Universität Stuttgart
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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 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 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 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 A variational framework for gradient-extended dissipative continua : application to damage mechanics, fracture, and plasticity(2011) Welschinger, Fabian Richard; Miehe, Christian (Prof. Dr.-Ing.)The thesis addresses the development of a variational-based framework for gradient-type standard dissipative solids. A focus lies on the design of theoretical and computational approaches towards the description of length-scale effects in inelastically deforming solids. A strong emphasis is put on a unifying theoretical and numerical treatment of the incremental variational formulation that is applied to a broad class of gradient-type solids with intrinsic length scales. The coupled, symmetric multi-field formulation is first used to model gradient-type damage mechanics that overcomes drawbacks of local constitutive damage models regarding mesh sensitivity. A second application of the variational-based framework for gradient-type solids is concerned with the phase field modeling of fracture, allowing for the prediction of curvilinear crack patterns, crack kinking, and crack initiation in solids free of imperfections. This formulation avoids the modeling of sharp discontinuities usually done in classical approaches towards fracture and turns out to be conceptually in line with the previously discussed model of gradient-type damage mechanics. A challenge of the phase field modeling of fracture arises with regard to the approximate description of the crack topology. Accurate results demand the employment of highly densified finite element meshes in the crack evolution zone. An improvement of the numerical efficiency is obtained by an h-adaptive solution procedure that is exclusively governed by discrete configurational forces. A last application of the proposed framework covers models of phenomenological plasticity with gradient-type hardening at small and large deformations. These models allow for the regularization of shear bands and the description of the so-called Hall-Petch effect.Item Open Access Porous media viscoelasticity with application to polymeric foams. Second revised edition(2010) Markert, BerndThe goal of this contribution is to merge the advances in porous media theories and the state of the art in single-phase finite viscoelasticity within a well-founded thermodynamical framework. In particular, a thermodynamically consistent constitutive setting is presented where, based on the internal variable concept, an extended Ogden-type viscoelasticity formulation is embedded into the macroscopic Theory of Porous Media (TPM). By focusing on immiscible binary solid-fluid aggregates, essential nonlinearities of the strongly coupled problem are included in the formulation. Thus, the developed biphasic continuum mechanical model accounts for the relevant physical properties stemming from the porous microstructure, the moving and interacting viscous pore fluid (compressible or incompressible), and the directly coupled intrinsic viscoelasticity of the skeleton material itself. In order to demonstrate its suitability, the presented model is especially adapted to the behavior of open-celled polymer foams, as these materials combine all nonlinearities under absolute finite viscoelastic deformations. Finally, after the numerical treatment of the governing model equations through the mixed finite element method (FEM), large strain 3-d simulations reveal the capabilities of the proposed macroscopic formulation and the efficiency of its numerical implementation.Item Open Access On the formulation and numerical implementation of dissipative electro-mechanics at large strains(2010) Rosato, Daniele; Miehe, Christian (Prof. Dr.-Ing. habil.)In recent years an increasing interest in functional materials such as erroelectric polymers and ceramics has been shown. For those materials, viscous effects or electric polarizations cause hysteresis phenomena accompanied with possibly large remanent strains and rotations. In this work aspects of the formulation and numerical implementation of dissipative electro-mechanics at large strains are outlined. In particular continuous and discrete variational formulations for the treatment of the non-linear dissipative response of electro-mechanical solids are developed and these formulations are adapted to the modeling of the hysteretic material response of piezoceramics and ferroelectric polymers under electrical loading. The point of departure is a general internal variable formulation that determines the hysteretic response of the material as a generalized standard medium in terms of an energy storage and a rate-dependent dissipation function. Consistent with this type of standard dissipative continua, an incremental variational formulation of the coupled electro-mechanical boundary-value-problem is developed. The variational formulation for a setting based on a smooth rate-dependent dissipation function which governs the hysteretic response is specified. Further, the geometric nature of dissipative electro-mechanics is underlined. An important aspect is the numerical implementation of the coupled problem. The discretization of the two-field problem appears, as a consequence of the proposed incremental variational principle, in a symmetric and very compact format. Further, constitutive assumptions which account for specific problems arising in the geometric nonlinear setting are discussed. With regard to the choice of the internal variables entering the constitutive functions, a critical point are the kinematic assumptions. Here, the multiplicative decomposition of the local deformation gradient into reversible and remanent parts as well as the introduction of a remanent metric are discussed. Such a formulation allows us to reproduce the dielectric and butterfly hysteresis responses characteristic of the ferroelectric materials together with their rate-dependency and to account for macroscopically non-uniform distribution of the polarization in the specimen together with large attained deformations. The performance of the proposed methods is demonstrated by means of a spectrum of benchmark problems which eventually show large deformations.Item Open Access A physiologically based, multi-scale model of skeletal muscle structure and function(2012) Röhrle, Oliver; Davidson, John B.; Pullan, Andrew J.Models of skeletal muscle can be classified as phenomenological or biophysical. Phenomenological models predict the muscle’s response to a specified input based on experimental measurements. Prominent phenomenological models are the Hill-type muscle models, which have been incorporated into rigid-body modeling frameworks, and three-dimensional continuum-mechanical models. Biophysically based models attempt to predict the muscle’s response as emerging from the underlying physiology of the system. In this contribution, the conventional biophysically based modeling methodology is extended to include several structural and functional characteristics of skeletal muscle. The result is a physiologically based, multi-scale skeletal muscle finite element model that is capable of representing detailed, geometrical descriptions of skeletal muscle fibers and their grouping. Together with a well-established model of motor-unit recruitment, the electro-physiological behavior of single muscle fibers within motor units is computed and linked to a continuummechanical constitutive law. The bridging between the cellular level and the organ level has been achieved via a multi-scale constitutive law and homogenization. The effect of homogenization has been investigated by varying the number of embedded skeletal muscle fibers and/or motor units and computing the resulting exerted muscle forces while applying the same excitatory input. All simulations were conducted using an anatomically realistic finite element model of the tibialis anterior muscle. Given the fact that the underlying electro-physiological cellular muscle model is capable of modeling metabolic fatigue effects such as potassium accumulation in the T-tubular space and inorganic phosphate build-up, the proposed framework provides a novel simulation-based way to investigate muscle behavior ranging from motor-unit recruitment to force generation and fatigue.