Browsing by Author "Ehlers, Wolfgang (Prof. Dr.-Ing. Dr. h. c.)"

Now showing 1 - 7 of 7

Open Access
Continuum mechanics of multicomponent materials : modelling, numerics and applications for biological materials in the framework of the theory of porous media
(Stuttgart : Institut für Mechanik (Bauwesen), Lehrstuhl für Kontinuumsmechanik, Universität Stuttgart, 2021) Wagner, Arndt; Ehlers, Wolfgang (Prof. Dr.-Ing. Dr. h. c.)
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.)
Open Access
Model reduction applied to finite-element techniques for the solution of porous-media problems
(Stuttgart : Institut für Mechanik (Bauwesen), Lehrstuhl für Kontinuumsmechanik, Universität Stuttgart, 2019) Fink, Davina; Ehlers, Wolfgang (Prof. Dr.-Ing. Dr. h. c.)
In the present contribution, the developments in the modelling and the simulation of porous materials in the framework of the well-founded Theorie of Porous Media (TPM) are combined with the current state of research in the field of model reduction using projection-based methods. In terms of the continuum-mechanical modelling, this work is focusing on problems developed on the basis of detailed and thermodynamically consistent TPM models. The present work makes use of a biphasic model for the simulation of a saturated porous soil, a multiphasic and multicomponent model for the simulation of drug-infusion processes in brain tissue and an extended biphasic model for the description of an inhomogeneous and anisotropic intervertebral disc. The continuum-mechanical fundamentals of the TPM, required for the description of these models, are outlined. Therefore, the TPM is introduced, all necessary kinematical relations are provided and the balance relations are presented. Furthermore, the general continuum-mechanical fundamentals are specified for the models used in this work. A convenient technique for the solution of arbitrary initial-boundary-value problems is the Finite Element Method (FEM), which is used in this contribution for the numerical treatment of the TPM models. Starting from the weak forms of the governing equations, the spatial and temporal discretisation strategies are described. In this regard, a reduction of the descriptive set of (strongly) coupled partial differential equations provides an enormous benefit to significantly reduce the dimension of these systems and, thus, the computation time and the numerical effort of the FE simulations. Particularly with regard to nonlinear systems, the computational effort is usually immense as high-dimensional equation systems need to be solved repeatedly for the determination of the nonlinearities. Following this, a suitable reduction of these systems essentially improves the efficiency by solving only a subset of equations of the original model. Under consideration of these circumstances, efficient reduced models for the simulation of different porous materials are provided in the present work by an application-driven approach. Thereby, only model-reduction techniques applied to the monolithic solution of the strongly coupled equation systems are considered. The applied model-reduction techniques are explained in detail. In particular, projection-based model-reduction techniques are used to transform a high-dimensional system to a low-dimensional subspace. The advantage of such an approach is to maintain the detailed theoretical basis of the modelling process while an efficient numerical computation is provided. In this contribution, the method of proper orthogonal decomposition (POD) is used as a starting point for the model reduction. However, since the POD-Galerkin approximation does in fact significantly reduce the dimension of the equation system but not the effort to evaluate the nonlinear terms, the computational effort of nonlinear problems cannot be (sufficiently) reduced when exclusively using the POD method. This drawback motivates the application of additional methods for the reduction of the nonlinear terms. Within the scope of this work, the discrete-empirical-interpolation method (DEIM) is used in combination with the POD method to reduce arising nonlinearities. The high complexity of the underlying multiphasic and multicomponent modelling of the treated materials and the resultant strongly coupled equation systems require for individual adaptations and modifications of the used reduction methods to achieve satisfying results. Therefore, the scope of this monograph is the development of an application-driven approach for providing reduced models, which are capable of simulating specific porous materials in a time-efficient manner. The necessary modifications are discussed in detail in this work and are additionally illustrated with examples. In this regard, an in-depth knowledge of the form and the characteristics of the underlying equation system is essential and is therefore treated intensively. Since the outlined modifications might be of great interest for other applications, a generalised approach for an adaptation to other models is finally presented.
Open Access
Parallel simulation of volume-coupled multi-field problems with special application to soil dynamics
(Stuttgart : Institut für Mechanik (Bauwesen), Lehrstuhl für Kontinuumsmechanik, Universität Stuttgart, 2017) Schenke, Maik; Ehlers, Wolfgang (Prof. Dr.-Ing. Dr. h. c.)
Zur Lösung vieler ingenieur- und naturwissenschaftlichen Problemstellungen sind numerische Simulationen ein wichtiges Hilfsmittel. Sie dienen beispielsweise der Wettervorhersage in der Meteorologie oder der Strukturanalyse und Strukturoptimierung im Maschinenbau. In vielen Aufgabenstellungen kann das untersuchte Problem, aufgrund seiner starken Wechselwirkung mit den angrenzenden Systemen, nicht losgelöst betrachtet werden, so dass eine gesamtheitliche Betrachtungsweise notwendig wird. Diese Systeme werden in der Literatur als gekoppelte Probleme bezeichnet. Aufgrund der Komplexität der betrachteten Probleme sind zur effizienten Lösung der zugrunde liegenden Gleichungen parallele Lösungsstrategien von Vorteil. Hierbei wird das Gesamtproblem in kleinere Teilprobleme zerlegt, die gleichzeitig auf verschiedenen Rechnern oder Prozessoren gelöst werden. Um die Vorteile dieses Lösungsverfahrens bestmöglich nutzen zu können, sind erhebliche Anstrengungen zunächst für die initiale Entwicklung und Umsetzung eines effizienten Lösungsverfahrens sowie anschließend für dessen kontinuierliche Weiterentwicklung notwendig. Die vorliegende Monographie beschreibt einen Ansatz zur Kosimulation numerischer Probleme zwischen dem kommerziellen auf der Finite-Elemente-Methode (FEM) basierenden Programmpaket Abaqus und dem für die Forschung entwickelten Löser PANDAS. Durch die Entwicklung einer allgemeinen Schnittstelle können die Materialmodelle von PANDAS direkt, ohne eine langwierige und fehleranfällige Reimplementierung, in eine für die industrielle Anwendung wichtige Simulationsumgebung überführt werden. Hierbei kann direkt auf die umfangreiche Materialmodellbibliothek von PANDAS zurückgegriffen werden. Zur Illustration der Anwendungsmöglichkeiten der Abaqus-PANDAS-Kopplung wird diese exemplarisch zur Simulation verschiedener volumengekoppelter Mehrfeldprobleme herangezogen. Als bodenmechanisches Anwendungsbeispiel wird die Tragfähigkeit eines flüssigkeitgesättigten granularen Materials unter quasi-statischen und dynamischen zyklischen Belastungen untersucht. Weiterhin werden mehrphasige Strömungsprozesse, wie sie z. B. im Produktionsprozess von faserverstärkten Kunststoffen auftreten, numerisch simuliert. Im sogenannten Vaccum-Assisted-Resin-Transfer-Moulding (VARTM), wird ein zunächst trockenes (gasgesättigtes) Fasergewebe kontinuierlich mit Harz getränkt, wobei für die praktische Anwendung insbesondere die Zeit bis zur vollständigen Sättigung und der sich einstellende Faservolumenanteil im fertigen Bauteil von großem Interesse sind. Weiterhin werden die Effizienz und die parallele Skalierbarkeit des vorgeschlagenen Kosimulationsansatzes untersucht.
Open Access
Partially saturated porous solids under dynamic hydraulic fracturing
(Stuttgart : Institut für Mechanik (Bauwesen), Lehrstuhl für Kontinuumsmechanik, Universität Stuttgart, 2023) Sonntag, Alixa; Ehlers, Wolfgang (Prof. Dr.-Ing. Dr. h. c.)
Hydraulic fracturing is a technique where fracking fluids are pressed into the ground to initiate and open fractures, increasing the rock’s permeability. Although this technique is widely used in practice, the fracturing process is controversially discussed and scientifically still not well established. Based on methodical developments, this doctoral thesis enlarges the understanding of the coupled processes occurring during fluid-driven fracturing in partially saturated porous media, where the pore space of the solid skeleton contains both an incompressible liquid and a compressible pore gas. Two main issues are treated simultaneously: the multiphasic nature of solid-fluid interactions in porous media and the crack initiation and propagation in the solid skeleton. The Theory of Porous Media (TPM) allows a rigorous and consistent formulation of the coupled behaviour of the abovementioned three phases. The setup of the continuum-mechanical model is based on the first principles of continuum thermodynamics. In addition, considering the fracturing process in porous media, the phase-field approach to fracture is embedded in the elaborated TPM model. Thereby, the unbroken and broken states of the solid skeleton are differentiated with a scalar phase-field variable. This method avoids the occurrence of a discontinuous jump in the fracturing process and facilitates numerical implementation. The phase field is added to the process variables and integrated into the free energy formulation. This latter is based on a spectral decomposition of the solid strain, such that the phase-field variable reduces the elastic energy under tension, not compression. The model is further enhanced by introducing a crack-opening indicator into the fluid constitutive relations. This procedure enables a transfer from Darcy-type flow in the intact porous material to Stokes-type flow in the fully broken area in a consistent manner. Moreover, special attention is given to the fluid pressure. The liquid and gas phases interact in partially saturated porous material under equilibrium through capillary forces. However, considering injection is a highly dynamic process, the standard hydromechanical relations do not apply here. Therefore, a modified pressure-difference-saturation relation, mapping both equilibrium and dynamic fluid interactions, is proposed and discussed in this thesis. The numerical study builds on the Finite-Element Method. The coupled partial differential equations are solved monolithically with the numerical code PANDAS. Different numerical examples are computed. Specifically, proceeding from a single crack, the solid skeleton’s coupled deformation and fracturing behaviour is examined by considering the different energy proportions. Then, the mutual interaction of the fluids during fracturing is considered in detail. Among others, a gas pressure compression and subsequent gas reflux into the crack are observed. A comparison of fully saturated and partially saturated simulations reveals that the existence of pore gas mainly slows down the fracturing process. This deceleration results from a slower pore pressure build-up induced by gas compressibility. Finally, two kinds of heterogeneities are assessed, going one step further towards realistic scenarios. First, heterogeneities caused by external loads are evaluated. This case is relevant as soils and rocks are frequently under external stresses in nature. Numerical examples with two differently oriented cracks are computed under distinct loading conditions and compared. These examples show the model’s capability to describe open and closed cracks and to discuss the flow behaviour of the liquid and gas phases in both cases. Second, heterogeneities in the porous structure are considered by defining location-dependent material parameters. In this sense, a fluid-driven fracturing process with predefined imperfection areas of higher stiffness is juxtaposed with the homogenous case. As a result, crack branching is observed in the two-field case. Additionally, the model is improved by implementing statistical fields of geomechanical properties. In order to study the influence of this latter, numerical examples with different statistical correlation lengths are compared. Due to the statistical fields of the solid properties, the local stresses spatially vary, and the crack path deviates characteristically. Conclusively, this thesis applied the phase-field approach to fracture within the Theory of Porous Media for fully dynamical problems of partially saturated porous media. It was shown that the gas phase slows down the crack propagation and to what extent local and global heterogeneities influence the crack and flow behaviour. The presented methodical and basis-oriented model can be used for various applications.
Open Access
A phase-field model embedded in the theory of porous media with application to hydraulic fracturing
(Stuttgart : Institut für Mechanik (Bauwesen), Lehrstuhl für Kontinuumsmechanik, Universität Stuttgart, 2019) Luo, Chenyi; Ehlers, Wolfgang (Prof. Dr.-Ing. Dr. h. c.)
Open Access
Variational multiphysics modeling of diffusion in elastic solids and hydraulic fracturing in porous media
(Stuttgart : Institut für Mechanik (Bauwesen), Lehrstuhl für Kontinuumsmechanik, Universität Stuttgart, 2017) Mauthe, Steffen Alexander; Ehlers, Wolfgang (Prof. Dr.-Ing. Dr. h. c.)