@phdthesis{Jaouadi,
  author    = {Jaouadi, Zouhour},
  title     = {Pareto and Reliability-Oriented Aeroelastic Shape Optimization of Bridge Decks},
  doi       = {10.25643/bauhaus-universitaet.4935},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20230303-49352},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {167},
  abstract  = {Due to the development of new technologies and materials, optimized bridge design has recently gained more attention. The aim is to reduce the bridge components materials and the CO2 emission from the cement manufacturing process. Thus, most long-span bridges are designed to be with high flexibility, low structural damping, and longer and slender spans. Such designs lead, however, to aeroelastic challenges. Moreover, the consideration of both the structural and aeroelastic behavior in bridges leads to contradictory solutions as the structural constraints lead to deck prototypes with high depth which provide high inertia to material volume ratios. On the other hand, considering solely the aerodynamic requirements, slender airfoil-shaped bridge box girders are recommended since they prevent vortex shedding and exhibit minimum drag. Within this framework comes this study which provides approaches to find optimal bridge deck cross-sections while considering the aerodynamic effects. Shape optimization of deck cross-section is usually formulated to minimize the amount of material by finding adequate parameters such as the depth, the height, and the thickness and while ensuring the overall stability of the structure by the application of some constraints. Codes and studies have been implemented to analyze the wind phenomena and the structural responses towards bridge deck cross-sections where simplifications have been adopted due to the complexity and the uniqueness of such components besides the difficulty of obtaining a final model of the aerodynamic behavior. In this thesis, two main perspectives have been studied; the first is fully deterministic and presents a novel framework on generating optimal aerodynamic shapes for streamlined and trapezoidal cross-sections based on the meta-modeling approach. Single and multi-objective optimizations were both carried out and a Pareto Front is generated. The performance of the optimal designs is checked afterwards. In the second part, a new strategy based on Reliability-Based Design Optimization (RBDO) to mitigate the vortex-induced vibration (VIV) on the Trans-Tokyo Bay bridge is proposed. Small changes in the leading and trailing edges are presented and uncertainties are considered in the structural system. Probabilistic constraints based on polynomial regression are evaluated and the problem is solved while applying the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). The results obtained in the first part showed that the aspect ratio has a significant effect on the aerodynamic behavior where deeper cross-sections have lower resistance against flutter and should be avoided. In the second part, the adopted RBDO approach succeeded to mitigate the VIV, and it is proven that designs with narrow or prolonged bottom-base length and featuring an abrupt surface change in the leading and trailing edges can lead to high vertical vibration amplitude. It is expected that this research will help engineers with the selections of the adequate deck cross-section layout, and encourage researchers to apply concepts of optimization regarding this field and develop the presented approaches for further studies.},
  subject      = {Gestaltoptimierung},
  language  = {en}
}
@phdthesis{Ashour,
  author    = {Ashour, Mohammed},
  title     = {Electromechanics and Hydrodynamics of Single Vesicles and Vesicle Doublet Using Phase-Field Isogeometric Analysis},
  doi       = {10.25643/bauhaus-universitaet.6400},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20230628-64003},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {175},
  abstract  = {Biomembranes are selectively permeable barriers that separate the internal components of the cell from its surroundings. They have remarkable mechanical behavior which is characterized by many phenomena, but most noticeably their fluid-like in-plane behavior and solid-like out-of-plane behavior. Vesicles have been studied in the context of discrete models, such as Molecular Dynamics, Monte Carlo methods, Dissipative Particle Dynamics, and Brownian Dynamics. Those methods, however, tend to have high computational costs, which limited their uses for studying atomistic details. In order to broaden the scope of this research, we resort to the continuum models, where the atomistic details of the vesicles are neglected, and the focus shifts to the overall morphological evolution. Under the umbrella of continuum models, vesicles morphology has been studied extensively. However, most of those studies were limited to the mechanical response of vesicles by considering only the bending energy and aiming for the solution by minimizing the total energy of the system. Most of the literature is divided between two geometrical representation methods; the sharp interface methods and the diffusive interface methods. Both of those methods track the boundaries and interfaces implicitly. In this research, we focus our attention on solving two non-trivial problems. In the first one, we study a constrained Willmore problem coupled with an electrical field, and in the second one, we investigate the hydrodynamics of a vesicle doublet suspended in an external viscous fluid flow. For the first problem, we solve a constrained Willmore problem coupled with an electrical field using isogeometric analysis to study the morphological evolution of vesicles subjected to static electrical fields. The model comprises two phases, the lipid bilayer, and the electrolyte. This two-phase problem is modeled using the phase-field method, which is a subclass of the diffusive interface methods mentioned earlier. The bending, flexoelectric, and dielectric energies of the model are reformulated using the phase-field parameter. A modified Augmented-Lagrangian (ALM) approach was used to satisfy the constraints while maintaining numerical stability and a relatively large time step. This approach guarantees the satisfaction of the constraints at each time step over the entire temporal domain. In the second problem, we study the hydrodynamics of vesicle doublet suspended in an external viscous fluid flow. Vesicles in this part of the research are also modeled using the phase-field model. The bending energy and energies associated with enforcing the global volume and area are considered. In addition, the local inextensibility condition is ensured by introducing an additional equation to the system. To prevent the vesicles from numerically overlapping, we deploy an interaction energy definition to maintain a short-range repulsion between the vesicles. The fluid flow is modeled using the incompressible Navier-Stokes equations and the vesicle evolution in time is modeled using two advection equations describing the process of advecting each vesicle by the fluid flow. To overcome the velocity-pressure saddle point system, we apply the Residual-Based Variational MultiScale (RBVMS) method to the Navier-Stokes equations and solve the coupled systems using isogeometric analysis. We study vesicle doublet hydrodynamics in shear flow, planar extensional flow, and parabolic flow under various configurations and boundary conditions. The results reveal several interesting points about the electrodynamics and hydrodynamics responses of single vesicles and vesicle doublets. But first, it can be seen that isogeometric analysis as a numerical tool has the ability to model and solve 4th-order PDEs in a primal variational framework at extreme efficiency and accuracy due to the abilities embedded within the NURBS functions without the need to reduce the order of the PDE by creating an intermediate environment. Refinement whether by knot insertion, order increasing or both is far easier to obtain than traditional mesh-based methods. Given the wide variety of phenomena in natural sciences and engineering that are mathematically modeled by high-order PDEs, the isogeometric analysis is among the most robust methods to address such problems as the basis functions can easily attain high global continuity. On the applicational side, we study the vesicle morphological evolution based on the electromechanical liquid-crystal model in 3D settings. This model describing the evolution of vesicles is composed of time-dependent, highly nonlinear, high-order PDEs, which are nontrivial to solve. Solving this problem requires robust numerical methods, such as isogeometric analysis. We concluded that the vesicle tends to deform under increasing magnitudes of electric fields from the original sphere shape to an oblate-like shape. This evolution is affected by many factors and requires fine-tuning of several parameters, mainly the regularization parameter which controls the thickness of the diffusive interface width. But it is most affected by the method used for enforcing the constraints. The penalty method in presence of an electrical field tends to lock on the initial phase-field and prevent any evolution while a modified version of the ALM has proven to be sufficiently stable and accurate to let the phase-field evolve while satisfying the constraints over time at each time step. We show additionally the effect of including the flexoelectric nature of the Biomembranes in the computation and how it affects the shape evolution as well as the effect of having different conductivity ratios. All the examples were solved based on a staggered scheme, which reduces the computational cost significantly. For the second part of the research, we consider vesicle doublet suspended in a shear flow, in a planar extensional flow, and in a parabolic flow. When the vesicle doublet is suspended in a shear flow, it can either slip past each other or slide on top of each other based on the value of the vertical displacement, that is the vertical distance between the center of masses between the two vesicles, and the velocity profile applied. When the vesicle doublet is suspended in a planar extensional flow in a configuration that resembles a junction, the time in which both vesicles separate depends largely on the value of the vertical displacement after displacing as much fluid from between the two vesicles. However, when the vesicles are suspended in a tubular channel with a parabolic fluid flow, they develop a parachute-like shape upon converging towards each other before exiting the computational domain from the predetermined outlets. This shape however is affected largely by the height of the tubular channel in which the vesicle is suspended. The velocity essential boundary conditions are imposed weakly and strongly. The weak implementation of the boundary conditions was used when the velocity profile was defined on the entire boundary, while the strong implementation was used when the velocity profile was defined on a part of the boundary. The strong implementation of the essential boundary conditions was done by selectively applying it to the predetermined set of elements in a parallel-based code. This allowed us to simulate vesicle hydrodynamics in a computational domain with multiple inlets and outlets. We also investigate the hydrodynamics of oblate-like shape vesicles in a parabolic flow. This work has been done in 2D configuration because of the immense computational load resulting from a large number of degrees of freedom, but we are actively seeking to expand it to 3D settings and test a broader set of parameters and geometrical configurations.},
  subject      = {Isogeometrische Analyse},
  language  = {en}
}
@phdthesis{Nouri,
  author    = {Nouri, Hamidreza},
  title     = {Mechanical Behavior of two dimensional sheets and polymer compounds based on molecular dynamics and continuum mechanics approach},
  doi       = {10.25643/bauhaus-universitaet.4670},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220713-46700},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {152},
  abstract  = {Compactly, this thesis encompasses two major parts to examine mechanical responses of polymer compounds and two dimensional materials: 1- Molecular dynamics approach is investigated to study transverse impact behavior of polymers, polymer compounds and two dimensional materials. 2- Large deflection of circular and rectangular membranes is examined by employing continuum mechanics approach. Two dimensional materials (2D), including, Graphene and molybdenum disulfide (MoS2), exhibited new and promising physical and chemical properties, opening new opportunities to be utilized alone or to enhance the performance of conventional materials. These 2D materials have attracted tremendous attention owing to their outstanding physical properties, especially concerning transverse impact loading. Polymers, with the backbone of carbon (organic polymers) or do not include carbon atoms in the backbone (inorganic polymers) like polydimethylsiloxane (PDMS), have extraordinary characteristics particularly their flexibility leads to various easy ways of forming and casting. These simple shape processing label polymers as an excellent material often used as a matrix in composites (polymer compounds). In this PhD work, Classical Molecular Dynamics (MD) is implemented to calculate transverse impact loading of 2D materials as well as polymer compounds reinforced with graphene sheets. In particular, MD was adopted to investigate perforation of the target and impact resistance force . By employing MD approach, the minimum velocity of the projectile that could create perforation and passes through the target is obtained. The largest investigation was focused on how graphene could enhance the impact properties of the compound. Also the purpose of this work was to discover the effect of the atomic arrangement of 2D materials on the impact problem. To this aim, the impact properties of two different 2D materials, graphene and MoS2, are studied. The simulation of chemical functionalization was carried out systematically, either with covalently bonded molecules or with non-bonded ones, focusing the following efforts on the covalently bounded species, revealed as the most efficient linkers. To study transverse impact behavior by using classical MD approach , Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software, that is well-known among most researchers, is employed. The simulation is done through predefined commands in LAMMPS. Generally these commands (atom style, pair style, angle style, dihedral style, improper style, kspace style, read data, fix, run, compute and so on) are used to simulate and run the model for the desired outputs. Depends on the particles and model types, suitable inter-atomic potentials (force fields) are considered. The ensembles, constraints and boundary conditions are applied depends upon the problem definition. To do so, atomic creation is needed. Python codes are developed to generate particles which explain atomic arrangement of each model. Each atomic arrangement introduced separately to LAMMPS for simulation. After applying constraints and boundary conditions, LAMMPS also include integrators like velocity-Verlet integrator or Brownian dynamics or other types of integrator to run the simulation and finally the outputs are emerged. The outputs are inspected carefully to appreciate the natural behavior of the problem. Appreciation of natural properties of the materials assist us to design new applicable materials. In investigation on the large deflection of circular and rectangular membranes, which is related to the second part of this thesis, continuum mechanics approach is implemented. Nonlinear F{\"o}ppl membrane theory, which carefully release nonlinear governing equations of motion, is considered to establish the non-linear partial differential equilibrium equations of the membranes under distributed and centric point loads. The Galerkin and energy methods are utilized to solve non-linear partial differential equilibrium equations of circular and rectangular plates respectively. Maximum deflection as well as stress through the film region, which are kinds of issue in many industrial applications, are obtained.},
  subject      = {Molekulardynamik},
  language  = {en}
}
@phdthesis{Jenabidehkordi,
  author    = {Jenabidehkordi, Ali},
  title     = {An Efficient Adaptive PD Formulation for Complex Microstructures},
  doi       = {10.25643/bauhaus-universitaet.4742},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221124-47422},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {118},
  abstract  = {The computational costs of newly developed numerical simulation play a critical role in their acceptance within both academic use and industrial employment. Normally, the refinement of a method in the area of interest reduces the computational cost. This is unfortunately not true for most nonlocal simulation, since refinement typically increases the size of the material point neighborhood. Reducing the discretization size while keep- ing the neighborhood size will often require extra consideration. Peridy- namic (PD) is a newly developed numerical method with nonlocal nature. Its straightforward integral form equation of motion allows simulating dy- namic problems without any extra consideration required. The formation of crack and its propagation is known as natural to peridynamic. This means that discontinuity is a result of the simulation and does not demand any post-processing. As with other nonlocal methods, PD is considered an expensive method. The refinement of the nodal spacing while keeping the neighborhood size (i.e., horizon radius) constant, emerges to several nonphysical phenomena. This research aims to reduce the peridynamic computational and imple- mentation costs. A novel refinement approach is introduced. The pro- posed approach takes advantage of the PD flexibility in choosing the shape of the horizon by introducing multiple domains (with no intersections) to the nodes of the refinement zone. It will be shown that no ghost forces will be created when changing the horizon sizes in both subdomains. The approach is applied to both bond-based and state-based peridynamic and verified for a simple wave propagation refinement problem illustrating the efficiency of the method. Further development of the method for higher dimensions proves to have a direct relationship with the mesh sensitivity of the PD. A method for solving the mesh sensitivity of the PD is intro- duced. The application of the method will be examined by solving a crack propagation problem similar to those reported in the literature. New software architecture is proposed considering both academic and in- dustrial use. The available simulation tools for employing PD will be collected, and their advantages and drawbacks will be addressed. The challenges of implementing any node base nonlocal methods while max- imizing the software flexibility to further development and modification will be discussed and addressed. A software named Relation-Based Sim- ulator (RBS) is developed for examining the proposed architecture. The exceptional capabilities of RBS will be explored by simulating three dis- tinguished models. RBS is available publicly and open to further develop- ment. The industrial acceptance of the RBS will be tested by targeting its performance on one Mac and two Linux distributions.},
  subject      = {Peridynamik},
  language  = {en}
}
@phdthesis{Vogler,
  author    = {Vogler, Verena},
  title     = {A framework for artificial coral reef design: Integrating computational modelling and high precision monitoring strategies for artificial coral reefs - an Ecosystem-aware design approach in times of climate change},
  isbn      = {978-3-00-074495-2},
  doi       = {10.25643/bauhaus-universitaet.4611},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220322-46115},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {243},
  abstract  = {Tropical coral reefs, one of the world's oldest ecosystems which support some of the highest levels of biodiversity on the planet, are currently facing an unprecedented ecological crisis during this massive human-activity-induced period of extinction. Hence, tropical reefs symbolically stand for the destructive effects of human activities on nature [4], [5]. Artificial reefs are excellent examples of how architectural design can be combined with ecosystem regeneration [6], [7], [8]. However, to work at the interface between the artificial and the complex and temporal nature of natural systems presents a challenge, i.a. in respect to the B-rep modelling legacy of computational modelling. The presented doctorate investigates strategies on how to apply digital practice to realise what is an essential bulwark to retain reefs in impossibly challenging times. Beyond the main question of integrating computational modelling and high precision monitoring strategies in artificial coral reef design, this doctorate explores techniques, methods, and linking frameworks to support future research and practice in ecology led design contexts. Considering the many existing approaches for artificial coral reefs design, one finds they often fall short in precisely understanding the relationships between architectural and ecological aspects (e.g. how a surface design and material composition can foster coral larvae settlement, or structural three-dimensionality enhance biodiversity) and lack an integrated underwater (UW) monitoring process. Such a process is necessary in order to gather knowledge about the ecosystem and make it available for design, and to learn whether artificial structures contribute to reef regeneration or rather harm the coral reef ecosystem. For the research, empirical experimental methods were applied: Algorithmic coral reef design, high precision UW monitoring, computational modelling and simulation, and validated through parallel real-world physical experimentation - two Artificial Reef Prototypes (ARPs) in Gili Trawangan, Indonesia (2012-today). Multiple discrete methods and sub techniques were developed in seventeen computational experiments and applied in a way in which many are cross valid and integrated in an overall framework that is offered as a significant contribution to the field. Other main contributions include the Ecosystem-aware design approach, Key Performance Indicators (KPIs) for coral reef design, algorithmic design and fabrication of Biorock cathodes, new high precision UW monitoring strategies, long-term real-world constructed experiments, new digital analysis methods and two new front-end web-based tools for reef design and monitoring reefs. The methodological framework is a finding of the research that has many technical components that were tested and combined in this way for the very first time. In summary, the thesis responds to the urgency and relevance in preserving marine species in tropical reefs during this massive extinction period by offering a differentiated approach towards artificial coral reefs - demonstrating the feasibility of digitally designing such 'living architecture' according to multiple context and performance parameters. It also provides an in-depth critical discussion of computational design and architecture in the context of ecosystem regeneration and Planetary Thinking. In that respect, the thesis functions as both theoretical and practical background for computational design, ecology and marine conservation - not only to foster the design of artificial coral reefs technically but also to provide essential criteria and techniques for conceiving them. Keywords: Artificial coral reefs, computational modelling, high precision underwater monitoring, ecology in design.},
  subject      = {Korallenriff},
  language  = {en}
}
@phdthesis{Legatiuk,
  author    = {Legatiuk, Anastasiia},
  title     = {Discrete potential and function theories on a rectangular lattice and their applications},
  doi       = {10.25643/bauhaus-universitaet.4865},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221220-48654},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {The growing complexity of modern engineering problems necessitates development of advanced numerical methods. In particular, methods working directly with discrete structures, and thus, representing exactly some important properties of the solution on a lattice and not just approximating the continuous properties, become more and more popular nowadays. Among others, discrete potential theory and discrete function theory provide a variety of methods, which are discrete counterparts of the classical continuous methods for solving boundary value problems. A lot of results related to the discrete potential and function theories have been presented in recent years. However, these results are related to the discrete theories constructed on square lattices, and, thus, limiting their practical applicability and potentially leading to higher computational costs while discretising realistic domains. This thesis presents an extension of the discrete potential theory and discrete function theory to rectangular lattices. As usual in the discrete theories, construction of discrete operators is strongly influenced by a definition of discrete geometric setting. For providing consistent constructions throughout the whole thesis, a detailed discussion on the discrete geometric setting is presented in the beginning. After that, the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice, which is the core of the discrete potential theory, its numerical analysis, and practical calculations are presented. By using the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice, the discrete potential theory is then constructed for interior and exterior settings. Several discrete interior and exterior boundary value problems are then solved. Moreover, discrete transmission problems are introduced and several numerical examples of these problems are discussed. Finally, a discrete fundamental solution of the discrete Cauchy-Riemann operator on a rectangular lattice is constructed, and basics of the discrete function theory on a rectangular lattice are provided. This work indicates that the discrete theories provide solution methods with very good numerical properties to tackle various boundary value problems, as well as transmission problems coupling interior and exterior problems. The results presented in this thesis provide a basis for further development of discrete theories on irregular lattices.},
  subject      = {Diskrete Funktionentheorie},
  language  = {en}
}
@phdthesis{Tatarin,
  author    = {Tatarin, Ren{\´e}},
  title     = {Charakterisieren struktureller Ver{\"a}nderungen in zementgebundenen Baustoffen durch akustische zerst{\"o}rungsfreie Pr{\"u}fverfahren},
  publisher = {Cuvillier Verlag},
  address   = {G{\"o}ttingen},
  isbn      = {978-3-7369-7575-0},
  doi       = {10.25643/bauhaus-universitaet.4592},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220215-45920},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {293},
  abstract  = {Im Rahmen dieser Arbeit wird das Charakterisieren struktureller Ver{\"a}nderungen zementgebundener Baustoffe durch zwei auf dem Ultraschall-Transmissionsverfahren beruhenden Methoden der zerst{\"o}rungsfreien Pr{\"u}fung (ZfP) mit mechanischen Wellen vorgenommen. Zur kontinuierlichen Charakterisierung der Erstarrung und Erh{\"a}rtung frischer zementgebundener Systeme wird ein auf Ultraschallsensoren f{\"u}r Longitudinal- und Scherwellen basierendes Messsystem in Kombination mit zugeh{\"o}rigen Verfahrensweisen zur Datenauswertung konzipiert, charakterisiert und angewandt. Gegen{\"u}ber der bislang {\"u}blichen alleinigen Bewertung der Verfestigung anhand indirekter Ultraschallparameter wie Ausbreitungsgeschwindigkeit, Signalenergie oder Frequenzgehalt der Longitudinalwelle l{\"a}sst sich damit eine direkte, sensible Erfassung der sich w{\"a}hrend der Strukturbildung entwickelnden dynamischen elastischen Eigenschaften auf der Basis prim{\"a}rer physikalischer Werkstoffparameter erreichen. Insbesondere Scherwellen und der dynamische Schubmodul sind geeignet, den graduellen {\"U}bergang zum Festk{\"o}rper mit {\"U}berschreiten der Perkolationsschwelle sensibel und unabh{\"a}ngig vom Luftgehalt zu erfassen. Die zeitliche Entwicklung der dynamischen elastischen Eigenschaften, die Strukturbildungsraten sowie die daraus extrahierten diskreten Ergebnisparameter erm{\"o}glichen eine vergleichende quantitative Charakterisierung der Strukturbildung zementgebundener Baustoffe aus mechanischer Sicht. Dabei lassen sich typische, oft unvermeidbare Unterschiede in der Zusammensetzung der Versuchsmischungen ber{\"u}cksichtigen. Der Einsatz laserbasierter Methoden zur Anregung und Erfassung von mechanischen Wellen und deren Kombination zu Laser-Ultraschall zielt darauf ab, die mit der Anwendung des konventionellen Ultraschall-Transmissionsverfahrens verbundenen Nachteile zu eliminieren. Diese resultieren aus der Sensorgeometrie, der mechanischen Ankopplung und bei einer Vielzahl von Oberfl{\"a}chenpunkten aus einem hohen pr{\"u}ftechnischen Aufwand. Die laserbasierte, interferometrische Erfassung mechanischer Wellen ist gegen{\"u}ber Ultraschallsensoren rauschbehaftet und vergleichsweise unsensibel. Als wesentliche Voraussetzung der scannenden Anwendung von Laser-Ultraschall auf zementgebundene Baustoffe erfolgen systematische experimentelle Untersuchungen zur laserinduzierten ablativen Anregung. Diese sollen zum Verst{\"a}ndnis des Anregungsmechanismus unmittelbar auf den Oberfl{\"a}chen von zementgebundenen Baustoffen, Gesteinsk{\"o}rnungen und metallischen Werkstoffen beitragen, relevante Einflussfaktoren aus den charakteristischen Materialeigenschaften identifizieren, geeignete Prozessparameter gewinnen und die Verfahrensgrenzen aufzeigen. Unter Einsatz von Longitudinalwellen erfolgt die Anwendung von Laser-Ultraschall zur zeit- und ortsaufgel{\"o}sten Charakterisierung der Strukturbildung und Homogenit{\"a}t frischer sowie erh{\"a}rteter Proben zementgebundener Baustoffe. W{\"a}hrend der Strukturbildung wird erstmals eine simultane ber{\"u}hrungslose Erfassung von Longitudinal- und Scherwellen vorgenommen. Unter Anwendung von tomographischen Methoden (2D-Laufzeit¬tomo¬graphie) werden {\"u}berlagerungsfreie Informationen zur r{\"a}umlichen Verteilung struktureller Gef{\"u}gever{\"a}nderungen anhand der longitudinalen Ausbreitungsgeschwindigkeit bzw. des relativen dynamischen Elastizit{\"a}tsmoduls innerhalb von virtuellen Schnittebenen gesch{\"a}digter Probek{\"o}rper gewonnen. Als beton-sch{\"a}digende Mechanismen werden exemplarisch der kombinierte Frost-Tausalz-Angriff sowie die Alkali-Kiesels{\"a}ure-Reaktion (AKR) herangezogen. Die im Rahmen dieser Arbeit entwickelten Verfahren der zerst{\"o}rungsfreien Pr{\"u}fung bieten erweiterte M{\"o}glichkeiten zur Charakterisierung zementgebundener Baustoffe und deren strukturellen Ver{\"a}nderungen und lassen sich zielgerichtet in der Werkstoffentwicklung, bei der Qualit{\"a}tssicherung sowie zur Analyse von Schadensprozessen und -ursachen einsetzen.},
  subject      = {Beton},
  language  = {de}
}
@phdthesis{Jenabidehkordi,
  author    = {Jenabidehkordi, Ali},
  title     = {An efficient adaptive PD formulation for complex microstructures},
  doi       = {10.25643/bauhaus-universitaet.4738},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221116-47389},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {118},
  abstract  = {The computational costs of newly developed numerical simulation play a critical role in their acceptance within both academic use and industrial employment. Normally, the refinement of a method in the area of interest reduces the computational cost. This is unfortunately not true for most nonlocal simulation, since refinement typically increases the size of the material point neighborhood. Reducing the discretization size while keep- ing the neighborhood size will often require extra consideration. Peridynamic (PD) is a newly developed numerical method with nonlocal nature. Its straightforward integral form equation of motion allows simulating dynamic problems without any extra consideration required. The formation of crack and its propagation is known as natural to peridynamic. This means that discontinuity is a result of the simulation and does not demand any post-processing. As with other nonlocal methods, PD is considered an expensive method. The refinement of the nodal spacing while keeping the neighborhood size (i.e., horizon radius) constant, emerges to several nonphysical phenomena. This research aims to reduce the peridynamic computational and imple- mentation costs. A novel refinement approach is introduced. The pro- posed approach takes advantage of the PD flexibility in choosing the shape of the horizon by introducing multiple domains (with no intersections) to the nodes of the refinement zone. It will be shown that no ghost forces will be created when changing the horizon sizes in both subdomains. The approach is applied to both bond-based and state-based peridynamic and verified for a simple wave propagation refinement problem illustrating the efficiency of the method. Further development of the method for higher dimensions proves to have a direct relationship with the mesh sensitivity of the PD. A method for solving the mesh sensitivity of the PD is intro- duced. The application of the method will be examined by solving a crack propagation problem similar to those reported in the literature. New software architecture is proposed considering both academic and in- dustrial use. The available simulation tools for employing PD will be collected, and their advantages and drawbacks will be addressed. The challenges of implementing any node base nonlocal methods while max- imizing the software flexibility to further development and modification will be discussed and addressed. A software named Relation-Based Sim- ulator (RBS) is developed for examining the proposed architecture. The exceptional capabilities of RBS will be explored by simulating three distinguished models. RBS is available publicly and open to further develop- ment. The industrial acceptance of the RBS will be tested by targeting its performance on one Mac and two Linux distributions.},
  subject      = {Peridynamik},
  language  = {en}
}
@phdthesis{Partschefeld,
  author    = {Partschefeld, Stephan},
  title     = {Synthese von Fließmitteln aus St{\"a}rke und Untersuchung der Wechselwirkung mit Portlandzement},
  doi       = {10.25643/bauhaus-universitaet.4640},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220505-46402},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {145},
  abstract  = {Das Ziel dieser Arbeit war es, neuartige Fließmittel auf Basis von St{\"a}rke als nachwachsenden Rohstoff zu synthetisieren und die Wechselwirkung mit Portlandzement zu charakterisieren. Die Notwendigkeit, Alternativen zu synthetischen Zusatzmittel zu erforschen, ergibt sich aus der ben{\"o}tigten Menge zur Verarbeitung von ca. 4,1 Gt/a, wobei ca. 85 \% der Zusatzmittel auf die Fließmittel entfallen. Um Fließmittel aus St{\"a}rke zu synthetisieren, wurden drei Basisst{\"a}rken unterschiedlicher Herkunft verwendet. Es wurde eine Maniokst{\"a}rke mit einer niedrigen Molekularmasse und eine Weizenst{\"a}rke mit einer hohen Molekularmasse verwendet. Dar{\"u}ber hinaus wurde eine Kartoffelst{\"a}rke mit einer mittleren Molekularmasse, die ein Abfallprodukt der kartoffelverarbeitenden Industrie darstellt, genutzt. Die St{\"a}rkefließmittel wurden durch chemische Modifikation in einem zweistufigen Prozess synthetisiert. Im ersten Schritt wurde das Molekulargewicht der Weizen- und Kartoffelst{\"a}rke durch s{\"a}urehydrolytischen Abbau verringert. F{\"u}r die kurzkettige Maniokst{\"a}rke war eine Degradation der Molekularmasse nicht notwendig. Im zweiten Syntheseschritt wurden anionische Ladungen durch das Versetzen der degradierten St{\"a}rken und Maniokst{\"a}rke mit Natriumvinylsulfonat in die St{\"a}rkemolek{\"u}le eingef{\"u}hrt. Beurteilung der Synthesemethode zur Erzeugung von St{\"a}rkefließmitteln In diesem Zusammenhang sollten molekulare Parameter der St{\"a}rkefließmittel gezielt eingestellt werden, um eine Fließwirkung im Portlandzement zu erhalten. Insbesondere die Molekularmasse und die Menge anionischer Ladungen sollte variiert werden, um Abh{\"a}ngigkeiten mit der Dispergierleistung zu identifizieren. 1. Es konnte durch GPC-Messungen gezeigt werden, dass die Molekularmasse der langkettigen Weizenst{\"a}rke durch die gew{\"a}hlten Modifizierungsbedingungen zum s{\"a}urehydrolytischen Abbau verringert werden konnte. Durch Variation der s{\"a}urehydrolytischen Bedingungen wurden 4 degradierte Weizenst{\"a}rken erzeugt, die eine Reduzierung der Molekularmasse um 27,5 - 43 \% aufwiesen. Die Molekularmasse der Kartoffelst{\"a}rke konnte durch s{\"a}urehydrolytischen Abbau um ca. 26 \% verringert werden. 2. Durch PCD-Messungen wurde gezeigt, dass anionische Ladungen durch Sulfoethylierung der freien Hydroxylgruppen in die degradierten St{\"a}rken eingef{\"u}hrt werden konnten. Durch Variation der Dauer der Sulfoethylierung konnte die Menge der anionischen Ladungen gesteuert und gezielt variiert werden, so dass St{\"a}rkefließmittel mit steigender Ladungsmenge in folgender Reihenfolge synthetisiert wurden: W-3 < W-2 < K-1 < W¬-4 < W¬1 < M-1 Im Ergebnis der chemischen Modifizierung konnten 6 St{\"a}rkefließmittel mit variierten Molekularmassen und anionischen Ladungen erzeugt werden. Es konnte gezeigt werden, dass die Herkunft der St{\"a}rke f{\"u}r die chemische Modifizierung unerheblich ist. Die Fließmittel lagen synthesebedingt als basische, w{\"a}ssrige Suspensionen mit Wirkstoffgehalten im Bereich von 23,5 - 50 \% vor. Beurteilung der Dispergierleistung der synthetisierten St{\"a}rkefließmittel Die Dispergierperformance wurde durch rheologische Experimente mit einem Rotationsviskosimeter erfasst. Dabei wurden der Einfluss auf die Fließkurven und die Viskosit{\"a}tskurven betrachtet. Durch Vergleich der Dispergierleistung mit einem Polykondensat- und einem PCE-Fließmittel konnte eine Einordnung und Bewertung der Fließmittel vorgenommen werden. 3. Die rheologische Experimente haben gezeigt, dass die St{\"a}rkefließmittel eine vergleichbar hohe Dispergierleistung aufweisen, wie das zum Vergleich herangezogen PCE-Fließmittel. Dar{\"u}ber hinaus zeigte sich, dass die Fließwirkung der 6 St{\"a}rkefließmittel gegen{\"u}ber dem Polykondensatfließmittel deutlich h{\"o}her ist. Das aus der Literatur bekannte Einbrechen der Dispergierleistung der Polykondensat-fließmittel bei w/z-Werten < 0,4 konnte best{\"a}tigt werden. 4. Alle 6 St{\"a}rkefließmittel f{\"u}hrten zu einer Verringerung der Fließgrenze und der dynamischen Viskosit{\"a}t des Zementleimes bei einem w/z-Wert von 0,35. 5. Der Vergleich der Dispergierleistung der St{\"a}rkefließmittel untereinander zeigte, dass die anionische Ladungsmenge einen Schl{\"u}sselparameter darstellt. Die St{\"a}rkefließmittel M-1, K-1, W-1 und W-4 mit anionischen Ladungsmengen > 6 C/g zeigten die h{\"o}chste Dispergier¬performance. Die vergleichend herangezogenen klassischen Fließmittel wiesen anionische Ladungsmengen im Bereich von 1,2 C/g (Polycondensat) und 1,6 C/g (PCE) auf. Die Molekularmasse schien f{\"u}r die Dispergierleistung zun{\"a}chst unerheblich zu sein. Aus diesem Grund wurde die Basisweizenst{\"a}rke erneut chemisch modifiziert, indem anionische Ladungen eingef{\"u}hrt wurden, ohne die Molekularmasse jedoch zu verringern. Das St{\"a}rkederivat wies verdickende Eigenschaften im Zementleim auf. Daraus konnte geschlussfolgert werden, dass eine definierte Grenzmolekularmasse (150.000 Da) existiert, die unterschritten werden muss, um Fließmittel aus St{\"a}rke zu erzeugen. Des Weiteren zeigen die Ergebnisse, dass durch die chemische Modifizierung sowohl Fließmittel als auch Verdicker aus St{\"a}rke erzeugt werden k{\"o}nnen. Beurteilung der Beeinflussung der Hydratation und der Porenl{\"o}sung des Portlandzementes Aus der Literatur ist bekannt, dass Fließmittel die Hydratation von Portlandzement maßgeblich beeinflussen k{\"o}nnen. Aus diesem Grund wurden kalorimetrische und konduktometrische Untersuchungen an Zementsuspensionen, die mit den synthetisierten St{\"a}rkefließmitteln versetzt wurden, durchgef{\"u}hrt. Erg{\"a}nzt wurden die Untersuchungen durch Porenl{\"o}sungsanalysen zu verschiedenen Zeitpunkten der Hydratation. 6. Die kalorimetrischen Untersuchungen zur Beeinflussung der Hydratation des Portlandzementes zeigten, dass die dormante Periode durch die Zugabe der St{\"a}rkefließmittel z.T. erheblich verl{\"a}ngert wird. Es konnte gezeigt werden, dass, je h{\"o}her die anionische Ladungsmenge der St{\"a}rkefließmittel ist, desto l{\"a}nger dauert die dormante Periode andauert. Dar{\"u}ber hinaus zeigte sich, dass eine niedrige Molekularmasse der St{\"a}rkefließmittel die Verl{\"a}ngerung der dormanten Periode beg{\"u}nstigt. 7. Durch die konduktometrischen Untersuchungen konnte gezeigt werden, dass alle St{\"a}rkefließmittel die Dauer des freien- und diffusionskontrollierten CSH-Phasenwachstums verlangsamen. Insbesondere die Ausf{\"a}llung des Portlandits, welches mit dem Erstarrungsbeginn korreliert, erfolgt zu deutlich sp{\"a}teren Zeitpunkten. Des Weiteren korrelierten die konduktometrischen Untersuchungen mit der zeitlichen Entwicklung der Calciumkonzentration der Porenl{\"o}sungen. Der Vergleich der St{\"a}rkefließmittel untereinander zeigte, dass die Molekularmasse ein Schl{\"u}sselparameter ist. Das St{\"a}rkefließmittel M-1 mit der geringsten Molekularmasse, welches geringe Mengen kurzkettiger Anhydroglucoseeinheiten aufweist, verz{\"o}gert die Hydratphasenbildung am st{\"a}rksten. Diese Wirkung ist vergleichbar mit der von Zuckern. Dar{\"u}ber hinaus deuteten die Ergebnisse daraufhin, dass die St{\"a}rkefließmittel auf den ersten Hydratationsprodukten adsorbieren, wodurch die Hydratphasenbildung verlangsamt wird. Die kalorimetrischen und konduktometrischen Daten sowie die Ergebnisse der Porenl{\"o}sungsanalytik des Zementes, erforderten eine genauere Betrachtung der Beeinflussung der Hydratation der Klinkerphasen C3A und C3S, durch die St{\"a}rkefließmittel. Demzufolge wurden die Untersuchungen mit den Klinkerphasen C3A und C3S in Analogie zum Portlandzement durchgef{\"u}hrt. Beurteilung der Beeinflussung der Hydratation und der Porenl{\"o}sung des C3A W{\"a}hrend die kalorimetrischen Untersuchungen zur C3A-Hydratation eine Tendenz zur verlangsamten Hydratphasenbildung durch die St{\"a}rkefließmittel aufzeigten, lieferten die konduktometrischen Ergebnisse grundlegende Erkenntnisse zur Beeinflussung der C3A-Hydratation. Das Stadium I der C3A-Hydratation ist durch einen Abfall der elektrischen Leitf{\"a}higkeit gepr{\"a}gt. Dies korreliert mit dem Absinken der Calciumionenkonzentration und dem Anstieg der Aluminiumionenkonzentration in der Porenl{\"o}sung der C3A-Suspensionen. Im Anschluss an das Stadium I bildet sich ein Plateau in den elektrischen Leitf{\"a}higkeitskurven aus. 8. Es konnte gezeigt werden, dass die St{\"a}rkefließmittel das Stadium I der C3A-Hydratation, d.h. die Aufl{\"o}sung und Bildung erster Calciumaluminathydrate verlangsamen. Insbesondere die St{\"a}rkefließmittel mit h{\"o}herer Molekularmasse erh{\"o}hten die Dauer des Stadium I. Das Stadium II wird durch die St{\"a}rkefließmittel in folgender Reihenfolge am st{\"a}rksten verl{\"a}ngert: M-1 > W-3 > K-1 > W-2 ≥ W-4 und verdeutlicht, dass keine Abh{\"a}ngigkeit von der anionischen Ladungsmenge identifiziert werden konnte. Die Ergebnisse zeigten, dass speziell die kurzkettige St{\"a}rke M-1, das Stadium II l{\"a}nger aufrechterhalten. 9. Das Stadium III und IV der C3A-Hydratation wird insbesondere durch die St{\"a}rkefließmittel mit h{\"o}herer Molekularmasse verl{\"a}ngert. Die Ergebnisse der Porenl{\"o}sungsanalytik korrelieren mit den Ergebnissen der elektrischen Leitf{\"a}higkeit. Speziell die zeitlichen Verl{\"a}ufe der Calciumionenkonzentration bildeten die Verl{\"a}ufe der Konduktivit{\"a}tskurven der C3A-Hydratation mit großer {\"U}bereinstimmung ab. Beurteilung der Beeinflussung der Hydratation und der Porenl{\"o}sung des C3S Die Ergebnisse der kalorimetrischen Untersuchungen zur Beeinflussung der C3S-Hydratation durch die St{\"a}rkefließmittel zeigen, dass diese maßgeblich verlangsamt wird. Das Maximum des Haupthydratationspeaks wird zu sp{\"a}teren Zeiten verschoben und auch die H{\"o}he des Maximums wird deutlich verringert. Durch die konduktometrischen Experimente wurde aufgekl{\"a}rt, welche Stadien der C3S-Hydrataion beeinflusst wurden. 10. Es konnte gezeigt werden, dass sowohl die Menge der eingebrachten anionischen Ladungen als auch das Vorhandensein sehr kleiner St{\"a}rkefließmittelmolek{\"u}le (Zucker), Schl{\"u}sselparameter der verz{\"o}gerten Hydratationskinetik des C3S sind. Der grundlegende Mechanismus der Hydratationsverz{\"o}gerung beruht auf einer Kombination aus verminderter CSH-Keimbildung und Adsorptionsprozessen auf den ersten gebildeten CSH-Phasen der C3S-Partikel. Beurteilung des Adsorptionsverhaltens am Zement, C3A und C3S Die Bestimmung des Adsorptionsverhaltens der St{\"a}rkefließmittel erfolgte mit der Phenol-Schwefels{\"a}ure-Methode an Zement,- C3A- und C3S-Suspensionen. Durch den Vergleich der Adsorptionsraten und Adsorptionsmengen in Abh{\"a}ngigkeit von den molekularen Parametern der St{\"a}rkefließmittel wurde ein Wechselwirkungsmodell identifiziert. 11. Die Ursache f{\"u}r die hohe Dispergierleistung der St{\"a}rkefließmittel liegt in Adsorptionsprozessen an den ersten gebildeten Hydratphasen des Zementes begr{\"u}ndet. Die Molekularmasse der St{\"a}rkefließmittel ist ein Schl{\"u}sselparameter der entscheidend f{\"u}r den Mechanismus der Adsorption ist. W{\"a}hrend anionische, langkettige St{\"a}rken an mehreren Zementpartikeln gleichzeitig adsorbieren und f{\"u}r eine Vernetzung der Zementpartikel untereinander sorgen (Verdickerwirkung), adsorbieren kurzkettige anionische St{\"a}rken lediglich an den ersten gebildeten Hydratphasen der einzelnen Zementpartikel und f{\"u}hren zu elektrostatischer Abstoßung (Fließmittelwirkung). 12. Es konnte gezeigt werden, dass die St{\"a}rkefließmittel mit geringerem Molekulargewicht bei h{\"o}heren Konzentrationen an den Hydratphasen des Zementes adsorbieren. Die St{\"a}rkefließmittel mit h{\"o}herer Molekularmasse erreichen bei einer Zugabemenge von 0,7 \% ein Plateau. Daraus wird geschlussfolgert, dass die gr{\"o}ßeren Fließmittelmolek{\"u}le einen erh{\"o}hten Platzbedarf erfordern und zur Abs{\"a}ttigung der hydratisierenden Oberfl{\"a}chen bei geringeren Zugabemengen f{\"u}hren. Dar{\"u}ber hinaus konnte gezeigt werden, dass die St{\"a}rkefließmittel mit h{\"o}herer anionischer Ladungsmenge zu h{\"o}heren Adsorptionsmengen auf den Zement-, C3A- und C3S-Partikeln f{\"u}hren. 13. Die Adsorptionsprozesse finden an den ersten gebildeten Hydratphasen der C3A-Partikel statt, wodurch sowohl die Aufl{\"o}sung des C3A als auch die Bildung der Calciumhydroaluminate verlangsamt wird. Dar{\"u}ber hinaus wurde festgestellt, dass die Verlangsamung des freien- und diffusionskontrollierten Hydratphasenwachstums des C3S, durch die Adsorption der St{\"a}rkefließmittel auf den ersten gebildeten CSH-Phasen hervorgerufen wird. Des Weiteren wurde festgestellt, dass sehr kleine zucker{\"a}hnliche Molek{\"u}le in der kurzkettigen Maniokst{\"a}rke in der Lage sind, die Bildung der ersten CSH-Keime zu unterdr{\"u}cken. Dadurch kann die langanhaltende Plateauphase der elektrischen Leitf{\"a}higkeit der C3S-Hydratation erkl{\"a}rt werden. Beurteilung der Porenstruktur- und Festigkeitsausbildung Die Beurteilung der Qualit{\"a}t der Mikrostruktur erfolgte durch die Bestimmung der Rohdichte und der Porenradienverteilung mit Hilfe der Quecksilberhochdruckporosimetrie. Durch das Versetzen der Zementleime mit den St{\"a}rkefließmitteln konnten bei gleichbleibender Verarbeitbarkeit Zementsteinprobek{\"o}rper mit einem um 17,5 \% geringeren w/z-Wert von 0,35 hergestellt werden. Die Absenkung des w/z-Wertes f{\"u}hrt zu einem Anstieg der Rohdichte des Zementsteins. 14. Durch die Zugabe der St{\"a}rkefließmittel und den verringerten w/z-Wert wird die Porenstruktur der Zementsteinproben im Vergleich zum Referenzzementstein verfeinert, da die Gesamtporosit{\"a}t sinkt. Insbesondere der Kapillarporenanteil wird verringert und der Gelporenanteil erh{\"o}ht. Im Unterschied zu den PCE-Fließmitteln f{\"u}hrt die Zugabe der St{\"a}rkefließmittel zu keinem erh{\"o}hten Eintrag von Luftporen. Dies wiederum hat zur Folge, dass bei der Verwendung der St{\"a}rkefließmittel auf Entsch{\"a}umer verzichtet werden kann. 15. Entsprechend der dichteren Zementsteinmatrix wurden f{\"u}r die Zementsteine mit den St{\"a}rkefließmitteln nach 7 d und 28 d, erh{\"o}hte Biegezug- und Druckfestigkeiten ermittelt. Insbesondere die 28 d Druckfestigkeit wurde durch den verringerten w/z-Wert um die Faktoren 3,5 - 6,6 erh{\"o}ht.},
  subject      = {Bauchemie},
  language  = {de}
}
@phdthesis{Zhang,
  author    = {Zhang, Yongzheng},
  title     = {A Nonlocal Operator Method for Quasi-static and Dynamic Fracture Modeling},
  doi       = {10.25643/bauhaus-universitaet.4732},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221026-47321},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {Material failure can be tackled by so-called nonlocal models, which introduce an intrinsic length scale into the formulation and, in the case of material failure, restore the well-posedness of the underlying boundary value problem or initial boundary value problem. Among nonlocal models, peridynamics (PD) has attracted a lot of attention as it allows the natural transition from continuum to discontinue and thus allows modeling of discrete cracks without the need to describe and track the crack topology, which has been a major obstacle in traditional discrete crack approaches. This is achieved by replacing the divergence of the Cauchy stress tensor through an integral over so-called bond forces, which account for the interaction of particles. A quasi-continuum approach is then used to calibrate the material parameters of the bond forces, i.e., equating the PD energy with the energy of a continuum. One major issue for the application of PD to general complex problems is that they are limited to fairly simple material behavior and pure mechanical problems based on explicit time integration. PD has been extended to other applications but losing simultaneously its simplicity and ease in modeling material failure. Furthermore, conventional PD suffers from instability and hourglass modes that require stabilization. It also requires the use of constant horizon sizes, which drastically reduces its computational efficiency. The latter issue was resolved by the so-called dual-horizon peridynamics (DH-PD) formulation and the introduction of the duality of horizons. Within the nonlocal operator method (NOM), the concept of nonlocality is further extended and can be considered a generalization of DH-PD. Combined with the energy functionals of various physical models, the nonlocal forms based on the dual-support concept can be derived. In addition, the variation of the energy functional allows implicit formulations of the nonlocal theory. While traditional integral equations are formulated in an integral domain, the dual-support approaches are based on dual integral domains. One prominent feature of NOM is its compatibility with variational and weighted residual methods. The NOM yields a direct numerical implementation based on the weighted residual method for many physical problems without the need for shape functions. Only the definition of the energy or boundary value problem is needed to drastically facilitate the implementation. The nonlocal operator plays an equivalent role to the derivatives of the shape functions in meshless methods and finite element methods (FEM). Based on the variational principle, the residual and the tangent stiffness matrix can be obtained with ease by a series of matrix multiplications. In addition, NOM can be used to derive many nonlocal models in strong form. The principal contributions of this dissertation are the implementation and application of NOM, and also the development of approaches for dealing with fractures within the NOM, mostly for dynamic fractures. The primary coverage and results of the dissertation are as follows: -The first/higher-order implicit NOM and explicit NOM, including a detailed description of the implementation, are presented. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combining with the method of weighted residuals and variational principles, NOM establishes the residual and tangent stiffness matrix of operate energy functional through some simple matrix without the need of shape functions as in other classical computational methods such as FEM. NOM only requires the definition of the energy drastically simplifying its implementation. For the sake of conciseness, the implementation in this chapter is focused on linear elastic solids only, though the NOM can handle more complex nonlinear problems. An explicit nonlocal operator method for the dynamic analysis of elasticity solid problems is also presented. The explicit NOM avoids the calculation of the tangent stiffness matrix as in the implicit NOM model. The explicit scheme comprises the Verlet-velocity algorithm. The NOM can be very flexible and efficient for solving partial differential equations (PDEs). It's also quite easy for readers to use the NOM and extend it to solve other complicated physical phenomena described by one or a set of PDEs. Several numerical examples are presented to show the capabilities of this method. -A nonlocal operator method for the dynamic analysis of (thin) Kirchhoff plates is proposed. The nonlocal Hessian operator is derived from a second-order Taylor series expansion. NOM is higher-order continuous, which is exploited for thin plate analysis that requires \$C^1\$ continuity. The nonlocal dynamic governing formulation and operator energy functional for Kirchhoff plates are derived from a variational principle. The Verlet-velocity algorithm is used for time discretization. After confirming the accuracy of the nonlocal Hessian operator, several numerical examples are simulated by the nonlocal dynamic Kirchhoff plate formulation. -A nonlocal fracture modeling is developed and applied to the simulation of quasi-static and dynamic fractures using the NOM. The phase field's nonlocal weak and associated strong forms are derived from a variational principle. The NOM requires only the definition of energy. We present both a nonlocal implicit phase field model and a nonlocal explicit phase field model for fracture; the first approach is better suited for quasi-static fracture problems, while the key application of the latter one is dynamic fracture. To demonstrate the performance of the underlying approach, several benchmark examples for quasi-static and dynamic fracture are solved.},
  subject      = {Variationsprinzip},
  language  = {en}
}