Universität Stuttgart
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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 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.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 The role of parvalbumin, sarcoplasmatic reticulum calcium pump rate, rates of cross-bridge dynamics, and ryanodine receptor calcium current on peripheral muscle fatigue: a simulation study(2016) Röhrle, Oliver; Neumann, Verena; Heidlauf, ThomasItem Open Access Coupled problems in the mechanics of multi-physics and multi-phase materials(2015) Zinatbakhsh, Seyedmohammad; Ehlers, Wolfgang (Prof. Dr.-Ing.)To select a suitable solution strategy is certainly a vital step towards successful simulation of physical phenomena. Considering this, the presented study was set out to explore the important aspects regarding numerical treatment of couple problems stemming from mathematical modelling of coupled multi-field systems. Such coupled systems are observed in a broad range of applications in distinct disciplines. The versatility of the applications has attracted many experts, who have examined coupled problems from different angles. Thus, the mission to fulfil the goals of the present project entailed scrutinising a complex field comprising a vast number of publications incorporating various nomenclatures, classifications, solution strategies, stability analysis procedures, etc. Reviewing the related works, it was noticed that in many cases either a proper explanation of the presented procedures is missing or authors interpret the methods in a rather mathematical way that makes it puzzling for researchers from more application-oriented disciplines. Recognising this flaw, the focus was especially directed towards avoiding abstraction and, instead, presenting an interpretation of the related concepts in an application-friendly style. To this end, a great amount of effort was invested in understanding and explaining the solution strategies proposed for the coupled problems and revealing the relations between them. In particular, several partitioning techniques, including the primal and the dual Schur complement methods, the global and the localised Lagrange-multiplier schemes, and also partitioning methods that follow a staggered integration were investigated and the relations between them were established. Apart from that, the notions related to the stability of the numerical schemes were introduced and their significance was explained. In particular, the terminologies, the stability criteria and the relation between them were reinterpreted in an application-related manner, where the explanations were supported by several examples. This study eventually led to the development of a stability analysis algorithm that can be employed to find the critical grid sizes in different scenarios with minimum difficulty and without any need to solve the whole problem. Furthermore, our attempt in employing the localised Lagrange-multiplier method for partitioning of the surface- coupled problem of fluid-porous-media interaction led to a parallel decoupled solution strategy, comprising a novel application of the concept of modified Eulerian description for describing the motion of a fluid body within moving boundaries, implementation of the penalty method for modelling of fluid as well as porous bodies using the FE-solver PANDAS, and generation of a workflow structure facilitating communication between existing modules of PANDAS.Item 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.Item 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.Item 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.