2015) Heidlauf, Thomas; Röhrle, Oliver (Prof., PhD)
Body movement is the result of cascades of complex chemical, electrical, and mechanical processes taking place at different length and time scales. This thesis deals with the biophysical modelling of these processes. In detail, the generation of electrical signals in spinal motor neurons is investigated based on the Hodgkin-Huxley formalism. Next, the complex signaling pathway leading from electrical excitation to contraction and force generation of the muscle fibres is modelled. Based on a structural model of the muscle and the bidomain equations, a method is proposed to predict electromyographic signals, which are frequently recorded in the clinic and result from the propagation of electrical signals along the muscle fibres to induce the contraction. Extending this model by a continuum-mechanical approach, a multiscale model of the neuromuscular system is obtained that considers chemical, electrical, and mechanical properties and allows to predict force generation, muscle deformation, and the EMG signal during fixed-length and non-isometric contractions. The proposed framework can potentially be used as an in-silico laboratory to investigate changes in the behaviour resulting from pathological conditions or drug treatment.

Universität Stuttgart

Browse

Filters

Settings

Sort By

Results per page

Search Results