02 Fakultät Bau- und Umweltingenieurwissenschaften
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/3
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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 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 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.Item Open Access Variational homogenization in electro-mechanics : from micro-electro-elasticity to electroactive polymers(2014) Zäh, Dominic; Miehe, Christian (Prof. Dr.-Ing.)In recent years an increasing interest in functional or smart materials such as ferroelectric polymers and ceramics has been shown. Regarding the technical implementation of smart systems a broad variety of physically-based phenomena and materials are available, where some of the most important coupling effects are the shape memory effect, magnetostriction, electrostriction, and piezoelectricity. Typical fields of application are adaptive or controlled systems such as actuators and sensors, micro-electro-mechanical systems (MEMS), fuel injectors for common rail diesel engines, ferroelectric random access memories, and artificial muscles used in robotics. A highly interesting class of these materials are piezoceramics, coming up with short response times, high precision positioning, relatively low power requirements, and high generative forces, providing an excellent opportunity for mass production. Typical examples of such materials are barium titanate and lead zirconate titanate crystals and polycrystals, which exhibit linear and nonlinear coupling phenomena as well as hysteresis under high cyclic loading. At the microscale level, these materials are composed of several homogeneously polarized regions, called ferroelectric domains, whose evolution in time is driven by external electric fields and stresses applied to a sample of the material. Ferroelectric domains are regions of parallel and hence aligned polarization. Electric poling can be achieved by the application of a sufficiently strong electric field, inducing the reorientation and alignment of spontaneous polarization. As a consequence, piezoceramics exhibit a macroscopic remanent polarization. On the other hand, there are electroactive polymers (EAPs) responding by a (possibly large) deformation to an applied electrical stimulus, an effect discovered by the physicist Wilhem Röntgen in 1880 in an experiment on a rubber strip subjected to an electric field. They are divided into two main groups: electronic and ionic materials. The description of these effects through models of continuum physics is a subject of extensive research. Physically predictive material modeling can be performed on different length- and time scales. The classical setting of continuum mechanics develops phenomenological material models "smeared" over some continuously distributed material, where the material parameters are determined from experimental data. Nowadays developed multiscale techniques focus predominantly on the efficient bridging of neighboring length- and time scales, e.g. the incorporation of the microscopic polarization in order to predict macroscopic hysteresis phenomena. With a continuous increase in computational power and the development of efficient numerical solvers, real multiscale simulations seem to be a reachable goal. Computational homogenization schemes determine, in contrast to initially developed Voigt and Reuss bounds, the effective properties numerically. No constitutive model is explicitly assumed at the macroscale, and the material response at each point is determined by performing a separate numerical analysis at the micro-level. The macroscopic material behavior in this two-scale scenario is then determined by separate FE computations at the microscale. Main ingredients of such a framework are, on the one hand, the solution of a microscopic material model describing mechanical behavior at the representative volume element and, on the other hand, a homogenization rule determining the macroscopic stress tensor by its microscopic counterpart. Goal of these computational homogenization techniques is the modeling of the overall response based on well-defined microstructural information. Concerning the scale transition for functional materials, it is necessary to extend the homogenization principles to coupled problems, incorporating besides the mechanical displacement further primary variables such as the electric potential and the electric polarization. The key aspect of every homogenization scheme is the determination of macroscopic quantities in terms of their microscopic counterpart, driven by appropriate constraints or boundary conditions on the representative volume element. The micro-to-macro transition can be described in a canonical manner by variational principles of homogenization, determining macroscopic potentials in terms of their microscopic counterparts.Item Open Access Approaches to the description of anisotropic material behaviour at finite elastic and plastic deformations : theory and numerics(2004) Apel, Nikolas; Miehe, Christian (Prof. Dr.-Ing.)The present work deals with purely macroscopic descriptions of anisotropic material behaviour. Key aspects are new developments in the theory and numerics of anisotropic plasticity. After a short discussion of the classification of solids by symmetry transformations a survey about representation theory of isotropic tensor functions and tensor polynomials is given. Next alternative macroscopic approaches to finite plasticity are discussed. When considering a multiplicative decomposition of the deformation gradient into an elastic part and a plastic part, a nine dimensional flow rule is obtained that allows the modeling of plastic rotation. An alternative approach bases on the introduction of a metric-like internal variable, the so-called plastic metric, that accounts for the plastic deformation of the material. In this context, a new class of constitutive models is obtained for the choice of logarithmic strains and an additive decomposition of the total strain measure into elastic and plastic parts. The attractiveness of this class of models is due to their modular structure as well as the affinity of the constitutive model and the algorithms inside the logarithmic strain space to models from geometric linear theory. On the numerical side, implicit and explicit integration algorithms and stress update algorithms for anisotropic plasticity are developed. Their numerical efficiency crucially bases on their careful construction. Special focus is put on algorithms that are suitable for variational formulations. Due to their (incremental) potential property, the corresponding algorithms can be formulated in terms of symmetric quantities. A reduced storage effort and less required solver capacity are key advantages compared to their standard counterparts.Item Open Access A multiphasic continuum mechanical model for design investigations of an effusion-cooled rocket thrust chamber(2005) Ghadiani, Saeed Reza; Ehlers, Wolfgang (Prof. Dr.-Ing)In this thesis, the new concept of the German Aerospace Center (DLR) for an effusion-cooled ceramic rocket combustion chamber is investigated. Using effusion cooling, the porous inner liner of the chamber is cooled by passing the coolant through its pores. The theoretical treatment of the fluid-saturated deformable porous construction under non-isothermal conditions leads to a coupled solid-fluid model which is formulated in this thesis within the framework of the Theory of Porous Media (TPM). The multiphasic continuum mechanical model created allows for the definition of mechanical loads, thermal loads as well as a fluid mass flow across the boundary. All necessary constitutive equations are physically expedient conclusions resulting from the evaluation of the determining entropy inequality. The FE-tool PANDAS from the Institute of Mechanics (civil engineering) at University of Stuttgart is used as numerical solver. The numerical simulations discussed in this work are restricted to the qualitative demonstration of the most important physical effects occurring in the construction under study. For a real design study, material parameters have to be determined by experiments which are not the subject of this thesis. Corresponding experiments are being performed in ongoing activities at the DLR. The model presented in this work has to be understood as a general tool for the design investigation of actively cooled porous constructions.