@phdthesis{LopezZermeno,
  author    = {L{\´o}pez Zerme{\~n}o, Jorge Alberto},
  title     = {Isogeometric and CAD-based methods for shape and topology optimization: Sensitivity analysis, B{\´e}zier elements and phase-field approaches},
  doi       = {10.25643/bauhaus-universitaet.4710},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220831-47102},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {The Finite Element Method (FEM) is widely used in engineering for solving Partial Differential Equations (PDEs) over complex geometries. To this end, it is required to provide the FEM software with a geometric model that is typically constructed in a Computer-Aided Design (CAD) software. However, FEM and CAD use different approaches for the mathematical description of the geometry. Thus, it is required to generate a mesh, which is suitable for FEM, based on the CAD model. Nonetheless, this procedure is not a trivial task and it can be time consuming. This issue becomes more significant for solving shape and topology optimization problems, which consist in evolving the geometry iteratively. Therefore, the computational cost associated to the mesh generation process is increased exponentially for this type of applications. The main goal of this work is to investigate the integration of CAD and CAE in shape and topology optimization. To this end, numerical tools that close the gap between design and analysis are presented. The specific objectives of this work are listed below: • Automatize the sensitivity analysis in an isogeometric framework for applications in shape optimization. Applications for linear elasticity are considered. • A methodology is developed for providing a direct link between the CAD model and the analysis mesh. In consequence, the sensitivity analysis can be performed in terms of the design variables located in the design model. • The last objective is to develop an isogeometric method for shape and topological optimization. This method should take advantage of using Non-Uniform Rational B-Splines (NURBS) with higher continuity as basis functions. Isogeometric Analysis (IGA) is a framework designed to integrate the design and analysis in engineering problems. The fundamental idea of IGA is to use the same basis functions for modeling the geometry, usually NURBS, for the approximation of the solution fields. The advantage of integrating design and analysis is two-fold. First, the analysis stage is more accurate since the system of PDEs is not solved using an approximated geometry, but the exact CAD model. Moreover, providing a direct link between the design and analysis discretizations makes possible the implementation of efficient sensitivity analysis methods. Second, the computational time is significantly reduced because the mesh generation process can be avoided. Sensitivity analysis is essential for solving optimization problems when gradient-based optimization algorithms are employed. Automatic differentiation can compute exact gradients, automatically by tracking the algebraic operations performed on the design variables. For the automation of the sensitivity analysis, an isogeometric framework is used. Here, the analysis mesh is obtained after carrying out successive refinements, while retaining the coarse geometry for the domain design. An automatic differentiation (AD) toolbox is used to perform the sensitivity analysis. The AD toolbox takes the code for computing the objective and constraint functions as input. Then, using a source code transformation approach, it outputs a code for computing the objective and constraint functions, and their sensitivities as well. The sensitivities obtained from the sensitivity propagation method are compared with analytical sensitivities, which are computed using a full isogeometric approach. The computational efficiency of AD is comparable to that of analytical sensitivities. However, the memory requirements are larger for AD. Therefore, AD is preferable if the memory requirements are satisfied. Automatic sensitivity analysis demonstrates its practicality since it simplifies the work of engineers and designers. Complex geometries with sharp edges and/or holes cannot easily be described with NURBS. One solution is the use of unstructured meshes. Simplex-elements (triangles and tetrahedra for two and three dimensions respectively) are particularly useful since they can automatically parameterize a wide variety of domains. In this regard, unstructured B{\´e}zier elements, commonly used in CAD, can be employed for the exact modelling of CAD boundary representations. In two dimensions, the domain enclosed by NURBS curves is parameterized with B{\´e}zier triangles. To describe exactly the boundary of a two-dimensional CAD model, the continuity of a NURBS boundary representation is reduced to C^0. Then, the control points are used to generate a triangulation such that the boundary of the domain is identical to the initial CAD boundary representation. Thus, a direct link between the design and analysis discretizations is provided and the sensitivities can be propagated to the design domain. In three dimensions, the initial CAD boundary representation is given as a collection of NURBS surfaces that enclose a volume. Using a mesh generator (Gmsh), a tetrahedral mesh is obtained. The original surface is reconstructed by modifying the location of the control points of the tetrahedral mesh using B{\´e}zier tetrahedral elements and a point inversion algorithm. This method offers the possibility of computing the sensitivity analysis using the analysis mesh. Then, the sensitivities can be propagated into the design discretization. To reuse the mesh originally generated, a moving B{\´e}zier tetrahedral mesh approach was implemented. A gradient-based optimization algorithm is employed together with a sensitivity propagation procedure for the shape optimization cases. The proposed shape optimization approaches are used to solve some standard benchmark problems in structural mechanics. The results obtained show that the proposed approach can compute accurate gradients and evolve the geometry towards optimal solutions. In three dimensions, the moving mesh approach results in faster convergence in terms of computational time and avoids remeshing at each optimization step. For considering topological changes in a CAD-based framework, an isogeometric phase-field based shape and topology optimization is developed. In this case, the diffuse interface of a phase-field variable over a design domain implicitly describes the boundaries of the geometry. The design variables are the local values of the phase-field variable. The descent direction to minimize the objective function is found by using the sensitivities of the objective function with respect to the design variables. The evolution of the phase-field is determined by solving the time dependent Allen-Cahn equation. Especially for topology optimization problems that require C^1 continuity, such as for flexoelectric structures, the isogeometric phase field method is of great advantage. NURBS can achieve the desired continuity more efficiently than the traditional employed functions. The robustness of the method is demonstrated when applied to different geometries, boundary conditions, and material configurations. The applications illustrate that compared to piezoelectricity, the electrical performance of flexoelectric microbeams is larger under bending. In contrast, the electrical power for a structure under compression becomes larger with piezoelectricity.},
  subject      = {CAD},
  language  = {en}
}
@phdthesis{NguyenThanh,
  author    = {Nguyen-Thanh, Nhon},
  title     = {Isogeometric analysis based on rational splines over hierarchical T-mesh and alpha finite element method for structural analysis},
  issn      = {1610-7381},
  doi       = {10.25643/bauhaus-universitaet.2078},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20131125-20781},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {196},
  abstract  = {This thesis presents two new methods in finite elements and isogeometric analysis for structural analysis. The first method proposes an alternative alpha finite element method using triangular elements. In this method, the piecewise constant strain field of linear triangular finite element method models is enhanced by additional strain terms with an adjustable parameter a, which results in an effectively softer stiffness formulation compared to a linear triangular element. In order to avoid the transverse shear locking of Reissner-Mindlin plates analysis the alpha finite element method is coupled with a discrete shear gap technique for triangular elements to significantly improve the accuracy of the standard triangular finite elements. The basic idea behind this element formulation is to approximate displacements and rotations as in the standard finite element method, but to construct the bending, geometrical and shear strains using node-based smoothing domains. Several numerical examples are presented and show that the alpha FEM gives a good agreement compared to several other methods in the literature. Second method, isogeometric analysis based on rational splines over hierarchical T-meshes (RHT-splines) is proposed. The RHT-splines are a generalization of Non-Uniform Rational B-splines (NURBS) over hierarchical T-meshes, which is a piecewise bicubic polynomial over a hierarchical T-mesh. The RHT-splines basis functions not only inherit all the properties of NURBS such as non-negativity, local support and partition of unity but also more importantly as the capability of joining geometric objects without gaps, preserving higher order continuity everywhere and allow local refinement and adaptivity. In order to drive the adaptive refinement, an efficient recovery-based error estimator is employed. For this problem an imaginary surface is defined. The imaginary surface is basically constructed by RHT-splines basis functions which is used for approximation and interpolation functions as well as the construction of the recovered stress components. Numerical investigations prove that the proposed method is capable to obtain results with higher accuracy and convergence rate than NURBS results.},
  subject      = {Isogeometric analysis},
  language  = {en}
}
@phdthesis{Schwedler,
  author    = {Schwedler, Michael},
  title     = {Integrated structural analysis using isogeometric finite element methods},
  doi       = {10.25643/bauhaus-universitaet.2737},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170130-27372},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {209},
  abstract  = {The gradual digitization in the architecture, engineering, and construction industry over the past fifty years led to an extremely heterogeneous software environment, which today is embodied by the multitude of different digital tools and proprietary data formats used by the many specialists contributing to the design process in a construction project. Though these projects become increasingly complex, the demands on financial efficiency and the completion within a tight schedule grow at the same time. The digital collaboration of project partners has been identified as one key issue in successfully dealing with these challenges. Yet currently, the numerous software applications and their respective individual views on the design process severely impede that collaboration. An approach to establish a unified basis for the digital collaboration, regardless of the existing software heterogeneity, is a comprehensive digital building model contributed to by all projects partners. This type of data management known as building information modeling (BIM) has many benefits, yet its adoption is associated with many difficulties and thus, proceeds only slowly. One aspect in the field of conflicting requirements on such a digital model is the cooperation of architects and structural engineers. Traditionally, these two disciplines use different abstractions of reality for their models that in consequence lead to incompatible digital representations thereof. The onset of isogeometric analysis (IGA) promised to ease the discrepancy in design and analysis model representations. Yet, that initial focus quickly shifted towards using these methods as a more powerful basis for numerical simulations. Furthermore, the isogeometric representation alone is not capable of solving the model abstraction problem. It is thus the intention of this work to contribute to an improved digital collaboration of architects and engineers by exploring an integrated analysis approach on the basis of an unified digital model and solid geometry expressed by splines. In the course of this work, an analysis framework is developed that utilizes such models to automatically conduct numerical simulations commonly required in construction projects. In essence, this allows to retrieve structural analysis results from BIM models in a fast and simple manner, thereby facilitating rapid design iterations and profound design feedback. The BIM implementation Industry Foundation Classes (IFC) is reviewed with regard to its capabilities of representing the unified model. The current IFC schema strongly supports the use of redundant model data, a major pitfall in digital collaboration. Additionally, it does not allow to describe the geometry by volumetric splines. As the pursued approach builds upon a unique model for both, architectural and structural design, and furthermore requires solid geometry, necessary schema modifications are suggested. Structural entities are modeled by volumetric NURBS patches, each of which constitutes an individual subdomain that, with regard to the analysis, is incompatible with the remaining full model. The resulting consequences for numerical simulation are elaborated in this work. The individual subdomains have to be weakly coupled, for which the mortar method is used. Different approaches to discretize the interface traction fields are implemented and their respective impact on the analysis results is evaluated. All necessary coupling conditions are automatically derived from the related geometry model. The weak coupling procedure leads to a linear system of equations in saddle point form, which, owed to the volumetric modeling, is large in size and, the associated coefficient matrix has, due to the use of higher degree basis functions, a high bandwidth. The peculiarities of the system require adapted solution methods that generally cause higher numerical costs than the standard procedures for symmetric, positive-definite systems do. Different methods to solve the specific system are investigated and an efficient parallel algorithm is finally proposed. When the structural analysis model is derived from the unified model in the BIM data, it does in general initially not meet the requirements on the discretization that are necessary to obtain sufficiently accurate analysis results. The consequently necessary patch refinements must be controlled automatically to allowfor an entirely automatic analysis procedure. For that purpose, an empirical refinement scheme based on the geometrical and possibly mechanical properties of the specific entities is proposed. The level of refinement may be selectively manipulated by the structural engineer in charge. Furthermore, a Zienkiewicz-Zhu type error estimator is adapted for the use with isogeometric analysis results. It is shown that also this estimator can be used to steer an adaptive refinement procedure.},
  subject      = {Finite-Elemente-Methode},
  language  = {en}
}
@phdthesis{Abeltshauser,
  author    = {Abeltshauser, Rainer},
  title     = {Identification and separation of physical effects of coupled systems by using defined model abstractions},
  doi       = {10.25643/bauhaus-universitaet.2860},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28600},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {The thesis investigates at the computer aided simulation process for operational vibration analysis of complex coupled systems. As part of the internal methods project "Absolute Values" of the BMW Group, the thesis deals with the analysis of the structural dynamic interactions and excitation interactions. The overarching aim of the methods project is to predict the operational vibrations of engines. Simulations are usually used to analyze technical aspects (e. g. operational vibrations, strength, ...) of single components in the industrial development. The boundary conditions of submodels are mostly based on experiences. So the interactions with neighboring components and systems are neglected. To get physically more realistic results but still efficient simulations, this work wants to support the engineer during the preprocessing phase by useful criteria. At first suitable abstraction levels based on the existing literature are defined to identify structural dynamic interactions and excitation interactions of coupled systems. So it is possible to separate different effects of the coupled subsystems. On this basis, criteria are derived to assess the influence of interactions between the considered systems. These criteria can be used during the preprocessing phase and help the engineer to build up efficient models with respect to the interactions with neighboring systems. The method was developed by using several models with different complexity levels. Furthermore, the method is proved for the application in the industrial environment by using the example of a current combustion engine.},
  subject      = {Strukturdynamik},
  language  = {en}
}
@phdthesis{Schrader,
  author    = {Schrader, Kai},
  title     = {Hybrid 3D simulation methods for the damage analysis of multiphase composites},
  doi       = {10.25643/bauhaus-universitaet.2059},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20131021-20595},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {174},
  abstract  = {Modern digital material approaches for the visualization and simulation of heterogeneous materials allow to investigate the behavior of complex multiphase materials with their physical nonlinear material response at various scales. However, these computational techniques require extensive hardware resources with respect to computing power and main memory to solve numerically large-scale discretized models in 3D. Due to a very high number of degrees of freedom, which may rapidly be increased to the two-digit million range, the limited hardware ressources are to be utilized in a most efficient way to enable an execution of the numerical algorithms in minimal computation time. Hence, in the field of computational mechanics, various methods and algorithms can lead to an optimized runtime behavior of nonlinear simulation models, where several approaches are proposed and investigated in this thesis. Today, the numerical simulation of damage effects in heterogeneous materials is performed by the adaption of multiscale methods. A consistent modeling in the three-dimensional space with an appropriate discretization resolution on each scale (based on a hierarchical or concurrent multiscale model), however, still contains computational challenges in respect to the convergence behavior, the scale transition or the solver performance of the weak coupled problems. The computational efficiency and the distribution among available hardware resources (often based on a parallel hardware architecture) can significantly be improved. In the past years, high-performance computing (HPC) and graphics processing unit (GPU) based computation techniques were established for the investigationof scientific objectives. Their application results in the modification of existing and the development of new computational methods for the numerical implementation, which enables to take advantage of massively clustered computer hardware resources. In the field of numerical simulation in material science, e.g. within the investigation of damage effects in multiphase composites, the suitability of such models is often restricted by the number of degrees of freedom (d.o.f.s) in the three-dimensional spatial discretization. This proves to be difficult for the type of implementation method used for the nonlinear simulation procedure and, simultaneously has a great influence on memory demand and computational time. In this thesis, a hybrid discretization technique has been developed for the three-dimensional discretization of a three-phase material, which is respecting the numerical efficiency of nonlinear (damage) simulations of these materials. The increase of the computational efficiency is enabled by the improved scalability of the numerical algorithms. Consequently, substructuring methods for partitioning the hybrid mesh were implemented, tested and adapted to the HPC computing framework using several hundred CPU (central processing units) nodes for building the finite element assembly. A memory-efficient iterative and parallelized equation solver combined with a special preconditioning technique for solving the underlying equation system was modified and adapted to enable combined CPU and GPU based computations. Hence, it is recommended by the author to apply the substructuring method for hybrid meshes, which respects different material phases and their mechanical behavior and which enables to split the structure in elastic and inelastic parts. However, the consideration of the nonlinear material behavior, specified for the corresponding phase, is limited to the inelastic domains only, and by that causes a decreased computing time for the nonlinear procedure. Due to the high numerical effort for such simulations, an alternative approach for the nonlinear finite element analysis, based on the sequential linear analysis, was implemented in respect to scalable HPC. The incremental-iterative procedure in finite element analysis (FEA) during the nonlinear step was then replaced by a sequence of linear FE analysis when damage in critical regions occured, known in literature as saw-tooth approach. As a result, qualitative (smeared) crack initiation in 3D multiphase specimens has efficiently been simulated.},
  subject      = {high-performance computing},
  language  = {en}
}
@phdthesis{Habtemariam,
  author    = {Habtemariam, Abinet Kifle},
  title     = {Generalized Beam Theory for the analysis of thin-walled circular pipe members},
  doi       = {10.25643/bauhaus-universitaet.4572},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220127-45723},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {188},
  abstract  = {The detailed structural analysis of thin-walled circular pipe members often requires the use of a shell or solid-based finite element method. Although these methods provide a very good approximation of the deformations, they require a higher degree of discretization which causes high computational costs. On the other hand, the analysis of thin-walled circular pipe members based on classical beam theories is easy to implement and needs much less computation time, however, they are limited in their ability to approximate the deformations as they cannot consider the deformation of the cross-section. This dissertation focuses on the study of the Generalized Beam Theory (GBT) which is both accurate and efficient in analyzing thin-walled members. This theory is based on the separation of variables in which the displacement field is expressed as a combination of predetermined deformation modes related to the cross-section, and unknown amplitude functions defined on the beam's longitudinal axis. Although the GBT was initially developed for long straight members, through the consideration of complementary deformation modes, which amend the null transverse and shear membrane strain assumptions of the classical GBT, problems involving short members, pipe bends, and geometrical nonlinearity can also be analyzed using GBT. In this dissertation, the GBT formulation for the analysis of these problems is developed and the application and capabilities of the method are illustrated using several numerical examples. Furthermore, the displacement and stress field results of these examples are verified using an equivalent refined shell-based finite element model. The developed static and dynamic GBT formulations for curved thin-walled circular pipes are based on the linear kinematic description of the curved shell theory. In these formulations, the complex problem in pipe bends due to the strong coupling effect of the longitudinal bending, warping and the cross-sectional ovalization is handled precisely through the derivation of the coupling tensors between the considered GBT deformation modes. Similarly, the geometrically nonlinear GBT analysis is formulated for thin-walled circular pipes based on the nonlinear membrane kinematic equations. Here, the initial linear and quadratic stress and displacement tangent stiffness matrices are built using the third and fourth-order GBT deformation mode coupling tensors. Longitudinally, the formulation of the coupled GBT element stiffness and mass matrices are presented using a beam-based finite element formulation. Furthermore, the formulated GBT elements are tested for shear and membrane locking problems and the limitations of the formulations regarding the membrane locking problem are discussed.},
  subject      = {Finite-Elemente-Methode},
  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{Valizadeh,
  author    = {Valizadeh, Navid},
  title     = {Developments in Isogeometric Analysis and Application to High-Order Phase-Field Models of Biomembranes},
  doi       = {10.25643/bauhaus-universitaet.4565},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220114-45658},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {Isogeometric analysis (IGA) is a numerical method for solving partial differential equations (PDEs), which was introduced with the aim of integrating finite element analysis with computer-aided design systems. The main idea of the method is to use the same spline basis functions which describe the geometry in CAD systems for the approximation of solution fields in the finite element method (FEM). Originally, NURBS which is a standard technology employed in CAD systems was adopted as basis functions in IGA but there were several variants of IGA using other technologies such as T-splines, PHT splines, and subdivision surfaces as basis functions. In general, IGA offers two key advantages over classical FEM: (i) by describing the CAD geometry exactly using smooth, high-order spline functions, the mesh generation process is simplified and the interoperability between CAD and FEM is improved, (ii) IGA can be viewed as a high-order finite element method which offers basis functions with high inter-element continuity and therefore can provide a primal variational formulation of high-order PDEs in a straightforward fashion. The main goal of this thesis is to further advance isogeometric analysis by exploiting these major advantages, namely precise geometric modeling and the use of smooth high-order splines as basis functions, and develop robust computational methods for problems with complex geometry and/or complex multi-physics. As the first contribution of this thesis, we leverage the precise geometric modeling of isogeometric analysis and propose a new method for its coupling with meshfree discretizations. We exploit the strengths of both methods by using IGA to provide a smooth, geometrically-exact surface discretization of the problem domain boundary, while the Reproducing Kernel Particle Method (RKPM) discretization is used to provide the volumetric discretization of the domain interior. The coupling strategy is based upon the higher-order consistency or reproducing conditions that are directly imposed in the physical domain. The resulting coupled method enjoys several favorable features: (i) it preserves the geometric exactness of IGA, (ii) it circumvents the need for global volumetric parameterization of the problem domain, (iii) it achieves arbitrary-order approximation accuracy while preserving higher-order smoothness of the discretization. Several numerical examples are solved to show the optimal convergence properties of the coupled IGA-RKPM formulation, and to demonstrate its effectiveness in constructing volumetric discretizations for complex-geometry objects. As for the next contribution, we exploit the use of smooth, high-order spline basis functions in IGA to solve high-order surface PDEs governing the morphological evolution of vesicles. These governing equations are often consisted of geometric PDEs, high-order PDEs on stationary or evolving surfaces, or a combination of them. We propose an isogeometric formulation for solving these PDEs. In the context of geometric PDEs, we consider phase-field approximations of mean curvature flow and Willmore flow problems and numerically study the convergence behavior of isogeometric analysis for these problems. As a model problem for high-order PDEs on stationary surfaces, we consider the Cahn-Hilliard equation on a sphere, where the surface is modeled using a phase-field approach. As for the high-order PDEs on evolving surfaces, a phase-field model of a deforming multi-component vesicle, which consists of two fourth-order nonlinear PDEs, is solved using the isogeometric analysis in a primal variational framework. Through several numerical examples in 2D, 3D and axisymmetric 3D settings, we show the robustness of IGA for solving the considered phase-field models. Finally, we present a monolithic, implicit formulation based on isogeometric analysis and generalized-alpha time integration for simulating hydrodynamics of vesicles according to a phase-field model. Compared to earlier works, the number of equations of the phase-field model which need to be solved is reduced by leveraging high continuity of NURBS functions, and the algorithm is extended to 3D settings. We use residual-based variational multi-scale method (RBVMS) for solving Navier-Stokes equations, while the rest of PDEs in the phase-field model are treated using a standard Galerkin-based IGA. We introduce the resistive immersed surface (RIS) method into the formulation which can be employed for an implicit description of complex geometries using a diffuse-interface approach. The implementation highlights the robustness of the RBVMS method for Navier-Stokes equations of incompressible flows with non-trivial localized forcing terms including bending and tension forces of the vesicle. The potential of the phase-field model and isogeometric analysis for accurate simulation of a variety of fluid-vesicle interaction problems in 2D and 3D is demonstrated.},
  subject      = {Phasenfeldmodell},
  language  = {en}
}
@phdthesis{Vollmering,
  author    = {Vollmering, Max},
  title     = {Damage Localization of Mechanical Structures by Subspace Identification and Krein Space Based H-infinity Estimation},
  doi       = {10.25643/bauhaus-universitaet.3772},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20180730-37728},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {205},
  abstract  = {This dissertation is devoted to the theoretical development and experimental laboratory verification of a new damage localization method: The state projection estimation error (SP2E). This method is based on the subspace identification of mechanical structures, Krein space based H-infinity estimation and oblique projections. To explain method SP2E, several theories are discussed and laboratory experiments have been conducted and analysed. A fundamental approach of structural dynamics is outlined first by explaining mechanical systems based on first principles. Following that, a fundamentally different approach, subspace identification, is comprehensively explained. While both theories, first principle and subspace identification based mechanical systems, may be seen as widespread methods, barely known and new techniques follow up. Therefore, the indefinite quadratic estimation theory is explained. Based on a Popov function approach, this leads to the Krein space based H-infinity theory. Subsequently, a new method for damage identification, namely SP2E, is proposed. Here, the introduction of a difference process, the analysis by its average process power and the application of oblique projections is discussed in depth. Finally, the new method is verified in laboratory experiments. Therefore, the identification of a laboratory structure at Leipzig University of Applied Sciences is elaborated. Then structural alterations are experimentally applied, which were localized by SP2E afterwards. In the end four experimental sensitivity studies are shown and discussed. For each measurement series the structural alteration was increased, which was successfully tracked by SP2E. The experimental results are plausible and in accordance with the developed theories. By repeating these experiments, the applicability of SP2E for damage localization is experimentally proven.},
  subject      = {Strukturmechanik},
  language  = {en}
}
@phdthesis{ZHANG2018,
  author    = {ZHANG, CHAO},
  title     = {Crack Identification using Dynamic Extended Finite Element Method and Thermal Conductivity Engineering for Nanomaterials},
  doi       = {10.25643/bauhaus-universitaet.3847},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20190119-38478},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {2018},
  abstract  = {Identification of flaws in structures is a critical element in the management of maintenance and quality assurance processes in engineering. Nondestructive testing (NDT) techniques based on a wide range of physical principles have been developed and are used in common practice for structural health monitoring. However, basic NDT techniques are usually limited in their ability to provide the accurate information on locations, dimensions and shapes of flaws. One alternative to extract additional information from the results of NDT is to append it with a computational model that provides detailed analysis of the physical process involved and enables the accurate identification of the flaw parameters. The aim here is to develop the strategies to uniquely identify cracks in two-dimensional 2D) structures under dynamic loadings. A local NDT technique combined eXtended Finite Element Method (XFEM) with dynamic loading in order to identify the cracks in the structures quickly and accurately is developed in this dissertation. The Newmark-b time integration method with Rayleigh damping is used for the time integration. We apply Nelder-Mead (NM)and Quasi-Newton (QN) methods for identifying the crack tip in plate. The inverse problem is solved iteratively, in which XFEM is used for solving the forward problem in each iteration. For a timeharmonic excitation with a single frequency and a short-duration signal measured along part of the external boundary, the crack is detected through the solution of an inverse time-dependent problem. Compared to the static load, we show that the dynamic loads are more effective for crack detection problems. Moreover, we tested different dynamic loads and find that NM method works more efficient under the harmonic load than the pounding load while the QN method achieves almost the same results for both load types. A global strategy, Multilevel Coordinate Search (MCS) with XFEM (XFEM-MCS) methodology under the dynamic electric load, to detect multiple cracks in 2D piezoelectric plates is proposed in this dissertation. The Newmark-b method is employed for the time integration and in each iteration the forward problem is solved by XFEM for various cracks. The objective functional is minimized by using a global search algorithm MCS. The test problems show that the XFEM-MCS algorithm under the dynamic electric load can be effectively employed for multiple cracks detection in piezoelectric materials, and it proves to be robust in identifying defects in piezoelectric structures. Fiber-reinforced composites (FRCs) are extensively applied in practical engineering since they have high stiffness and strength. Experiments reveal a so-called interphase zone, i.e. the space between the outside interface of the fiber and the inside interface of the matrix. The interphase strength between the fiber and the matrix strongly affects the mechanical properties as a result of the large ratio of interface/volume. For the purpose of understanding the mechanical properties of FRCs with functionally graded interphase (FGI), a closed-form expression of the interface strength between a fiber and a matrix is obtained in this dissertation using a continuum modeling approach according to the ver derWaals (vdW) forces. Based on the interatomic potential, we develop a new modified nonlinear cohesive law, which is applied to study the interface delamination of FRCs with FGI under different loadings. The analytical solutions show that the delamination behavior strongly depends on the interphase thickness, the fiber radius, the Young's moduli and Poisson's ratios of the fiber and the matrix. Thermal conductivity is the property of a material to conduct heat. With the development and deep research of 2D materials, especially graphene and molybdenum disulfide (MoS2), the thermal conductivity of 2D materials attracts wide attentions. The thermal conductivity of graphene nanoribbons (GNRs) is found to appear a tendency of decreasing under tensile strain by classical molecular dynamics (MD) simulations. Hence, the strain effects of graphene can play a key role in the continuous tunability and applicability of its thermal conductivity property at nanoscale, and the dissipation of thermal conductivity is an obstacle for the applications of thermal management. Up to now, the thermal conductivity of graphene under shear deformation has not been investigated yet. From a practical point of view, good thermal managements of GNRs have significantly potential applications of future GNR-based thermal nanodevices, which can greatly improve performances of the nanosized devices due to heat dissipations. Meanwhile, graphene is a thin membrane structure, it is also important to understand the wrinkling behavior under shear deformation. MoS2 exists in the stable semiconducting 1H phase (1H-MoS2) while the metallic 1T phase (1T-MoS2) is unstable at ambient conditions. As it's well known that much attention has been focused on studying the nonlinear optical properties of the 1H-MoS2. In a very recent research, the 1T-type monolayer crystals of TMDCs, MX2 (MoS2, WS2 ...) was reported having an intrinsic in-plane negative Poisson's ratio. Luckily, nearly at the same time, unprecedented long-term (>3months) air stability of the 1T-MoS2 can be achieved by using the donor lithium hydride (LiH). Therefore, it's very important to study the thermal conductivity of 1T-MoS2. The thermal conductivity of graphene under shear strain is systematically studied in this dissertation by MD simulations. The results show that, in contrast to the dramatic decrease of thermal conductivity of graphene under uniaxial tensile, the thermal conductivity of graphene is not sensitive to the shear strain, and the thermal conductivity decreases only 12-16\%. The wrinkle evolves when the shear strain is around 5\%-10\%, but the thermal conductivity barely changes. The thermal conductivities of single-layer 1H-MoS2(1H-SLMoS2) and single-layer 1T-MoS2 (1T-SLMoS2) with different sample sizes, temperatures and strain rates have been studied systematically in this dissertation. We find that the thermal conductivities of 1H-SLMoS2 and 1T-SLMoS2 in both the armchair and the zigzag directions increase with the increasing of the sample length, while the increase of the width of the sample has minor effect on the thermal conductions of these two structures. The thermal conductivity of 1HSLMoS2 is smaller than that of 1T-SLMoS2 under size effect. Furthermore, the temperature effect results show that the thermal conductivities of both 1H-SLMoS2 and 1T-SLMoS2 decrease with the increasing of the temperature. The thermal conductivities of 1HSLMoS2 and 1T-SLMoS2 are nearly the same (difference <6\%) in both of the chiral orientations under corresponding temperatures, especially in the armchair direction (difference <2.8\%). Moreover, we find that the strain effects on the thermal conductivity of 1HSLMoS2 and 1T-SLMoS2 are different. More specifically, the thermal conductivity decreases with the increasing tensile strain rate for 1T-SLMoS2, while fluctuates with the growth of the strain for 1HSLMoS2. Finally, we find that the thermal conductivity of same sized 1H-SLMoS2 is similar with that of the strained 1H-SLMoS2 structure.},
  subject      = {crack},
  language  = {en}
}
@phdthesis{Bianco,
  author    = {Bianco, Marcelo Jos{\´e}},
  title     = {Coupling between Shell and Generalized Beam Theory (GBT) elements},
  doi       = {10.25643/bauhaus-universitaet.4391},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210315-43914},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {265},
  abstract  = {In the last decades, Finite Element Method has become the main method in statics and dynamics analysis in engineering practice. For current problems, this method provides a faster, more flexible solution than the analytic approach. Prognoses of complex engineer problems that used to be almost impossible to solve are now feasible. Although the finite element method is a robust tool, it leads to new questions about engineering solutions. Among these new problems, it is possible to divide into two major groups: the first group is regarding computer performance; the second one is related to understanding the digital solution. Simultaneously with the development of the finite element method for numerical solutions, a theory between beam theory and shell theory was developed: Generalized Beam Theory, GBT. This theory has not only a systematic and analytical clear presentation of complicated structural problems, but also a compact and elegant calculation approach that can improve computer performance. Regrettably, GBT was not internationally known since the most publications of this theory were written in German, especially in the first years. Only in recent years, GBT has gradually become a fertile research topic, with developments from linear to non-linear analysis. Another reason for the misuse of GBT is the isolated application of the theory. Although recently researches apply finite element method to solve the GBT's problems numerically, the coupling between finite elements of GBT and other theories (shell, solid, etc) is not the subject of previous research. Thus, the main goal of this dissertation is the coupling between GBT and shell/membrane elements. Consequently, one achieves the benefits of both sides: the versatility of shell elements with the high performance of GBT elements. Based on the assumptions of GBT, this dissertation presents how the separation of variables leads to two calculation's domains of a beam structure: a cross-section modal analysis and the longitudinal amplification axis. Therefore, there is the possibility of applying the finite element method not only in the cross-section analysis, but also the development for an exact GBT's finite element in the longitudinal direction. For the cross-section analysis, this dissertation presents the solution of the quadratic eigenvalue problem with an original separation between plate and membrane mechanism. Subsequently, one obtains a clearer representation of the deformation mode, as well as a reduced quadratic eigenvalue problem. Concerning the longitudinal direction, this dissertation develops the novel exact elements, based on hyperbolic and trigonometric shape functions. Although these functions do not have trivial expressions, they provide a recursive procedure that allows periodic derivatives to systematise the development of stiffness matrices. Also, these shape functions enable a single-element discretisation of the beam structure and ensure a smooth stress field. From these developments, this dissertation achieves the formulation of its primary objective: the connection of GBT and shell elements in a mixed model. Based on the displacement field, it is possible to define the coupling equations applied in the master-slave method. Therefore, one can model the structural connections and joints with finite shell elements and the structural beams and columns with GBT finite element. As a side effect, the coupling equations limit the displacement field of the shell elements under the assumptions of GBT, in particular in the neighbourhood of the coupling cross-section. Although these side effects are almost unnoticeable in linear analysis, they lead to cumulative errors in non-linear analysis. Therefore, this thesis finishes with the evaluation of the mixed GBT-shell models in non-linear analysis.},
  subject      = {Biegetheorie},
  language  = {en}
}
@phdthesis{AbuBakar,
  author    = {Abu Bakar, Ilyani Akmar},
  title     = {Computational Analysis of Woven Fabric Composites: Single- and Multi-Objective Optimizations and Sensitivity Analysis in Meso-scale Structures},
  issn      = {1610-7381},
  doi       = {10.25643/bauhaus-universitaet.4176},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20200605-41762},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {151},
  abstract  = {This study permits a reliability analysis to solve the mechanical behaviour issues existing in the current structural design of fabric structures. Purely predictive material models are highly desirable to facilitate an optimized design scheme and to significantly reduce time and cost at the design stage, such as experimental characterization. The present study examined the role of three major tasks; a) single-objective optimization, b) sensitivity analyses and c) multi-objective optimization on proposed weave structures for woven fabric composites. For single-objective optimization task, the first goal is to optimize the elastic properties of proposed complex weave structure under unit cells basis based on periodic boundary conditions. We predict the geometric characteristics towards skewness of woven fabric composites via Evolutionary Algorithm (EA) and a parametric study. We also demonstrate the effect of complex weave structures on the fray tendency in woven fabric composites via tightness evaluation. We utilize a procedure which does not require a numerical averaging process for evaluating the elastic properties of woven fabric composites. The fray tendency and skewness of woven fabrics depends upon the behaviour of the floats which is related to the factor of weave. Results of this study may suggest a broader view for further research into the effects of complex weave structures or may provide an alternative to the fray and skewness problems of current weave structure in woven fabric composites. A comprehensive study is developed on the complex weave structure model which adopts the dry woven fabric of the most potential pattern in singleobjective optimization incorporating the uncertainties parameters of woven fabric composites. The comprehensive study covers the regression-based and variance-based sensitivity analyses. The second task goal is to introduce the fabric uncertainties parameters and elaborate how they can be incorporated into finite element models on macroscopic material parameters such as elastic modulus and shear modulus of dry woven fabric subjected to uni-axial and biaxial deformations. Significant correlations in the study, would indicate the need for a thorough investigation of woven fabric composites under uncertainties parameters. The study describes here could serve as an alternative to identify effective material properties without prolonged time consumption and expensive experimental tests. The last part focuses on a hierarchical stochastic multi-scale optimization approach (fine-scale and coarse-scale optimizations) under geometrical uncertainties parameters for hybrid composites considering complex weave structure. The fine-scale optimization is to determine the best lamina pattern that maximizes its macroscopic elastic properties, conducted by EA under the following uncertain mesoscopic parameters: yarn spacing, yarn height, yarn width and misalignment of yarn angle. The coarse-scale optimization has been carried out to optimize the stacking sequences of symmetric hybrid laminated composite plate with uncertain mesoscopic parameters by employing the Ant Colony Algorithm (ACO). The objective functions of the coarse-scale optimization are to minimize the cost (C) and weight (W) of the hybrid laminated composite plate considering the fundamental frequency and the buckling load factor as the design constraints. Based on the uncertainty criteria of the design parameters, the appropriate variation required for the structural design standards can be evaluated using the reliability tool, and then an optimized design decision in consideration of cost can be subsequently determined.},
  subject      = {Verbundwerkstoff},
  language  = {en}
}
@phdthesis{Mojahedin,
  author    = {Mojahedin, Arvin},
  title     = {Analysis of Functionally Graded Porous Materials Using Deep Energy Method and Analytical Solution},
  doi       = {10.25643/bauhaus-universitaet.4867},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221220-48674},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {Porous materials are an emerging branch of engineering materials that are composed of two elements: One element is a solid (matrix), and the other element is either liquid or gas. Pores can be distributed within the solid matrix of porous materials with different shapes and sizes. In addition, porous materials are lightweight, and flexible, and have higher resistance to crack propagation and specific thermal, mechanical, and magnetic properties. These properties are necessary for manufacturing engineering structures such as beams and other engineering structures. These materials are widely used in solid mechanics and are considered a good replacement for classical materials by many researchers recently. Producing lightweight materials has been developed because of the possibility of exploiting the properties of these materials. Various types of porous material are generated naturally or artificially for a specific application such as bones and foams. Like functionally graded materials, pore distribution patterns can be uniform or non-uniform. Biot's theory is a well-developed theory to study the behavior of poroelastic materials which investigates the interaction between fluid and solid phases of a fluid-saturated porous medium. Functionally graded porous materials (FGPM) are widely used in modern industries, such as aerospace, automotive, and biomechanics. These advanced materials have some specific properties compared to materials with a classic structure. They are extremely light, while they have specific strength in mechanical and high-temperature environments. FGPMs are characterized by a gradual variation of material parameters over the volume. Although these materials can be made naturally, it is possible to design and manufacture them for a specific application. Therefore, many studies have been done to analyze the mechanical and thermal properties of FGPM structures, especially beams. Biot was the pioneer in formulating the linear elasticity and thermoelasticity equations of porous material. Since then, Biot's formulation has been developed in continuum mechanics which is named poroelasticity. There are obstacles to analyzing the behavior of these materials accurately like the shape of the pores, the distribution of pores in the material, and the behavior of the fluid (or gas) that saturated pores. Indeed, most of the engineering structures made of FGPM have nonlinear governing equations. Therefore, it is difficult to study engineering structures by solving these complicated equations. The main purpose of this dissertation is to analyze porous materials in engineering structures. For this purpose, the complex equations of porous materials have been simplified and applied to engineering problems so that the effect of all parameters of porous materials on the behavior of engineering structure has been investigated. The effect of important parameters of porous materials on beam behavior including pores compressibility, porosity distribution, thermal expansion of fluid within pores, the interaction of stresses between pores and material matrix due to temperature increase, effects of pore size, material thickness, and saturated pores with fluid and unsaturated conditions are investigated. Two methods, the deep energy method, and the exact solution have been used to reduce the problem hypotheses, increase accuracy, increase processing speed, and apply these in engineering structures. In both methods, they are analyzed nonlinear and complex equations of porous materials. To increase the accuracy of analysis and study of the effect of shear forces, Timoshenko and Reddy's beam theories have been used. Also, neural networks such as residual and fully connected networks are designed to have high accuracy and less processing time than other computational methods.},
  subject      = {Por{\"o}ser Stoff},
  language  = {en}
}
@phdthesis{Alalade,
  author    = {Alalade, Muyiwa},
  title     = {An Enhanced Full Waveform Inversion Method for the Structural Analysis of Dams},
  doi       = {10.25643/bauhaus-universitaet.3956},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20190813-39566},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {Since the Industrial Revolution in the 1700s, the high emission of gaseous wastes into the atmosphere from the usage of fossil fuels has caused a general increase in temperatures globally. To combat the environmental imbalance, there is an increase in the demand for renewable energy sources. Dams play a major role in the generation of "green" energy. However, these structures require frequent and strict monitoring to ensure safe and efficient operation. To tackle the challenges faced in the application of convention dam monitoring techniques, this work proposes the inverse analysis of numerical models to identify damaged regions in the dam. Using a dynamic coupled hydro-mechanical Extended Finite Element Method (XFEM) model and a global optimization strategy, damage (crack) in the dam is identified. By employing seismic waves to probe the dam structure, a more detailed information on the distribution of heterogeneous materials and damaged regions are obtained by the application of the Full Waveform Inversion (FWI) method. The FWI is based on a local optimization strategy and thus it is highly dependent on the starting model. A variety of data acquisition setups are investigated, and an optimal setup is proposed. The effect of different starting models and noise in the measured data on the damage identification is considered. Combining the non-dependence of a starting model of the global optimization strategy based dynamic coupled hydro-mechanical XFEM method and the detailed output of the local optimization strategy based FWI method, an enhanced Full Waveform Inversion is proposed for the structural analysis of dams.},
  subject      = {Talsperre},
  language  = {en}
}
@phdthesis{Budarapu,
  author    = {Budarapu, Pattabhi Ramaiah},
  title     = {Adaptive multiscale methods for fracture},
  doi       = {10.25643/bauhaus-universitaet.2391},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20150507-23918},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {One major research focus in the Material Science and Engineering Community in the past decade has been to obtain a more fundamental understanding on the phenomenon 'material failure'. Such an understanding is critical for engineers and scientists developing new materials with higher strength and toughness, developing robust designs against failure, or for those concerned with an accurate estimate of a component's design life. Defects like cracks and dislocations evolve at nano scales and influence the macroscopic properties such as strength, toughness and ductility of a material. In engineering applications, the global response of the system is often governed by the behaviour at the smaller length scales. Hence, the sub-scale behaviour must be computed accurately for good predictions of the full scale behaviour. Molecular Dynamics (MD) simulations promise to reveal the fundamental mechanics of material failure by modeling the atom to atom interactions. Since the atomistic dimensions are of the order of Angstroms ( A), approximately 85 billion atoms are required to model a 1 micro- m^3 volume of Copper. Therefore, pure atomistic models are prohibitively expensive with everyday engineering computations involving macroscopic cracks and shear bands, which are much larger than the atomistic length and time scales. To reduce the computational effort, multiscale methods are required, which are able to couple a continuum description of the structure with an atomistic description. In such paradigms, cracks and dislocations are explicitly modeled at the atomistic scale, whilst a self-consistent continuum model elsewhere. Many multiscale methods for fracture are developed for "fictitious" materials based on "simple" potentials such as the Lennard-Jones potential. Moreover, multiscale methods for evolving cracks are rare. Efficient methods to coarse grain the fine scale defects are missing. However, the existing multiscale methods for fracture do not adaptively adjust the fine scale domain as the crack propagates. Most methods, therefore only "enlarge" the fine scale domain and therefore drastically increase computational cost. Adaptive adjustment requires the fine scale domain to be refined and coarsened. One of the major difficulties in multiscale methods for fracture is to up-scale fracture related material information from the fine scale to the coarse scale, in particular for complex crack problems. Most of the existing approaches therefore were applied to examples with comparatively few macroscopic cracks. Key contributions The bridging scale method is enhanced using the phantom node method so that cracks can be modeled at the coarse scale. To ensure self-consistency in the bulk, a virtual atom cluster is devised providing the response of the intact material at the coarse scale. A molecular statics model is employed in the fine scale where crack propagation is modeled by naturally breaking the bonds. The fine scale and coarse scale models are coupled by enforcing the displacement boundary conditions on the ghost atoms. An energy criterion is used to detect the crack tip location. Adaptive refinement and coarsening schemes are developed and implemented during the crack propagation. The results were observed to be in excellent agreement with the pure atomistic simulations. The developed multiscale method is one of the first adaptive multiscale method for fracture. A robust and simple three dimensional coarse graining technique to convert a given atomistic region into an equivalent coarse region, in the context of multiscale fracture has been developed. The developed method is the first of its kind. The developed coarse graining technique can be applied to identify and upscale the defects like: cracks, dislocations and shear bands. The current method has been applied to estimate the equivalent coarse scale models of several complex fracture patterns arrived from the pure atomistic simulations. The upscaled fracture pattern agree well with the actual fracture pattern. The error in the potential energy of the pure atomistic and the coarse grained model was observed to be acceptable. A first novel meshless adaptive multiscale method for fracture has been developed. The phantom node method is replaced by a meshless differential reproducing kernel particle method. The differential reproducing kernel particle method is comparatively more expensive but allows for a more "natural" coupling between the two scales due to the meshless interpolation functions. The higher order continuity is also beneficial. The centro symmetry parameter is used to detect the crack tip location. The developed multiscale method is employed to study the complex crack propagation. Results based on the meshless adaptive multiscale method were observed to be in excellent agreement with the pure atomistic simulations. The developed multiscale methods are applied to study the fracture in practical materials like Graphene and Graphene on Silicon surface. The bond stretching and the bond reorientation were observed to be the net mechanisms of the crack growth in Graphene. The influence of time step on the crack propagation was studied using two different time steps. Pure atomistic simulations of fracture in Graphene on Silicon surface are presented. Details of the three dimensional multiscale method to study the fracture in Graphene on Silicon surface are discussed.},
  subject      = {Material},
  language  = {en}
}
@phdthesis{Eckardt2009,
  author    = {Eckardt, Stefan},
  title     = {Adaptive heterogeneous multiscale models for the nonlinear simulation of concrete},
  doi       = {10.25643/bauhaus-universitaet.1416},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20100317-15023},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {2009},
  abstract  = {The nonlinear behavior of concrete can be attributed to the propagation of microcracks within the heterogeneous internal material structure. In this thesis, a mesoscale model is developed which allows for the explicit simulation of these microcracks. Consequently, the actual physical phenomena causing the complex nonlinear macroscopic behavior of concrete can be represented using rather simple material formulations. On the mesoscale, the numerical model explicitly resolves the components of the internal material structure. For concrete, a three-phase model consisting of aggregates, mortar matrix and interfacial transition zone is proposed. Based on prescribed grading curves, an efficient algorithm for the generation of three-dimensional aggregate distributions using ellipsoids is presented. In the numerical model, tensile failure of the mortar matrix is described using a continuum damage approach. In order to reduce spurious mesh sensitivities, introduced by the softening behavior of the matrix material, nonlocal integral-type material formulations are applied. The propagation of cracks at the interface between aggregates and mortar matrix is represented in a discrete way using a cohesive crack approach. The iterative solution procedure is stabilized using a new path following constraint within the framework of load-displacement-constraint methods which allows for an efficient representation of snap-back phenomena. In several examples, the influence of the randomly generated heterogeneous material structure on the stochastic scatter of the results is analyzed. Furthermore, the ability of mesoscale models to represent size effects is investigated. Mesoscale simulations require the discretization of the internal material structure. Compared to simulations on the macroscale, the numerical effort and the memory demand increases dramatically. Due to the complexity of the numerical model, mesoscale simulations are, in general, limited to small specimens. In this thesis, an adaptive heterogeneous multiscale approach is presented which allows for the incorporation of mesoscale models within nonlinear simulations of concrete structures. In heterogeneous multiscale models, only critical regions, i.e. regions in which damage develops, are resolved on the mesoscale, whereas undamaged or sparsely damage regions are modeled on the macroscale. A crucial point in simulations with heterogeneous multiscale models is the coupling of sub-domains discretized on different length scales. The sub-domains differ not only in the size of the finite elements but also in the constitutive description. In this thesis, different methods for the coupling of non-matching discretizations - constraint equations, the mortar method and the arlequin method - are investigated and the application to heterogeneous multiscale models is presented. Another important point is the detection of critical regions. An adaptive solution procedure allowing the transfer of macroscale sub-domains to the mesoscale is proposed. In this context, several indicators which trigger the model adaptation are introduced. Finally, the application of the proposed adaptive heterogeneous multiscale approach in nonlinear simulations of concrete structures is presented.},
  subject      = {Beton},
  language  = {en}
}
@phdthesis{Luther2010,
  author    = {Luther, Torsten},
  title     = {Adaptation of atomistic and continuum methods for multiscale simulation of quasi-brittle intergranular damage},
  doi       = {10.25643/bauhaus-universitaet.1436},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20101101-15245},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {2010},
  abstract  = {The numerical simulation of damage using phenomenological models on the macroscale was state of the art for many decades. However, such models are not able to capture the complex nature of damage, which simultaneously proceeds on multiple length scales. Furthermore, these phenomenological models usually contain damage parameters, which are physically not interpretable. Consequently, a reasonable experimental determination of these parameters is often impossible. In the last twenty years, the ongoing advance in computational capacities provided new opportunities for more and more detailed studies of the microstructural damage behavior. Today, multiphase models with several million degrees of freedom enable for the numerical simulation of micro-damage phenomena in naturally heterogeneous materials. Therewith, the application of multiscale concepts for the numerical investigation of the complex nature of damage can be realized. The presented thesis contributes to a hierarchical multiscale strategy for the simulation of brittle intergranular damage in polycrystalline materials, for example aluminum. The numerical investigation of physical damage phenomena on an atomistic microscale and the integration of these physically based information into damage models on the continuum meso- and macroscale is intended. Therefore, numerical methods for the damage analysis on the micro- and mesoscale including the scale transfer are presented and the transition to the macroscale is discussed. The investigation of brittle intergranular damage on the microscale is realized by the application of the nonlocal Quasicontinuum method, which fully describes the material behavior by atomistic potential functions, but reduces the number of atomic degrees of freedom by introducing kinematic couplings. Since this promising method is applied only by a limited group of researchers for special problems, necessary improvements have been realized in an own parallelized implementation of the 3D nonlocal Quasicontinuum method. The aim of this implementation was to develop and combine robust and efficient algorithms for a general use of the Quasicontinuum method, and therewith to allow for the atomistic damage analysis in arbitrary grain boundary configurations. The implementation is applied in analyses of brittle intergranular damage in ideal and nonideal grain boundary models of FCC aluminum, considering arbitrary misorientations. From the microscale simulations traction separation laws are derived, which describe grain boundary decohesion on the mesoscale. Traction separation laws are part of cohesive zone models to simulate the brittle interface decohesion in heterogeneous polycrystal structures. 2D and 3D mesoscale models are presented, which are able to reproduce crack initiation and propagation along cohesive interfaces in polycrystals. An improved Voronoi algorithm is developed in 2D to generate polycrystal material structures based on arbitrary distribution functions of grain size. The new model is more flexible in representing realistic grain size distributions. Further improvements of the 2D model are realized by the implementation and application of an orthotropic material model with Hill plasticity criterion to grains. The 2D and 3D polycrystal models are applied to analyze crack initiation and propagation in statically loaded samples of aluminum on the mesoscale without the necessity of initial damage definition.},
  subject      = {Mechanik},
  language  = {en}
}
@phdthesis{Winkel,
  author    = {Winkel, Benjamin},
  title     = {A three-dimensional model of skeletal muscle for physiological, pathological and experimental mechanical simulations},
  doi       = {10.25643/bauhaus-universitaet.4300},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20201211-43002},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {In recent decades, a multitude of concepts and models were developed to understand, assess and predict muscular mechanics in the context of physiological and pathological events. Most of these models are highly specialized and designed to selectively address fields in, e.g., medicine, sports science, forensics, product design or CGI; their data are often not transferable to other ranges of application. A single universal model, which covers the details of biochemical and neural processes, as well as the development of internal and external force and motion patterns and appearance could not be practical with regard to the diversity of the questions to be investigated and the task to find answers efficiently. With reasonable limitations though, a generalized approach is feasible. The objective of the work at hand was to develop a model for muscle simulation which covers the phenomenological aspects, and thus is universally applicable in domains where up until now specialized models were utilized. This includes investigations on active and passive motion, structural interaction of muscles within the body and with external elements, for example in crash scenarios, but also research topics like the verification of in vivo experiments and parameter identification. For this purpose, elements for the simulation of incompressible deformations were studied, adapted and implemented into the finite element code SLang. Various anisotropic, visco-elastic muscle models were developed or enhanced. The applicability was demonstrated on the base of several examples, and a general base for the implementation of further material models was developed and elaborated.},
  subject      = {Biomechanik},
  language  = {en}
}
@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}
}