@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}
}