1,721,333 research outputs found
Nonlinear free vibrations of Timoshenko–Ehrenfest beams using finite element analysis and direct scheme
Full text linkIn this work, nonlinear free vibrations of fully geometrically exact Timoshenko-Ehrenfest beams are investigated. First, the exact strong form of the Timonshenko-Ehrenfest beam, considering the geometrical nonlinearity, is derived, and the required formulations are obtained. Since the strong forms of governing equations are highly nonlinear, a nonlinear finite element analysis (FEA) is employed to obtain the weak form. The FEA is utilized to compute natural frequencies and mode shapes; the direct scheme is adopted to solve the eigenvalue problem which is obtained by eliminating nonlinear terms. Then, each eigenvector is normalized, and the nonlinear stiffness matrix is derived and the nonlinear free vibration analysis is carried out. A recursive procedure is adopted to proceed until the convergence criterion is satisfied. Finally, the applicability of the proposed formulation is provided with some examples and results are compared with those available in the literature
Hygro-Thermo-Electro-Mechanical Coupled Modeling of Laminated Curved Panels
No full textThe manuscript presents a generalized two-dimensional model for evaluating the stationary hygro-thermo-mechanical response of laminated shell structures made of heterogeneous piezoelectric composite materials with thermal and hygrometric properties. In particular, the static bending response of these structures is studied, along with their coupled hygro-thermo-electrical behavior. A generalized kinematic model is introduced, enabling the assessment of arbitrary temperature and mass concentration variations with respect to the unvaried configuration at the top and bottom surfaces. This is achieved through an Equivalent Layer-Wise description of the unknown field variables using higher order polynomials and zigzag functions. Furthermore, an elastic foundation is modelled according to the Winkler-Pasternak theory. The fundamental equations, derived from the total free energy of the system, are solved analytically using Navier’s method. Then, the Fourier-based generalized differential quadrature numerical method is adopted to efficiently recover the through-the-thickness distribution of secondary variables, in agreement with the hygro-thermal loading conditions. The formulation is applied in some examples of investigation where the response of panels with different curvatures and lamination schemes is evaluated under external hygro-thermal fluxes and prescribed values of temperature and moisture concentration. In addition, we investigate the effect of the hygro-thermal coupling due to Dufour and Soret effect. The present formulation is verified to be a valuable tool for assessing the mechanical response of laminated structures in a thermal and hygrometric environment with reduced computational effort
Goal-oriented adaptive modeling of 3d elastoplasticity problems
Full text linkIn finite element simulation of engineering applications, accuracy is of great importance. By applying a mesh adaptivity procedure more accurate results with lower computational effort can be achieved. For this purpose error estimation methods are utilized as guidance for mesh adaptation. Conventional error estimations compute the error in energy norms which are not of interest in engineering applications. Therefore, goal-oriented error estimations have been developed in order to approximate the error with respect to a quantity of interest. In the present work an efficient adaptivity methodology for analysis of three-dimensional elastoplasticity problems based on goal-oriented error estimation is developed and its performance is investigated through several numerical investigations
Multi-Skalen-Modellierung Mechanischer und Elektrochemischer Eigenschaften von 1D- und 2D-Nanomaterialien, Anwendung im Batteriespeichersystem
Full text linkThe exploration of two-dimensional (2D) materials, including graphene, hexagonal boron nitride (h-BN), and borophene, has become a pivotal domain within materials science due to their extraordinary mechanical and electrical properties. This dissertation presents a comprehensive suite of molecular dynamics (MD) simulations, reactive molecular dynamics (RMD) and Density Functional Theory (DFT) calculations aimed at deciphering the multifaceted behaviors of these nanomaterials, focusing particularly on their mechanical and thermal responses under various conditions, which are crucial for real-world applications. The body of work detailed in this thesis scrutinizes the mechanical properties of single-layer h-BN nanosheets, revealing the influences of temperature, topological defects, and strain rates on their tensile strength and elasticity. By simulating a spectrum of grain boundary misorientations and defects across different temperatures, this research elucidates the dependence of mechanical strength on the misorientation angles of grain boundaries, highlighting a unique mechanical response in high-angle misorientation grain boundaries under uniaxial tension. Additionally, the temperature sensitivity of these properties is rigorously analyzed, with findings indicating a significant de-crease in fracture strength and strain-at-failure with increased temperatures, notably in low-angle grain boundaries. Furthermore, this dissertation delves into the realm of fracture mechanics, examining centered-crack and notch effects in both pristine and polycrystalline nanosheets. The impact of initial crack sizes on crack propagation under mixed-mode loading conditions is meticulously studied, revealing the tendency for crack bifurcation in polycrystalline borophene sheets, a phenomenon independent of initial crack size and strain rates. These insights are paramount for ad-vancing our understanding of material failure processes, especially for applications requiring robust mechanical performance. The thesis also ventures into the innovative field of nanopore sequencing technology, where the precision fabrication of nanopores within polycrystalline boron-nitride nanosheets is investigated through ion bombardment MD simulations. The study examines the effects of cluster size, kinetic energy, and bombardment location on nanopore formation, providing critical parameters for optimizing nanopore quality and size—factors essential for the advance- ment of genomic sequencing technologies. Reactive molecular dynam- ics simulations further shed light on the mechanical and thermal behav- ior of borophene nanofilms. The research presents a detailed analysis of mode I fracture behavior in polycrystalline borophene, studying crack propagation under various loading conditions and the influence of grain boundary misorientation on crack paths. Equilibrium molecular dynam- ics (EMD) simulations are employed to predict the thermal conductivity of pristine borophene, offering valuable data for its potential application in thermal management systems. In conclusion, this thesis contributes significant new knowledge to the field of nanomaterials engineering, pro- viding a detailed examination of the mechanical and thermal properties of 2D materials. The findings not only enhance the theoretical under- standing of these materials but also offer practical for their integration into advanced technologies. The multifaceted investigations carried out in this dissertation underscore the delicate balance between atomic-scale features and macroscopic material properties, revealing how intrinsic and extrinsic factors such as defects, grain boundaries, and environmental con- ditions play a defining role in the performance of 2D materials. The com- prehensive computational approach adopted here—spanning MD, RMD, and DFT simulations—has enabled a series of novel findings. Notably, it has been demonstrated that the mechanical strength of polycrystalline h-BN is robust across a range of grain boundary configurations and that this strength is maintained even at elevated temperatures, suggesting that grain boundaries may not significantly impair the material’s mechanical integrity in practical applications. The work also provides groundbreak- ing insights into the optimal conditions for nanopore creation within poly- crystalline boron-nitride, thereby paving the way for more precise and ef- ficient DNA sequencing devices. In addition, the dissertation presents a thorough examination of the fracture mechanics in borophene, a material with a bright future in nanoelectronics and energy applications due to its exceptional properties. The observations of crack propagation behavior under mixed-mode loading provide a deeper understanding of the mate- rial’s fracture dynamics, critical for designing borophene-based devices that can withstand mechanical stresses. The thermal conductivity analy- sis of borophene opens doors for its application in areas where superior thermal management is required. The outcomes of this research not only advance the fundamental science behind 2D materials but also hold the potential to significantly impact several key technological areas. By opti- mizing the mechanical and thermal properties of these materials, this work contributes to the development of the next generation of electronics, en- ergy storage systems, and nanotechnology-based medical devices. This dissertation stands as a testament to the power of computational simula- tions in materials science, offering predictive insights that guide experi- mental work and drive innovation. The depth and breadth of the research presented herein not only fill existing knowledge gaps but also create a springboard for future studies aimed at harnessing the full potential of 2D materials. It is anticipated that the methodologies and findings detailed in this comprehensive study will serve as a valuable resource for scientists and engineers seeking to explore and exploit the remarkable properties of graphene, h-BN, borophene, and beyond
Isogeometric boundary element analysis and structural shape optimization for Helmholtz acoustic problems
Full text linkn this thesis, a new approach is developed for applications of shape optimization on the time harmonic wave propagation (Helmholtz equation) for acoustic problems. This approach is introduced for different dimensional problems: 2D, 3D axi-symmetric and fully 3D problems. The boundary element method (BEM) is coupled with the isogeometric analysis (IGA) forming the so-called (IGABEM) which speeds up meshing and gives higher accuracy in comparison with standard BEM. BEM is superior for handling unbounded domains by modeling only the inner boundaries and avoiding the truncation error, present in the finite element method (FEM) since BEM solutions satisfy the Sommerfeld radiation condition automatically. Moreover, BEM reduces the space dimension by one from a volumetric three-dimensional problem to a surface two-dimensional problem, or from a surface two-dimensional problem to a perimeter one-dimensional problem. Non-uniform rational B-splines basis functions (NURBS) are used in an isogeometric setting to describe both the CAD geometries and the physical fields. IGABEM is coupled with one of the gradient-free optimization methods, the Particle Swarm Optimization (PSO) for structural shape optimization problems. PSO is a straightforward method since it does not require any sensitivity analysis but it has some trade-offs with regard to the computational cost. Coupling IGA with optimization problems enables the NURBS basis functions to represent the three models: shape design, analysis and optimization models, by a definition of a set of control points to be the control variables and the optimization parameters as well which enables an easy transition between the three models. Acoustic shape optimization for various frequencies in different mediums is performed with PSO and the results are compared with the benchmark solutions from the literature for different dimensional problems proving the efficiency of the proposed approach with the following remarks: - In 2D problems, two BEM methods are used: the conventional isogeometric boundary element method (IGABEM) and the eXtended IGABEM (XIBEM) enriched with the partition-of-unity expansion using a set of plane waves, where the results are generally in good agreement with the linterature with some computation advantage to XIBEM which allows coarser meshes. -In 3D axi-symmetric problems, the three-dimensional problem is simplified in BEM from a surface integral to a combination of two 1D integrals. The first is the line integral similar to a two-dimensional BEM problem. The second integral is performed over the angle of revolution. The discretization is applied only to the former integration. This leads to significant computational savings and, consequently, better treatment for higher frequencies over the full three-dimensional models. - In fully 3D problems, a detailed comparison between two BEM methods: the conventional boundary integral equation (CBIE) and Burton-Miller (BM) is provided including the computational cost. The proposed models are enhanced with a modified collocation scheme with offsets to Greville abscissae to avoid placing collocation points at the corners. Placing collocation points on smooth surface enables accurate evaluation of normals for BM formulation in addition to straightforward prediction of jump-terms and avoids singularities in integrals eliminating the need for polar integration. Furthermore, no additional special treatment is required for the hyper-singular integral while collocating on highly distorted elements, such as those containing sphere poles. The obtained results indicate that, CBIE with PSO is a feasible alternative (except for a small number of fictitious frequencies) which is easier to implement. Furthermore, BM presents an outstanding treatment of the complicated geometry of mufflers with internal extended inlet/outlet tube as an interior 3D Helmholtz acoustic problem instead of using mixed or dual BEM
Computational Analysis of Woven Fabric Composites: Single- and Multi-Objective Optimizations and Sensitivity Analysis in Meso-scale Structures
Full text linkThis 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
Adaptive Multiskalen-Methoden zur Modellierung von Materialversagen
Full text linkOne 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
Mechanical Behavior of two dimensional sheets and polymer compounds based on molecular dynamics and continuum mechanics approach
Full text linkCompactly, 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
Computational modelling of fracture with local maximum entropy approximations
Full text linkThe key objective of this research is to study fracture with a meshfree method, local maximum entropy approximations, and model fracture in thin shell structures with complex geometry and topology. This topic is of high relevance for real-world applications, for example in the automotive industry and in aerospace engineering. The shell structure can be described efficiently by meshless methods which are capable of describing complex shapes as a collection of points instead of a structured mesh. In order to find the appropriate numerical method to achieve this goal, the first part of the work was development of a method based on local maximum entropy (LME)
shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture mechanics. We obtain improved accuracy relative to the standard extended finite element method (XFEM) at a comparable computational cost. In addition, we keep the advantages of the LME shape functions,such as smoothness and non-negativity. We show numerically that optimal convergence (same as in FEM) for energy norm and stress intensity factors can be obtained through the use of geometric (fixed area) enrichment with no special treatment of the nodes
near the crack such as blending or shifting.
As extension of this method to three dimensional problems and complex thin shell structures with arbitrary crack growth is cumbersome, we developed a phase field model for fracture using LME. Phase field models provide a powerful tool to tackle moving interface problems, and have been extensively used in physics and materials science. Phase methods are gaining popularity in a wide set of applications in applied science and engineering, recently a second order phase field approximation for brittle fracture has gathered significant interest in computational fracture such that sharp cracks discontinuities are modeled by a diffusive crack. By minimizing the system energy with respect to the mechanical displacements and the phase-field, subject to an irreversibility condition to avoid crack healing, this model can describe crack nucleation, propagation, branching and merging. One of the main advantages of the phase field modeling of fractures is the unified treatment of the interfacial tracking and mechanics, which potentially leads to simple, robust, scalable computer codes applicable to complex systems. In other words, this approximation reduces considerably the implementation complexity because the numerical tracking of the fracture is not needed, at the expense of a high computational cost. We present a fourth-order phase field model for fracture based on local maximum entropy (LME) approximations. The higher order continuity of the meshfree LME approximation allows to directly solve the fourth-order phase field equations without splitting the fourth-order differential equation into two second order differential equations. Notably, in contrast to previous discretizations that use at least a quadratic basis, only linear completeness is needed in the LME approximation. We show that the crack surface can be captured more accurately in the fourth-order model than the second-order model. Furthermore, less nodes are needed for the fourth-order model to resolve the crack path. Finally, we demonstrate the performance of the proposed meshfree fourth order phase-field formulation for 5 representative numerical examples. Computational results will be compared to analytical solutions within linear elastic fracture mechanics and experimental data for three-dimensional crack propagation.
In the last part of this research, we present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximum-entropy (LME) meshfree method. Since the crack is a natural outcome of the analysis it does not require an explicit representation and tracking, which is advantageous over techniques as the extended finite element method that requires tracking of the crack paths. The geometric description of the shell is based on statistical learning techniques that allow dealing with general point set surfaces avoiding a global parametrization, which can be applied to tackle surfaces of complex geometry and topology. We show the flexibility and robustness of the present methodology for two examples: plate in tension and a set of open connected
pipes
Fourth order phase-field model for local max-ent approximants applied to crack propagation
Full text linkWe apply a fourth order phase-field model for fracture based on local maximum entropy (LME) approximants. The higher order continuity of the meshfree LME approximants allows to directly solve the fourth order phase-field equations without splitting the fourth order differential equation into two second order differential equations. We will first show that the crack surface can be captured more accurately in the fourth order model. Furthermore, less nodes are needed for the fourth order model to resolve the crack path. Finally, we demonstrate the performance of the proposed meshfree fourth order phase-field formulation for 5 representative numerical examples. Computational results will be compared to analytical solutions within linear elastic fracture mechanics and experimental data for three-dimensional crack propagation.Fil: Amiri, Fatemeh. Bauhaus University of Weimar; AlemaniaFil: Millán, Raúl Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Cuyo; ArgentinaFil: Arroyo, Marino. Universidad Politécnica de Catalunya; EspañaFil: Silani, Mohammad. Isfahan University of Technology; IránFil: Rabczuk, Timon. Ton Duc Thang University; Vietnam. Korea University; Corea del Sur. Bauhaus University of Weimar; Alemani
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