02 Fakultät Bau- und Umweltingenieurwissenschaften
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/3
Browse
116 results
Search Results
Item Open Access Phase-field modeling of microstructure and fracture evolution in magneto-electro-mechanics(Stuttgart : Institute of Applied Mechanics, 2020) Sridhar, Ashish; Keip, Marc-André (Prof. Dr.-Ing.)Item Open Access Multiphasic modelling and computation of metastatic lung-cancer cell proliferation and atrophy in brain tissue based on experimental data(2021) Ehlers, Wolfgang; Rehm, Markus; Schröder, Patrick; Stöhr, Daniela; Wagner, ArndtCancer is one of the most serious diseases for human beings, especially when metastases come into play. In the present article, the example of lung-cancer metastases in the brain is used to discuss the basic problem of cancer growth and atrophy as a result of both nutrients and medication. As the brain itself is a soft tissue that is saturated by blood and interstitial fluid, the biomechanical description of the problem is based on the Theory of Porous Media enhanced by the results of medication tests carried out in in-vitro experiments on cancer-cell cultures. Based on theoretical and experimental results, the consideration of proliferation, necrosis and apoptosis of metastatic cancer cells is included in the description by so-called mass-production terms added to the mass balances of the brain skeleton and the interstitial fluid. Furthermore, the mass interaction of nutrients and medical drugs between the solid and the interstitial fluid and its influence on proliferation, necrosis and apoptosis of cancer cells are considered. As a result, the overall model is appropriate for the description of brain tumour treatment combined with stress and deformation induced by cancer growth in the skull.Item Open Access Effects of enzymatically induced carbonate precipitation on capillary pressure : saturation relations(2022) Hommel, Johannes; Gehring, Luca; Weinhardt, Felix; Ruf, Matthias; Steeb, HolgerLeakage mitigation methods are an important part of reservoir engineering and subsurface fluid storage, in particular. In the context of multi-phase systems of subsurface storage, e.g., subsurface CO2 storage, a reduction in the intrinsic permeability is not the only parameter to influence the potential flow or leakage; multi-phase flow parameters, such as relative permeability and capillary pressure, are key parameters that are likely to be influenced by pore-space reduction due to leakage mitigation methods, such as induced precipitation. In this study, we investigate the effects of enzymatically induced carbonate precipitation on capillary pressure-saturation relations as the first step in accounting for the effects of induced precipitation on multi-phase flow parameters. This is, to our knowledge, the first exploration of the effect of enzymatically induced carbonate precipitation on capillary pressure-saturation relations thus far. First, pore-scale resolved microfluidic experiments in 2D glass cells and 3D sintered glass-bead columns were conducted, and the change in the pore geometry was observed by light microscopy and micro X-ray computed tomography, respectively. Second, the effects of the geometric change on the capillary pressure-saturation curves were evaluated by numerical drainage experiments using pore-network modeling on the pore networks extracted from the observed geometries. Finally, parameters of both the Brooks-Corey and Van Genuchten relations were fitted to the capillary pressure-saturation curves determined by pore-network modeling and compared with the reduction in porosity as an average measure of the pore geometry’s change due to induced precipitation. The capillary pressures increased with increasing precipitation and reduced porosity. For the 2D setups, the change in the parameters of the capillary pressure-saturation relation was parameterized. However, for more realistic initial geometries of the 3D samples, while the general patterns of increasing capillary pressure may be observed, such a parameterization was not possible using only porosity or porosity reduction, likely due to the much higher variability in the pore-scale distribution of the precipitates between the experiments. Likely, additional parameters other than porosity will need to be considered to accurately describe the effects of induced carbonate precipitation on the capillary pressure-saturation relation of porous media.Item 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.Item Open Access Fluid-phase transitions in a multiphasic model of CO2 sequestration into deep aquifers : a fully coupled analysis of transport phenomena and solid deformation(Stuttgart : Institut für Mechanik (Bauwesen), Lehrstuhl für Kontinuumsmechanik, Universität Stuttgart, 2017) Häberle, Kai; Ehlers, Wolfgang (Prof. Dr.-Ing. Dr. h. c.)Item Open Access Material forces in finite inelasticity and structural dynamics : topology optimization, mesh refinement and fracture(2008) Zimmermann, Dominik; Miehe, Christian (Prof. Dr.-Ing.)The present work serves two major purposes. On the one hand, theoretical approaches to configurational mechanics are elaborated. For inelastic problems, the spatial and material equilibrium conditions are derived by means of a global dissipation analysis. In the dynamical framework, a variational formulation based on Hamilton's principle is established inducing the balances of physical momentum, material pseudomomentum and kinetic energy. On the other hand, configurational-force-based computational algorithms are developed. At first, configurational forces are exploited in the context of topology optimization. The theoretical basis is provided by a dual variational formulation of finite elastostatics. This scenario is applied to the r-adaptive optimization of finite element meshes and the optimization of truss structures. In the second step, a configurational-force-based strategy for h-adaptvity is presented. The discrete version of the material balance equation is exploited to formulate global and local refinement criteria controlling the overall decision on mesh refinement and the local refinement procedure. The method is specified for problems of finite elasticity and plasticity including thermal and dynamical effects as well. Finally, a configurational-force-driven procedure for the simulation of crack propagation in brittle materials is introduced. The algorithm bases on the separation of the geometry model and the finite element mesh. The process of crack propagation is carried out by a structural update of the underlying geometry model. The generation of the new triangulation incorporates a configurational-force-based adaptive refinement criterion. The capabilities of the derived algorithms are demonstrated by means of a variety of numerical examples including the comparison with benchmark analyses and experimental observations.Item Open Access Spannungs-Verformungsverhalten granularer Materialien am Beispiel von Berliner Sand(2000) Müllerschön, Heiner; Ehlers, Wolfgang (Prof. Dr.-Ing.)Die makroskopische Beschreibung des komplexen Materialverhaltens einer granularen Struktur erfordert die Berücksichtigung verschiedenster materialspezifischer Eigenschaften. Hierzu wird in der vorliegenden Arbeit ein elasto-plastisches Stoffmodell vorgestellt, basierend auf experimentellen, theoretischen und numerischen Untersuchungen. Im experimentellen Bereich ist die Durchführung von Triaxialversuchen mit geeigneten Randbedingungen zu nennen. Dabei ist die Einhaltung homogener Spannungs- und Verzerrungsfelder im Inneren der Probe zu gewährleisten. Desweiteren wird eine neue Methode zur exakten Messung von sehr kleinen Probenvolumenänderung vorgestellt. Bei der theoretischen Materialmodellierung spielt die Entwicklung eines geeigneten Elastizitätsgesetzes für Reibungsmaterialien eine zentrale Rolle. Dazu wird zuerst eine Literaturrecherche mit einer Beurteilung von vorhandenen Elastizitätsgesetzen durchgeführt. Im Anschluß daran wird ein Vorschlag für eine neue Verzerrungsenergiefunktion gemacht, deren Eigenschaften ausführlich diskutiert werden. Auf der Basis von Ergebnissen aus experimentellen Entlastungsschleifen bei Triaxialversuchen wird eine Parameteridentifikation für das vorgestellte Elastizitätsmodell durchgeführt. Aufbauend auf Vorarbeiten von Ehlers (1993) im Bereich der Plastizitätstheorie werden zur Modellierung des plastischen Deformationsverhaltens vorhandene Konstitutivgleichungen erweitert und spezialisiert. Dazu werden Evolutionsgleichungen zur Beschreibung der Materialverfestigung in Abhängigkeit der akkumulierten plastischen Arbeit eingeführt. Auf der Basis von triaxialen Kompressions- und Extensionsversuchen sowie von hydrostatischen Kompressionsversuchen erfolgt eine Parameteridentifikation der im Modell enthaltenen Materialparameter mit Hilfe der Formulierung von Least-Squares-Funktionalen.Item Open Access Multi-level descriptions of failure phenomena with the strong discontinuity approach(2014) Raina, Arun; Miehe, Christian (Prof. Dr.-Ing.)The ever increasing demand of advanced engineered products also pushes the strengths of the materials used to their theoretical limits. It becomes crucially important to understand the behavior of such materials during failure for an efficient and safe design of the product. This thesis aims at the physical-based numerical modeling of complex failure phenomena in engineering materials, categorized into hard matter and soft matter. In Part I of this thesis, a modification of the well established strong discontinuity approach to model failure phenomena in hard matter by extending it to multiple levels is proposed. This is achieved by the resolution of the overall problem into a main boundary value problem and identified sub-domains based on the concepts of domain decomposition. Those sub- domains are subsequently adaptively discretized during run-time and comprise the so- called sub-boundary value problem to be solved simultaneously with the main boundary value problem. To model failure, only the sub-elements of those sub-boundary value problems are treated by the strong discontinuity approach which, depending on their state of stress, may develop cracks and shear bands. A single finite element of the main boundary value problem can therefore simulate the propagation of multiple propagating strong discontinuities specially arising for simulations of crack branching. The solutions of the different sub-boundary value problems are transferred to the main boundary value problem based on concepts of domain decomposition. The applied boundary conditions are also modified to account for the possible multiple jumps in the displacement fields. It is shown through the simulation of solids undergoing dynamic fracture that the modification allows to predict the onset of crack branching without the need for any artificial crack branching criterion. A close agreement with experiments of the simulation results in terms of micro- and macro branching in addition to studying certain key parameters like critical velocity, dynamic stress intensity factor, and the strain energy release rate at branching is found. In Part II of this thesis, failure phenomena in soft matter is modeled for which an advanced homogenization approach to model the highly anisotropic and non-linear stiffening response at finite strains is developed first. The constituent one-dimensional elements are modeled as linear elastic, by experimental justification, which are modified in the lower strain regime to account for the inherent fiber undulations and the associated fiber unfolding phenomena. Reorientation of these fibers is identified as one primary mechanism for the overall macroscopic stiffening which is achieved by a new bijective mapping asymptotically aligning these fibers with the maximum loading direction in the referential orientation space. A rate-independent evolution law for this map is sought by a physically motivated assumption to maintain the overall elastic framework of the proposed formulation. A closed form solution to the new evolution law is also presented which allows faster computation of updating orientations without resorting to numerical integration or storing history variables. The unit vectors upon reorientation in the referential orientation space are then mapped to the spatial orientation space by the macro deformation gradient to compute the macroscopic Kirchhoff stress and the associated spatial elasticity modulus. A direct comparison of the numerical results with the experimental results from the literature is made which demonstrates the predictive capabilities of the proposed formulation. Finally, the finite deformation extended strong discontinuity approach is utilized to simulate boundary value problems of failure in nonwoven felts. The simulation results of failure show a satisfactory agreement with the experimental data from literature.Item Open Access On the computational modeling of micromechanical phenomena in solid materials(2013) Linder, Christian; Miehe, Christian (Prof. Dr.-Ing. habil.)This work aims to contribute to the research on the constitutive modeling of solid materials, by investigating three particular micromechanical phenomena on three different length scales. The first microscopic phenomenon to be considered on the macroscopic scale is the process of failure in solid materials. Its characteristic non-smoothness in the displacement field results in the need for sophisticated numerical techniques in case one aims to capture those failure zones in a discrete way. One of the few finite element based methods successfully applied to such challenging problems is the so called strong discontinuity approach, for which failure can be described within the individual finite elements. To avoid stress locking, a higher order approximation of the resulting strong discontinuities is developed in the first part of this work for both, purely mechanical as well as electromechanical coupled materials. A sophisticated crack propagation concept relying on a combination of the widely used global tracking algorithm and the computer graphics based marching cubes algorithm is employed to obtain realistic crack paths in three dimensional simulations. Secondly, materials with an inherent network microstructures such as elastomers, hydrogels, non-woven fabrics or biological tissues are considered. The development of advanced homogenization principles accounting for such microstructures is the main focus in the second part of this work to better understand the mechanical and time-dependent effects displayed by such soft materials. Finally, the incorporation of wave functions into finite element based electronic structure calculations at the microscopic scale aims to account for the fact that the properties of condensed matter as for example electric conductivity, magnetism as well as the mechanical response upon external excitations are determined by the electronic structure of a material.Item Open Access Hybrid micro-macro modeling of texture evolution in polycrystal plasticity based on microstructural reorientation continua(2013) Zimmermann, Ilona Andrea; Miehe, Christian (Prof. Dr.-Ing.)The present work deals with the modeling of evolving crystal orientation microstructures in finite polycrystal plasticity and its impact on the macroscopic material behavior by means of a two-scale approach. A micro-mechanical plasticity model is developed that locally accounts for microscopic structural changes in the form of grain reorientations. The algorithmic treatment captures in a numerically efficient manner the crystal reorientation for evolving face- and body-centered cubic textures. Thereby, the parametrization of rotations is carried out in the Rodigues space. The performance is demonstrated by means of representative numerical examples. As a key ingredient the crystallographic texture is responsible for the development of macroscopic anisotropy, entailing the necessity of a multiscale approach for appropriately predicting the material behavior. Crystal orientation distribution functions govern the evolution of structural tensors, representing in a homogenized sense the crystal reorientation within a model-inherent scale bridging technique. The texture estimation is incorporated in a modular format into a micro-macro model resulting in a computationally manageable approach compared to straightforward homogenization-based multiscale methods, such as e.g. FE2. A macro-mechanical model of anisotropic finite plasticity is based on evolving structural tensors accounting for the texture-induced macroscopic anisotropy. The general framework for the micro-macro modeling is a purely phenomenological setting of anisotropic plasticity in the logarithmic strain space. The capabilities and computationally efficiency of his hybrid two-scale model of finite polycrystalline plasticity is demonstrated by means of a variety of numerical examples including the comparison with benchmark analyses and experimental observations.