@phdthesis{Zacharias,
  author    = {Zacharias, Christin},
  title     = {Numerical Simulation Models for Thermoelastic Damping Effects},
  doi       = {10.25643/bauhaus-universitaet.4735},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221116-47352},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {191},
  abstract  = {Finite Element Simulations of dynamically excited structures are mainly influenced by the mass, stiffness, and damping properties of the system, as well as external loads. The prediction quality of dynamic simulations of vibration-sensitive components depends significantly on the use of appropriate damping models. Damping phenomena have a decisive influence on the vibration amplitude and the frequencies of the vibrating structure. However, developing realistic damping models is challenging due to the multiple sources that cause energy dissipation, such as material damping, different types of friction, or various interactions with the environment. This thesis focuses on thermoelastic damping, which is the main cause of material damping in homogeneous materials. The effect is caused by temperature changes due to mechanical strains. In vibrating structures, temperature gradients arise in adjacent tension and compression areas. Depending on the vibration frequency, they result in heat flows, leading to increased entropy and the irreversible transformation of mechanical energy into thermal energy. The central objective of this thesis is the development of efficient simulation methods to incorporate thermoelastic damping in finite element analyses based on modal superposition. The thermoelastic loss factor is derived from the structure's mechanical mode shapes and eigenfrequencies. In subsequent analyses that are performed in the time and frequency domain, it is applied as modal damping. Two approaches are developed to determine the thermoelastic loss in thin-walled plate structures, as well as three-dimensional solid structures. The realistic representation of the dissipation effects is verified by comparing the simulation results with experimentally determined data. Therefore, an experimental setup is developed to measure material damping, excluding other sources of energy dissipation. The three-dimensional solid approach is based on the determination of the generated entropy and therefore the generated heat per vibration cycle, which is a measure for thermoelastic loss in relation to the total strain energy. For thin plate structures, the amount of bending energy in a modal deformation is calculated and summarized in the so-called Modal Bending Factor (MBF). The highest amount of thermoelastic loss occurs in the state of pure bending. Therefore, the MBF enables a quantitative classification of the mode shapes concerning the thermoelastic damping potential. The results of the developed simulations are in good agreement with the experimental results and are appropriate to predict thermoelastic loss factors. Both approaches are based on modal superposition with the advantage of a high computational efficiency. Overall, the modeling of thermoelastic damping represents an important component in a comprehensive damping model, which is necessary to perform realistic simulations of vibration processes.},
  subject      = {Werkstoffd{\"a}mpfung},
  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{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}
}