Universität Stuttgart
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Item 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 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 A microstructurally-based, multi-scale, continuum-mechanical model of skeletal muscle tissue(2019) Bleiler, Christian; Ponte Castañeda, Pedro; Röhrle, OliverItem 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.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 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 Variational multifield modeling of the formation and evolution of laminate microstructure(2013) Hildebrand, Felix Eberhard; Miehe, Christian (Prof. Dr.-Ing.)The optimization of material properties and the design of new materials with tailored material behavior are among the greatest challenges in the field of computational continuum mechanics. Since the macroscopic material behavior of many technically relevant materials is very closely linked to their microstructure, a profound physical and mathematical understanding and a reliable computational prediction of the formation and evolution of this microstructure is the necessary basis for any optimization or material design. In this work, we focus on the physical and mathematical understanding and the modeling and simulation of laminate microstructure and use the modeling framework of gradient-extended standard-dissipative solids to construct a phase field model for martensitic laminate microstructure in two-variant martensitic CuAlNi and a gradient crystal plasticity model for laminate deformation microstructure in Copper with two active slip systems on the same slip plane. We derive rate- and incremental-variational as well as finite element formulations for the two models and carry out numerical simulations. Basis for our modeling are the modeling framework of gradient-extended standard-dissipative solids on the one hand, and the continuum theory of non-material sharp interfaces with interface energy on the other hand, from which we derive the condition of kinematic compatibility, jump conditions in analogy to the balance equations and the dissipation postulate for the moving interface. We consider the variational origin of the formation of laminate microstructure and identify gradient-extended modeling approaches as the suitable choice for the modeling of the formation and dissipative evolution of laminate microstructure with interface energy. Based on these considerations, we propose a phase field model for the formation and evolution of laminate microstructure in two-variant martensitic CuAlNi that is based on the variational smooth approximation of sharp topologies and contains a coherence-dependent interface energy. We show that an internal mixing approach for the bulk energy allows a clear separation of interface and bulk energy and that the model is capable of predicting the formation and dissipative evolution of martensitic laminate microstructure and size effects. Furthermore, we propose a gradient crystal plasticity model for Copper with two active slip systems on the same slip plane that allows a prediction of both the formation and evolution of plastic laminate microstructure and incorporates the effect of geometrically necessary dislocations (GNDs). The model contains a biquadratic non-convex latent hardening function and a gradient contribution based on the dislocation density tensor. The evolution equations of the plastic slips and the accumulated plastic slips are obtained by use of a rate regularization that makes use of the approximation of |x| as a*ln(cosh(x/a)) for a<<1. The model is shown to be capable of predicting the formation and evolution of deformation laminate microstructure together with length-scale effects related to GNDs.Item 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.Item Open Access Modeling the chemoelectromechanical behavior of skeletal muscle using the parallel open-source software library OpenCMISS(2013) Heidlauf, Thomas; Röhrle, OliverAn 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.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.