1,721,099 research outputs found
Thermomechanische Modellierung von Formgedächtnislegierung-basierten Mikroaktuatoren
Full text linkModeling finite deformation inelasticity often involves an incompressibility constraint on the inelastic stretches, which arises from physical considerations. Regularly, this constraint is fulfilled by use of the exponential map as a geometric integrator for the evolution equations. However, in this dissertation, a new geometric integrator for the unimodularity constraint is developed and analyzed. It builds on the work of Hurtado et al. from 2014, where this projection scheme was introduced for crystal plasticity. However, to make use of this projection scheme efficiently in a finite element context, additional numerical problems have to be overcome. The work at hand aims to contribute to this aim and extend existing works for shape memory alloys. It comprises of three publications of the author and his co-authors concentrating on the modeling of materials with an incompressibility constraint. The overall goal is to implement an efficient shape memory alloy model for the simulation of cooperative bistable shape memory nanoactuators.Die Modellierung von Inelastizität unter finiten Deformationen beinhaltet häufig eine Inkompressibilitätsbeschränkung für die inelastischen Dehnungen, welche sich aus physikalischen Überlegungen ergibt. In der Regel wird diese Bedingung durch die Verwendung der Exponentialabbildung als geometrischer Integrator für die Evolutionsgleichungen exakt erfüllt. In dieser Dissertation wird jedoch ein neuer geometrischer Integrator für die Unimodularitätsbeschränkung entwickelt und analysiert. Er baut auf der Arbeit von Hurtado et al. aus dem Jahr 2014 auf, wo dieses Projektionsschema für die Kristallplastizität eingeführt wurde. Um dieses Projektionsschema in einem Finite-Elemente-Kontext effizient nutzen zu können, müssen jedoch zusätzliche numerische Probleme überwunden werden.Die vorliegende Arbeit soll dazu beitragen und bestehende Arbeiten für Formgedächtnislegierungen erweitern. Sie ist ein Zusammenschluss von drei Publikationen des Autors und seiner Mitautoren, die sich auf die Modellierung von Materialien mit einer Inkompressibilitätsbeschränkung konzentrieren. Das übergeordnete Ziel ist es, ein effizientes Modell für Formgedächtnislegierungen zur Simulation von kooperativen bistabilen Formgedächtnis-Nanoaktuatoren zu implementieren
Multiphysics modeling of manufacturing and failure processes
No full textThe development of modern technical devices demands a resource saving design for the manufacturing process in conjunction with optimal device performance during the application. The realization of these complex requirements necessitates an integrated evaluation approach that considers the manufacturing process plus the entire lifespan up to the potential failure of the device. The object's transfer into its digital twin allows for its numerical simulation and digital analysis at arbitrary time and length scales, which offer precious and experimentally hard to access process insights. This cumulative dissertation may provide a valuable contribution to the systemic product development process and, thus, addresses the digital modeling of multiphysical manufacturing and failure processes based on the finite element method. The works comprise the model development of an efficient modeling approach for material dissolution and moving boundary value problems in electrochemical machining and, for the product application, the modeling and regularization of anisotropic damage at finite strains. The first three articles deal with the efficient modeling of the manufacturing process of electrochemical machining. In the first article, a novel methodology for modeling material dissolution based on effective material parameters is developed that resolves the fundamental issue of computationally expensive remeshing during the simulation of dissolution processes of the workpiece. The second article features the application of effective material parameter modeling for the simulation of the tool and, thereby, enables the entire process simulation of the moving boundary value problem without mesh adaptation. The third article extends the isotropic rules of mixture for the identification of the effective material by an anisotropic formulation, which is based on the orientation of the electric current density. The subsequent four articles cover the gradient-extended modeling of anisotropic damage. In the fourth and fifth article, two energy formulations, which fulfill a physical stiffness reduction according to the damage growth criterion, are employed to develop an efficient and universal gradient-extension for inelastic processes with tensor-valued internal variables. A novel volumetric-deviatoric gradient-extension of the damage tensor using two micromorphic degrees of freedom yields an effective regularization capability to obtain mesh independent results. Further structural simulations in the sixth and seventh article confirm the performance of the developed regularization methodologies
Modeling of gradient-extended anisotropic damage using a second order damage tensor
No full textNumerical simulations are indispensible in many engineering disciplines since they can reduce the number of costly and time-consuming experiments. For the prediction of material and structural failure, damage and fracture models have been developed, which are constantly being further extended to consider more and more effects. State-of-the-art isotropic damage models apply scalar variables to describe damage/degradation of a material. Anisotropic damage models have already been developed for quite a time, but in this research field still pending issues exist. One challenging task concerns the mesh-objective description of anisotropic damage progression in finite element simulations. The present cumulative dissertation consists of three peer-reviewed articles that deal with state-of-the-art isotropic damage as well as anisotropic damage representations. In article 1, an application oriented design study utilizing a local isotropic damage model is presented. The other two articles (article 2 and 3) deal with gradient-extended anisotropic damage, for which a new formulation is established. The application areas of damage models are versatile and include e.g. the design of components in the automotive and aerospace sector. For the latter sector, article 1 presents a design study of a subscale rocket engine experiment utilizing a viscoplastic isotropic damage model. The material model takes into account nonlinear Voce isotropic hardening, nonlinear Armstrong-Frederick kinematic hardening, Perzyna rate dependence and Lemaitre-type isotropic damage. The goal is to design the experiment, such that a specific failure mode of the cooling channel structure is obtained which should occur already after a relatively small number of cycles. Thermomechanical finite element analyses are performed, for which the influence of geometry parameters such as the width and height of the cooling channels is studied first. Afterwards, a final design is found by properly adapting thermal and static boundary conditions and taking into account constructional aspects. With the designed experiment and its measuring equipment, damage models can be validated in future. The use of isotropic damage models, in which damage is described by one scalar damage variable, may be insufficient in certain situations (e.g. if the material exhibits preferred directions or two or more directional loads are applied sequentially). Furthermore, standard local material models with softening behaviour, such as the one used in article 1, show a pathological mesh dependence in finite element simulations due to localization. Therefore, a formulation including (i) anisotropic damage and (ii) a gradient extension is developed. For simplicity, plasticity is neglected. Article 2 presents this formulation, in which damage is represented by a second order tensor and the micromorphic approach is chosen to incorporate gradient effects. Although a damage tensor of second order is utilized, the proposed efficient gradient-extended formulation introduces only one additional scalar degree of freedom. The elastic strain energy of the model is derived starting from a general invariant representation of the strain tensor and the damage tensor. Invariants, which may lead to artificial stiffening, are neglected a priori. Furthermore, a novel additional damage hardening is introduced ensuring that the eigenvalues of the damage tensor do not exceed the value one. Besides the finite element implementation, the implementation at integration point level including the derivation of the consistent tangent operators is described in detail. The model's behaviour is exemplified with uniaxial loading cases (performed at integration point level) in which damage anisotropy is readily apparent. Several representative structural examples are investigated and it is demonstrated that the formulation delivers mesh-objective results although using only one additional scalar degree of freedom. Depending on the specific boundary value problem and the material parameters either localized or diffuse damage patterns are observed. Here, a salient result is that especially in the case of diffuse damage differences between isotropic and anisotropic damage modeling appear. In the last part of the thesis (article 3), the anisotropic damage model presented in article 2, is extended to consider tension compression asymmetry. The main reason for this extension is to prevent spurious failure in compression. The used tension compression asymmetry approach is based on the spectral decomposition of the strain tensor into a tension and a compression related part. The tension related part of the elastic strain energy function is fully damaged, whereas the compression related part is either only partially or not at all damaged. For the implementation of this approach, a new unifying algorithmic procedure is presented which reduces the implementation effort drastically. This is particularly evident for the derivation and implementation of the consistent tangent operators. Cyclic uniaxial and cyclic shear loading cases are studied at integration point level and show the effects of tension compression asymmetry: (i) different damage behaviour in tension and compression as well as (ii) stiffness recovery if the load is reversed from tension to compression. Finally, three representative structural examples are investigated in which mesh convergence upon mesh refinement is demonstrated. Spurious failure in compression is shown to be prevented and stiffness recovery takes place if the load is reversed. These two aspects succesfully verify tension compression asymmetry on structural level and lead to a more realistic failure behaviour
Crystal plasticity and grain boundaries on small scales : modeling and numerical implementation
No full textMetals are used for a wide range of applications in the industry due to their durability, strength and ductility. Since dislocations are the fundamental reasons for plastic deformation in metals, the movement of dislocations, their interactions with each other as well as with the grain boundaries (GBs) have been investigated by numerous authors for some decades. In this regard, the current dissertation represents a compilation of published articles of the author (and her coauthors). This thesis addresses geometrically nonlinear plastic deformation of face centered cubic (fcc) materials on the large and small scales using continuum approaches. In large-scale applications, classical plasticity (size-independent) models are mostly used which are in agreement with experimental data while inhomogeneous plastic deformation of materials on the microscale is investigated with strain-gradient theories by introducing an internal length scale into the models. In the study of large-scale crystalline materials, the main problem is to deal with the numerical issues when geometrically nonlinear plasticity approaches are implemented, e.g., locking phenomenon. Moreover, single crystal simulations at room temperature often necessitate a power-law-type flow rule with high rate sensitivity exponent to capture the actual behavior of the material deformation, which leads to a complicated convergence of nonlinear equations. To solve such issues, a regularization method for the power law with high value of the sensitivity exponent in combination with a new concept for hybrid discontinuous Galerkin (DG) methods-control points- is presented in geometrically nonlinear crystal plasticity framework, leading to a numerically efficient, robust and locking-free model (article 1). On the micro-scale, the presence of grain boundaries results in pile-ups of dislocations and strengthening of the material (Hall-Petch effect). Therefore, a grain boundary model in the concept of geometrically nonlinear viscoplasticity is presented to improve single crystal models(article 2). This model is based on the dislocation density tensor and plastic surface deformation which leads to a grain boundary yield criterion with isotropic and kinematic hardening. The grain boundary hardening effects are shown in cyclic shear deformation of bicrystals. In this model, the grain boundary strength is assumed to be a function of grain misorientation. Subsequently, the grain boundary model in article 2 is extended by evaluating the grain boundary strength with regard to the grain misorientation using a geometrical transmissibility parameter (article 3). To investigate the effect of mismatch between adjacent grains on the grain boundary strength and dislocation transmission at the grain boundaries, randomly oriented polycrystals are compared with textured polycrystals
Fully Coupled FEA Simulation of Re-programmable Origami Micro-Matter
Full text linkRe-programmable matter is an attempt to introduce reconfigurability to programmable matter. Programmable
matter is a material whose shape can be programmed through bending hinge actuators.
Programmable matter is based on the concept of self-folding origami. In principle, programmable
matter consists of a planar network of tiles and hinge actuators that can be folded into desired 3D
structures. This is possible through joule heating of the hinge actuator which is made of active materials.
Shape Memory Alloys (SMA) are amongst the most used active materials in the actuation of
microsystems. The synergy of active and passive actuators facilitates the reconfiguration of the 3D
origami structures back into the 2D planar structures and further folding in the opposite direction.
This is the bidirectional actuation of the origami structure.
The optimization of such actuation requires iterative Finite Element Method (FEM) simulations of
the entire origami system. This assists in understanding the coupling effects between the actuators in
the systems. In this thesis, we provide a holistic approach to achieve device simulation of the bidirectional
actuation of the origami system. First, following thermodynamic principles, we derive a fully
coupled material model to describe the shape memory effect and superelasticity properties of shape
memory alloy materials. The resolved time-dependent coupling between the mechanical, thermal,
and electrical field variables inherent to thermal actuation is described. Tensile and bending simulations
are conducted to validate the model by direct comparison with experimental results. A detailed
procedure to realize bidirectional actuation is provided. FEM simulation of Bidirectional actuation
of open-box and pyramid origami structures is achieved. Here, thermal transport during actuation is
found to influence the folding of the actuators in their attempt to fold to the programmed 3D structure.
Appropriate measures are recommended to prevent the problem and achieve optimal actuation
towards the programmed 3D structure. The combination of the shape memory alloy material model
and bidirectional simulation procedure developed in this thesis are found to be robust to simulate and
optimize the actuation of re-programmable micro origami systems
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Modeling micromorphic damage in long carbon fiber reinforced plastics at different scales
No full textComposites have been used for a long time in the history of mankind. Already in the times of the pharaohs, clay and straw were combined to build houses out of this material. In general, composites are used to combine the positive properties of the various components and produce materials with extreme properties or properties tailored to the application needs. Nowadays, composites made from a combination of epoxy resin with glass fibers (so-called glass fiber reinforced plastics or GFRPs) or carbon fibers (so-called carbon fiber reinforced plastics or CFRPs) are used primarily in lightweight construction. The latter offer particularly high stiffness and strength combined with low density, making them an ideal material for lightweight construction applications. CFRPs are manufactured either from layers of parallel fibers laid on top of each other in different directions or from woven fabrics with different weave structures, which are usually filled with an epoxy resin. Due to the complex microstructure, even simple load cases lead to complex stress states within the material. In addition, CFRP exhibits brittle material failure with significant scatter in material parameters, leading to high factors of safety in applications. A more accurate prediction of the material behavior, especially in the area of material damage, would lead to a reduction of the safety factors and thus to a better design of CFRP structures. This cumulative dissertation aims to contribute to a better understanding of the damage behavior of carbon fiber reinforced plastics. It consists mainly of three previously published scientific papers from the author and several co-authors. The aim of the publications was the simulation of the damage behavior of CFRPs both at the scale of the components and at the microscopic scale of the laminates and fabrics. Here, the material model used for brittle damage, without considering plasticity, is similar for all three publications. In the material model, gradient-extended (or micromorph) damage is used to produce mesh size-independent results.The dissertation begins with an introduction to illuminate the research-relevant questions and to present the current state of research. This is followed by the first of a total of three scientific publications. Here, an isotropic material model for large deformations was extended by an anisotropic component in order to simulate the material behavior of CFRP on a macroscopic level. Both the isotropic and anisotropic portions were given their own scalar damage variable to distinguish between damage to the epoxy matrix (isotropic part) and damage to the carbon fiber (anisotropic extension). A tension-compression asymmetry was also introduced for both parts to account for the effect of crack closure. In addition, an anisotropy was introduced in the gradient term of the isotropic material part to account for the direction dependence of the crack propagation. Finally, the material parameters of the numerical model were fitted to experimental results of unidirectional CFRP and the performance of the material model was evaluated.In the second publication, the material behavior of CFRP was investigated on the microscale. Since a geometric distinction between fiber and matrix is possible on the microscale, only the isotropic part of the previously implemented material model was used. The aim of the publication was to develop a new homogenization approach with and without consideration of the interface between epoxy matrix and carbon fiber. The homogenization approach was based on the so-called failure zone averaging and aimed at deriving a material behavior for the next larger scale from simulations of the microscale. The approach took into account the energetic components from both the mechanical part of the model and the micromorphic extension. An examination of the power components showed that the micromorphic power is non-zero in the case of failure zone averaging, and even shows power peaks that exceed those of the mechanical power. However, in terms of the total energy dissipated in the system, it was shown that the energy dissipated by the micromorphic components is negligible. The publication concluded with simulations that included the interface between fiber and matrix. Here, a generally reduced strength with simultaneously increased dissipated energy was observed. In the last publication, the previously presented homogenization method was applied to the load cases of simple shear, pure shear and mixed mode loading. It was shown that different load-deformation curves formed depending on the type of load, the geometry and whether the tension-compression asymmetry is activated. In particular, the orientation of the failure zone had a significant influence here. The publication again concluded with simulations that took into account the interface between fiber and matrix. Here, as before, an increased dissipation with simultaneously reduced strength was shown.The dissertation concludes with an outlook on research-relevant questions arising from the results of the three published papers for future work in this area of research
Unsicherheitsquantifizierung von Biodegradationsmodellen mithilfe von Surrogatmodellen
Full text linkMagnesium and its alloys are being investigated increasingly as temporary bone implant materials due to their non-toxicity, biocompatibility, and biodegradability properties. The most challenging aspect of Mg-based implants involves adapting the degradation rate to the human body, which requires extensive in vitro and in vivo testing. Reliable computational models can aid by simulating the degradation and predict its rates. Initially, a comprehensive and in-depth review of the developed degradation models up to date, revealed the fact that developing reliable degradation models is challenging. This is due to the complexity and multi-scale nature of the biodegradation process. Furthermore, biodegradation models are inevitably characterized by uncertainty associated with different aspects of them, i.e. uncertain validation data, parameters, hypothesis and concept as well as simulator limitations. Therefore, it is critical to quantify the uncertainties within these models. Uncertainty quantification (UQ) provides several methods to quantify different sources of uncertainty within computational models. Overall, UQ methods are computationally expensive and require a substantial number of model iterations. Thus, surrogate modelling has gained significant interest in recent years, as these models can substitute expensive models within the UQ analysis. Overall, the current cumulative dissertation presents a clear workflow to quantify uncertainty within different types of biodegradation models. The published work and proposed workflow can serve as a foundation for assessing the influence of uncertainty on the reliability and robustness of the computational models of biodegradation while optimizing the ratio of accuracy and computational cost
Direktor-basierte Kontinuumsmodellierung und Analyse von Schädigungsmechanik und gekoppelter Mikro-Magneto-Mechanik
Full text linkComplex material behavior often involves a local material orientation that is subject to evolution over time. One example of such an orientation is the direction of magnetization in magnetic materials. To represent this behavior in a continuum model, each material point (described by a position vector) is additionally endowed with an orientation and associated balance equations. In many cases, the aforementioned orientation can be represented by a unit vector (called director) which only contains directional but no magnitude information. Enforcing the length of the orientation vector to remain constant is a numerically challenging constraint. The aim of the present dissertation is to contribute to the advancement of material modeling and simulation involving directors. In particular, this contribution is intended to stretch into the realm of modeling magnetic materials with continuum models (both numerically and analytically).Komplexes Materialverhalten beinhaltet häufig eine lokale Materialorientierung, die sich zeitabhängig verändert. Ein Beispiel für eine solche Orientierung ist die Magnetisierungsrichtung in magnetischen Materialien. Um dieses Materialverhalten in einem Kontinuumsmodell abzubilden, wird jeder Punkt des Materials (beschrieben durch einen Ortsvektor) zusätzlich mit einer Orientierung und zugehörigen Bilanzgleichungen ausgestattet. In vielen Fällen kann die besagte Orientierung durch einen Einheitsvektor (Direktor genannt) dargestellt werden, der nur Richtungs-, aber keine Betragsinformation enthält. Das Beschränken des Orientierungsvektors auf eine konstante Länge ist eine numerisch herausfordernde Nebenbedingung. Mit der vorliegenden Dissertation soll ein Beitrag zur Weiterentwicklung der Materialmodellierung und -simulation mithilfe von Direktoren geleistet werden. Dieser Beitrag soll sich insbesondere in den Bereich der Modellierung magnetischer Materialien mit Kontinuumsmodellen (sowohl numerisch als auch analytisch) erstrecken
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