@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{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{Nanthakumar,
  author    = {Nanthakumar, S.S.},
  title     = {Inverse and optimization problems in piezoelectric materials using Extended Finite Element Method and Level sets},
  doi       = {10.25643/bauhaus-universitaet.2709},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20161128-27095},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {Piezoelectric materials are used in several applications as sensors and actuators where they experience high stress and electric field concentrations as a result of which they may fail due to fracture. Though there are many analytical and experimental works on piezoelectric fracture mechanics. There are very few studies about damage detection, which is an interesting way to prevent the failure of these ceramics. An iterative method to treat the inverse problem of detecting cracks and voids in piezoelectric structures is proposed. Extended finite element method (XFEM) is employed for solving the inverse problem as it allows the use of a single regular mesh for large number of iterations with different flaw geometries. Firstly, minimization of cost function is performed by Multilevel Coordinate Search (MCS) method. The XFEM-MCS methodology is applied to two dimensional electromechanical problems where flaws considered are straight cracks and elliptical voids. Then a numerical method based on combination of classical shape derivative and level set method for front propagation used in structural optimization is utilized to minimize the cost function. The results obtained show that the XFEM-level set methodology is effectively able to determine the number of voids in a piezoelectric structure and its corresponding locations. The XFEM-level set methodology is improved to solve the inverse problem of detecting inclusion interfaces in a piezoelectric structure. The material interfaces are implicitly represented by level sets which are identified by applying regularisation using total variation penalty terms. The formulation is presented for three dimensional structures and inclusions made of different materials are detected by using multiple level sets. The results obtained prove that the iterative procedure proposed can determine the location and approximate shape of material subdomains in the presence of higher noise levels. Piezoelectric nanostructures exhibit size dependent properties because of surface elasticity and surface piezoelectricity. Initially a study to understand the influence of surface elasticity on optimization of nano elastic beams is performed. The boundary of the nano structure is implicitly represented by a level set function, which is considered as the design variable in the optimization process. Two objective functions, minimizing the total potential energy of a nanostructure subjected to a material volume constraint and minimizing the least square error compared to a target displacement, are chosen for the numerical examples. The numerical examples demonstrate the importance of size and aspect ratio in determining how surface effects impact the optimized topology of nanobeams. Finally a conventional cantilever energy harvester with a piezoelectric nano layer is analysed. The presence of surface piezoelectricity in nano beams and nano plates leads to increase in electromechanical coupling coefficient. Topology optimization of these piezoelectric structures in an energy harvesting device to further increase energy conversion using appropriately modified XFEM-level set algorithm is performed .},
  subject      = {Finite-Elemente-Methode},
  language  = {de}
}
@phdthesis{Ghasemi,
  author    = {Ghasemi, Hamid},
  title     = {Stochastic optimization of fiber reinforced composites considering uncertainties},
  doi       = {10.25643/bauhaus-universitaet.2704},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20161117-27042},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {140},
  abstract  = {Briefly, the two basic questions that this research is supposed to answer are: 1. Howmuch fiber is needed and how fibers should be distributed through a fiber reinforced composite (FRC) structure in order to obtain the optimal and reliable structural response? 2. How do uncertainties influence the optimization results and reliability of the structure? Giving answer to the above questions a double stage sequential optimization algorithm for finding the optimal content of short fiber reinforcements and their distribution in the composite structure, considering uncertain design parameters, is presented. In the first stage, the optimal amount of short fibers in a FRC structure with uniformly distributed fibers is conducted in the framework of a Reliability Based Design Optimization (RBDO) problem. Presented model considers material, structural and modeling uncertainties. In the second stage, the fiber distribution optimization (with the aim to further increase in structural reliability) is performed by defining a fiber distribution function through a Non-Uniform Rational BSpline (NURBS) surface. The advantages of using the NURBS surface as a fiber distribution function include: using the same data set for the optimization and analysis; high convergence rate due to the smoothness of the NURBS; mesh independency of the optimal layout; no need for any post processing technique and its non-heuristic nature. The output of stage 1 (the optimal fiber content for homogeneously distributed fibers) is considered as the input of stage 2. The output of stage 2 is the Reliability Index (b ) of the structure with the optimal fiber content and distribution. First order reliability method (in order to approximate the limit state function) as well as different material models including Rule of Mixtures, Mori-Tanaka, energy-based approach and stochastic multi-scales are implemented in different examples. The proposed combined model is able to capture the role of available uncertainties in FRC structures through a computationally efficient algorithm using all sequential, NURBS and sensitivity based techniques. The methodology is successfully implemented for interfacial shear stress optimization in sandwich beams and also for optimization of the internal cooling channels in a ceramic matrix composite. Finally, after some changes and modifications by combining Isogeometric Analysis, level set and point wise density mapping techniques, the computational framework is extended for topology optimization of piezoelectric / flexoelectric materials.},
  subject      = {Finite-Elemente-Methode},
  language  = {en}
}
@phdthesis{Msekh,
  author    = {Msekh, Mohammed Abdulrazzak},
  title     = {Phase Field Modeling for Fracture with Applications to Homogeneous and Heterogeneous Materials},
  doi       = {10.25643/bauhaus-universitaet.3229},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170615-32291},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {190},
  abstract  = {The thesis presents an implementation including different applications of a variational-based approach for gradient type standard dissipative solids. Phase field model for brittle fracture is an application of the variational-based framework for gradient type solids. This model allows the prediction of different crack topologies and states. Of significant concern is the application of theoretical and numerical formulation of the phase field modeling into the commercial finite element software Abaqus in 2D and 3D. The fully coupled incremental variational formulation of phase field method is implemented by using the UEL and UMAT subroutines of Abaqus. The phase field method considerably reduces the implementation complexity of fracture problems as it removes the need for numerical tracking of discontinuities in the displacement field that are characteristic of discrete crack methods. This is accomplished by replacing the sharp discontinuities with a scalar damage phase field representing the diffuse crack topology wherein the amount of diffusion is controlled by a regularization parameter. The nonlinear coupled system consisting of the linear momentum equation and a diffusion type equation governing the phase field evolution is solved simultaneously via a Newton- Raphson approach. Post-processing of simulation results to be used as visualization module is performed via an additional UMAT subroutine implemented in the standard Abaqus viewer. In the same context, we propose a simple yet effective algorithm to initiate and propagate cracks in 2D geometries which is independent of both particular constitutive laws and specific element technology and dimension. It consists of a localization limiter in the form of the screened Poisson equation with, optionally, local mesh refinement. A staggered scheme for standard equilibrium and screened Cauchy equations is used. The remeshing part of the algorithm consists of a sequence of mesh subdivision and element erosion steps. Element subdivision is based on edge split operations using a given constitutive quantity (either damage or void fraction). Mesh smoothing makes use of edge contraction as function of a given constitutive quantity such as the principal stress or void fraction. To assess the robustness and accuracy of this algorithm, we use both quasi-brittle benchmarks and ductile tests. Furthermore, we introduce a computational approach regarding mechanical loading in microscale on an inelastically deforming composite material. The nanocomposites material of fully exfoliated clay/epoxy is shaped to predict macroscopic elastic and fracture related material parameters based on their fine-scale features. Two different configurations of polymer nanocomposites material (PNCs) have been studied. These configurations are fully bonded PNCs and PNCs with an interphase zone formation between the matrix and the clay reinforcement. The representative volume element of PNCs specimens with different clay weight contents, different aspect ratios, and different interphase zone thicknesses are generated by adopting Python scripting. Different constitutive models are employed for the matrix, the clay platelets, and the interphase zones. The brittle fracture behavior of the epoxy matrix and the interphase zones material are modeled using the phase field approach, whereas the stiff silicate clay platelets of the composite are designated as a linear elastic material. The comprehensive study investigates the elastic and fracture behavior of PNCs composites, in addition to predict Young's modulus, tensile strength, fracture toughness, surface energy dissipation, and cracks surface area in the composite for different material parameters, geometry, and interphase zones properties and thicknesses.},
  subject      = {Finite-Elemente-Methode},
  language  = {en}
}
@phdthesis{Schemmann,
  author    = {Schemmann, Christoph},
  title     = {Optimierung von radialen Verdichterlaufr{\"a}dern unter Ber{\"u}cksichtigung empirischer und analytischer Vorinformationen mittels eines mehrstufigen Sampling Verfahrens},
  doi       = {10.25643/bauhaus-universitaet.3974},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20190910-39748},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {233},
  abstract  = {Turbomachinery plays an important role in many cases of energy generation or conversion. Therefore, turbomachinery is a promising approaching point for optimization in order to increase the efficiency of energy use. In recent years, the use of automated optimization strategies in combination with numerical simulation has become increasingly popular in many fields of engineering. The complex interactions between fluid and solid mechanics encountered in turbomachines on the one hand and the high computational expense needed to calculate the performance on the other hand, have, however, prevented a widespread use of these techniques in this field of engineering. The objective of this work was the development of a strategy for efficient metamodel based optimization of centrifugal compressor impellers. In this context, the main focus is the reduction of the required numerical expense. The central idea followed in this research was the incorporation of preliminary information acquired from low-fidelity computation methods and empirical correlations into the sampling process to identify promising regions of the parameter space. This information was then used to concentrate the numerically expensive high-fidelity computations of the fluid dynamic and structure mechanic performance of the impeller in these regions while still maintaining a good coverage of the whole parameter space. The development of the optimization strategy can be divided into three main tasks. Firstly, the available preliminary information had to be researched and rated. This research identified loss models based on one dimensional flow physics and empirical correlations as the best suited method to predict the aerodynamic performance. The loss models were calibrated using available performance data to obtain a high prediction quality. As no sufficiently exact models for the prediction of the mechanical loading of the impellercould be identified, a metamodel based on finite element computations was chosen for this estimation. The second task was the development of a sampling method which concentrates samples in regions of the parameter space where high quality designs are predicted by the preliminary information while maintaining a good overall coverage. As available methods like rejection sampling or Markov-chain Monte-Carlo methods did not meet the requirements in terms of sample distribution and input correlation, a new multi-fidelity sampling method called "Filtered Sampling"has been developed. The last task was the development of an automated computational workflow. This workflow encompasses geometry parametrization, geometry generation, grid generation and computation of the aerodynamic performance and the structure mechanic loading. Special emphasis was put into the development of a geometry parametrization strategy based on fluid mechanic considerations to prevent the generation of physically inexpedient designs. Finally, the optimization strategy, which utilizes the previously developed tools, was successfully employed to carry out three optimization tasks. The efficiency of the method was proven by the first and second testcase where an existing compressor design was optimized by the presented method. The results were comparable to optimizations which did not take preliminary information into account, while the required computational expense cloud be halved. In the third testcase, the method was applied to generate a new impeller design. In contrast to the previous examples, this optimization featuredlargervariationsoftheimpellerdesigns. Therefore, theapplicability of the method to parameter spaces with significantly varying designs could be proven, too.},
  subject      = {Simulation},
  language  = {en}
}
@phdthesis{Stang,
  author    = {Stang, Ren{\´e}},
  title     = {Methode zur {\"O}koeffizienzbewertung w{\"a}rmetechnischer Anlagen in Geb{\"a}uden},
  publisher = {VDI Verlag},
  address   = {D{\"u}sseldorf},
  isbn      = {978-3-18-300623-6 (print)},
  doi       = {10.25643/bauhaus-universitaet.4528},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20211119-45280},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {222},
  abstract  = {Die vorliegende Arbeit richtet sich an Ingenieur*innen und Wissenschaftler*innen der technischen Geb{\"a}udeausr{\"u}stung. Sie greift einen sich abzeichnenden {\"A}nderungsbedarf in der Umwelt- und Nachhaltigkeitsbewertung von Geb{\"a}uden und w{\"a}rmetechnischen Anlagen auf. Der aktuell genutzte nicht erneuerbare Prim{\"a}renergiebedarf wird insbesondere hinsichtlich k{\"u}nftiger politischer Klima- und Umweltschutzziele als alleinige Bewertungsgr{\"o}ße nicht ausreichend sein. Die mit dieser Arbeit vorgestellte {\"O}koeffizienzbewertungsmethode kann als geeignetes Instrument zur L{\"o}sung der Probleme beitragen. Sie erm{\"o}glicht systematische, ganzheitliche Bewertungen und reproduzierbare Vergleiche w{\"a}rmetechnischer Anlagen bez{\"u}glich ihrer {\"o}kologischen und {\"o}konomischen Nachhaltigkeit. Die wesentlichsten Neuentwicklungen sind die spezifische Umweltleistung, in Erweiterung zum genutzten Prim{\"a}renergiefaktor, und der {\"O}koeffizienzindikator UWI.},
  subject      = {Energiewirtschaft},
  language  = {de}
}
@phdthesis{Wang,
  author    = {Wang, Jiasheng},
  title     = {Lebensdauerabsch{\"a}tzung von Bauteilen aus globularem Grauguss auf der Grundlage der lokalen gießprozessabh{\"a}ngigen Werkstoffzust{\"a}nde},
  doi       = {10.25643/bauhaus-universitaet.4554},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220111-45542},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {165},
  abstract  = {Das Ziel der Arbeit ist, eine m{\"o}gliche Verbesserung der G{\"u}te der Lebensdauervorhersage f{\"u}r Gusseisenwerkstoffe mit Kugelgraphit zu erreichen, wobei die Gießprozesse verschiedener Hersteller ber{\"u}cksichtigt werden. Im ersten Schritt wurden Probenk{\"o}rper aus GJS500 und GJS600 von mehreren Gusslieferanten gegossen und daraus Schwingproben erstellt. Insgesamt wurden Schwingfestigkeitswerte der einzelnen gegossenen Proben sowie der Proben des Bauteils von verschiedenen Gussherstellern weltweit entweder durch direkte Schwingversuche oder durch eine Sammlung von Betriebsfestigkeitsversuchen bestimmt. Dank der metallografischen Arbeit und Korrelationsanalyse konnten drei wesentliche Parameter zur Bestimmung der lokalen Dauerfestigkeit festgestellt werden: 1. statische Festigkeit, 2. Ferrit- und Perlitanteil der Mikrostrukturen und 3. Kugelgraphitanzahl pro Fl{\"a}cheneinheit. Basierend auf diesen Erkenntnissen wurde ein neues Festigkeitsverh{\"a}ltnisdiagramm (sogenanntes Sd/Rm-SG-Diagramm) entwickelt. Diese neue Methodik sollte vor allem erm{\"o}glichen, die Bauteildauerfestigkeit auf der Grundlage der gemessenen oder durch eine Gießsimulation vorhersagten lokalen Zugfestigkeitswerte sowie Mikrogef{\"u}genstrukturen besser zu prognostizieren. Mithilfe der Versuche sowie der Gießsimulation ist es gelungen, unterschiedliche Methoden der Lebensdauervorhersage unter Ber{\"u}cksichtigung der Herstellungsprozesse weiterzuentwickeln.},
  subject      = {Grauguss},
  language  = {de}
}
@phdthesis{Ren,
  author    = {Ren, Huilong},
  title     = {Dual-horizon peridynamics and Nonlocal operator method},
  doi       = {10.25643/bauhaus-universitaet.4403},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210412-44039},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {223},
  abstract  = {In the last two decades, Peridynamics (PD) attracts much attention in the field of fracture mechanics. One key feature of PD is the nonlocality, which is quite different from the ideas in conventional methods such as FEM and meshless method. However, conventional PD suffers from problems such as constant horizon, explicit algorithm, hourglass mode. In this thesis, by examining the nonlocality with scrutiny, we proposed several new concepts such as dual-horizon (DH) in PD, dual-support (DS) in smoothed particle hydrodynamics (SPH), nonlocal operators and operator energy functional. The conventional PD (SPH) is incorporated in the DH-PD (DS-SPH), which can adopt an inhomogeneous discretization and inhomogeneous support domains. The DH-PD (DS-SPH) can be viewed as some fundamental improvement on the conventional PD (SPH). Dual formulation of PD and SPH allows h-adaptivity while satisfying the conservations of linear momentum, angular momentum and energy. By developing the concept of nonlocality further, we introduced the nonlocal operator method as a generalization of DH-PD. Combined with energy functional of various physical models, the nonlocal forms based on dual-support concept are derived. In addition, the variation of the energy functional allows implicit formulation of the nonlocal theory. At last, we developed the higher order nonlocal operator method which is capable of solving higher order partial differential equations on arbitrary domain in higher dimensional space. Since the concepts are developed gradually, we described our findings chronologically. In chapter 2, we developed a DH-PD formulation that includes varying horizon sizes and solves the "ghost force" issue. The concept of dual-horizon considers the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly with arbitrary particle discretization. All three peridynamic formulations, namely bond based, ordinary state based and non-ordinary state based peridynamics can be implemented within the DH-PD framework. A simple adaptive refinement procedure (h-adaptivity) is proposed reducing the computational cost. Both two- and three- dimensional examples including the Kalthoff-Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method. In chapter 3, a nonlocal operator method (NOM) based on the variational principle is proposed for the solution of waveguide problem in computational electromagnetic field. Common differential operators as well as the variational forms are defined within the context of nonlocal operators. The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease, which is necessary for the eigenvalue analysis of the waveguide problem. The present formulation is applied to solve 1D Schrodinger equation, 2D electrostatic problem and the differential electromagnetic vector wave equations based on electric fields. In chapter 4, a general nonlocal operator method is proposed which is applicable for solving partial differential equations (PDEs) of mechanical problems. The nonlocal operator can be regarded as the integral form, ``equivalent'' to the differential form in the sense of a nonlocal interaction model. The variation of a nonlocal operator plays an equivalent role as the derivatives of the shape functions in the meshless methods or those of the finite element method. Based on the variational principle, the residual and the tangent stiffness matrix can be obtained with ease. The nonlocal operator method is enhanced here also with an operator energy functional to satisfy the linear consistency of the field. A highlight of the present method is the functional derived based on the nonlocal operator can convert the construction of residual and stiffness matrix into a series of matrix multiplications using the predefined nonlocal operators. The nonlocal strong forms of different functionals can be obtained easily via the concept of support and dual-support. Several numerical examples of different types of PDEs are presented. In chapter 5, we extended the NOM to higher order scheme by using a higher order Taylor series expansion of the unknown field. Such a higher order scheme improves the original NOM in chapter 3 and chapter 4, which can only achieve one-order convergence. The higher order NOM obtains all partial derivatives with specified maximal order simultaneously without resorting to shape functions. The functional based on the nonlocal operators converts the construction of residual and stiffness matrix into a series of matrix multiplication on the nonlocal operator matrix. Several numerical examples solved by strong form or weak form are presented to show the capabilities of this method. In chapter 6, the NOM proposed as a particle-based method in chapter 3,4,5, has difficulty in imposing accurately the boundary conditions of various orders. In this paper, we converted the particle-based NOM into a scheme with interpolation property. The new scheme describes partial derivatives of various orders at a point by the nodes in the support and takes advantage of the background mesh for numerical integration. The boundary conditions are enforced via the modified variational principle. The particle-based NOM can be viewed a special case of NOM with interpolation property when nodal integration is used. The scheme based on numerical integration greatly improves the stability of the method, as a consequence, the operator energy functional in particle-based NOM is not required. We demonstrated the capabilities of current method by solving the gradient solid problems and comparing the numerical results with the available exact solutions. In chapter 7, we derived the DS-SPH in solid within the framework of variational principle. The tangent stiffness matrix of SPH can be obtained with ease, and can be served as the basis for the present implicit SPH. We proposed an hourglass energy functional, which allows the direct derivation of hourglass force and hourglass tangent stiffness matrix. The dual-support is {involved} in all derivations based on variational principles and is automatically satisfied in the assembling of stiffness matrix. The implementation of stiffness matrix comprises with two steps, the nodal assembly based on deformation gradient and global assembly on all nodes. Several numerical examples are presented to validate the method.},
  subject      = {Peridynamik},
  language  = {en}
}
@phdthesis{Goswami,
  author    = {Goswami, Somdatta},
  title     = {Phase field modeling of fracture with isogeometric analysis and machine learning methods},
  doi       = {10.25643/bauhaus-universitaet.4384},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210304-43841},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {168},
  abstract  = {This thesis presents the advances and applications of phase field modeling in fracture analysis. In this approach, the sharp crack surface topology in a solid is approximated by a diffusive crack zone governed by a scalar auxiliary variable. The uniqueness of phase field modeling is that the crack paths are automatically determined as part of the solution and no interface tracking is required. The damage parameter varies continuously over the domain. But this flexibility comes with associated difficulties: (1) a very fine spatial discretization is required to represent sharp local gradients correctly; (2) fine discretization results in high computational cost; (3) computation of higher-order derivatives for improved convergence rates and (4) curse of dimensionality in conventional numerical integration techniques. As a consequence, the practical applicability of phase field models is severely limited. The research presented in this thesis addresses the difficulties of the conventional numerical integration techniques for phase field modeling in quasi-static brittle fracture analysis. The first method relies on polynomial splines over hierarchical T-meshes (PHT-splines) in the framework of isogeometric analysis (IGA). An adaptive h-refinement scheme is developed based on the variational energy formulation of phase field modeling. The fourth-order phase field model provides increased regularity in the exact solution of the phase field equation and improved convergence rates for numerical solutions on a coarser discretization, compared to the second-order model. However, second-order derivatives of the phase field are required in the fourth-order model. Hence, at least a minimum of C1 continuous basis functions are essential, which is achieved using hierarchical cubic B-splines in IGA. PHT-splines enable the refinement to remain local at singularities and high gradients, consequently reducing the computational cost greatly. Unfortunately, when modeling complex geometries, multiple parameter spaces (patches) are joined together to describe the physical domain and there is typically a loss of continuity at the patch boundaries. This decrease of smoothness is dictated by the geometry description, where C0 parameterizations are normally used to deal with kinks and corners in the domain. Hence, the application of the fourth-order model is severely restricted. To overcome the high computational cost for the second-order model, we develop a dual-mesh adaptive h-refinement approach. This approach uses a coarser discretization for the elastic field and a finer discretization for the phase field. Independent refinement strategies have been used for each field. The next contribution is based on physics informed deep neural networks. The network is trained based on the minimization of the variational energy of the system described by general non-linear partial differential equations while respecting any given law of physics, hence the name physics informed neural network (PINN). The developed approach needs only a set of points to define the geometry, contrary to the conventional mesh-based discretization techniques. The concept of `transfer learning' is integrated with the developed PINN approach to improve the computational efficiency of the network at each displacement step. This approach allows a numerically stable crack growth even with larger displacement steps. An adaptive h-refinement scheme based on the generation of more quadrature points in the damage zone is developed in this framework. For all the developed methods, displacement-controlled loading is considered. The accuracy and the efficiency of both methods are studied numerically showing that the developed methods are powerful and computationally efficient tools for accurately predicting fractures.},
  subject      = {Phasenfeldmodell},
  language  = {en}
}