TY - THES A1 - Zhang, Yongzheng T1 - A Nonlocal Operator Method for Quasi-static and Dynamic Fracture Modeling N2 - 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. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2022,9 KW - Variationsprinzip KW - Partial Differential Equations KW - Taylor Series Expansion KW - Peridynamics KW - Variational principle KW - Phase field method KW - Peridynamik KW - Phasenfeldmodell KW - Partielle Differentialgleichung KW - Nichtlokale Operatormethode Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20221026-47321 ER - TY - JOUR A1 - Vu-Bac, N. A1 - Nguyen-Xuan, Hung A1 - Chen, Lei A1 - Lee, C.K. A1 - Zi, Goangseup A1 - Zhuang, Xiaoying A1 - Liu, G.R. A1 - Rabczuk, Timon T1 - A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics JF - Journal of Applied Mathematics N2 - This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions. KW - Finite-Elemente-Methode KW - Steifigkeit KW - Bruchmechanik KW - Riss Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170426-31676 ER - TY - JOUR A1 - Alkam, Feras A1 - Lahmer, Tom T1 - A robust method of the status monitoring of catenary poles installed along high-speed electrified train tracks JF - Results in Engineering N2 - Electric trains are considered one of the most eco-friendly and safest means of transportation. Catenary poles are used worldwide to support overhead power lines for electric trains. The performance of the catenary poles has an extensive influence on the integrity of the train systems and, consequently, the connected human services. It became a must nowadays to develop SHM systems that provide the instantaneous status of catenary poles in- service, making the decision-making processes to keep or repair the damaged poles more feasible. This study develops a data-driven, model-free approach for status monitoring of cantilever structures, focusing on pre-stressed, spun-cast ultrahigh-strength concrete catenary poles installed along high-speed train tracks. The pro-posed approach evaluates multiple damage features in an unfied damage index, which leads to straightforward interpretation and comparison of the output. Besides, it distinguishes between multiple damage scenarios of the poles, either the ones caused by material degradation of the concrete or by the cracks that can be propagated during the life span of the given structure. Moreover, using a logistic function to classify the integrity of structure avoids the expensive learning step in the existing damage detection approaches, namely, using the modern machine and deep learning methods. The findings of this study look very promising when applied to other types of cantilever structures, such as the poles that support the power transmission lines, antenna masts, chimneys, and wind turbines. KW - Fahrleitung KW - Catenary poles KW - SHM KW - Model-free status monitoring KW - Sigmoid function KW - High-speed electric train KW - Schaden KW - OA-Publikationsfonds2021 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20211011-45212 UR - https://www.sciencedirect.com/science/article/pii/S2590123021000906?via%3Dihub VL - 2021 IS - volume 12, article 100289 SP - 1 EP - 8 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Talebi, Hossein A1 - Zi, Goangseup A1 - Silani, Mohammad A1 - Samaniego, Esteban A1 - Rabczuk, Timon T1 - A simple circular cell method for multilevel finite element analysis JF - Journal of Applied Mathematics N2 - A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed. KW - Finite-Elemente-Methode KW - Feststoff Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170426-31639 ER - TY - CHAP A1 - Nguyen-Thanh, Nhon A1 - Rabczuk, Timon ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - A SMOOTHED FINITE ELEMENT METHOD FOR THE STATIC AND FREE VIBRATION ANALYSIS OF SHELLS N2 - A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Architektur KW - Computerunterstütztes Verfahren KW - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28777 UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html SN - 1611-4086 ER - TY - JOUR A1 - Harirchian, Ehsan A1 - Kumari, Vandana A1 - Jadhav, Kirti A1 - Rasulzade, Shahla A1 - Lahmer, Tom A1 - Raj Das, Rohan T1 - A Synthesized Study Based on Machine Learning Approaches for Rapid Classifying Earthquake Damage Grades to RC Buildings JF - Applied Sciences N2 - A vast number of existing buildings were constructed before the development and enforcement of seismic design codes, which run into the risk of being severely damaged under the action of seismic excitations. This poses not only a threat to the life of people but also affects the socio-economic stability in the affected area. Therefore, it is necessary to assess such buildings’ present vulnerability to make an educated decision regarding risk mitigation by seismic strengthening techniques such as retrofitting. However, it is economically and timely manner not feasible to inspect, repair, and augment every old building on an urban scale. As a result, a reliable rapid screening methods, namely Rapid Visual Screening (RVS), have garnered increasing interest among researchers and decision-makers alike. In this study, the effectiveness of five different Machine Learning (ML) techniques in vulnerability prediction applications have been investigated. The damage data of four different earthquakes from Ecuador, Haiti, Nepal, and South Korea, have been utilized to train and test the developed models. Eight performance modifiers have been implemented as variables with a supervised ML. The investigations on this paper illustrate that the assessed vulnerability classes by ML techniques were very close to the actual damage levels observed in the buildings. KW - Maschinelles Lernen KW - Neuronales Netz KW - Machine learning KW - Building safety assessment KW - artificial neural networks KW - supervised learning KW - damaged buildings KW - rapid classification KW - OA-Publikationsfonds2021 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210818-44853 UR - https://www.mdpi.com/2076-3417/11/16/7540 VL - 2021 IS - Volume 11, issue 16, article 7540 SP - 1 EP - 33 PB - MDPI CY - Basel ER - TY - THES A1 - Winkel, Benjamin T1 - A three-dimensional model of skeletal muscle for physiological, pathological and experimental mechanical simulations T1 - Ein dreidimensionales Skelettmuskel-Modell für physiologische, pathologische und experimentelle mechanische Simulationen N2 - 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. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2020,3 KW - Biomechanik KW - Nichtlineare Finite-Elemente-Methode KW - Muskel KW - Brustkorb KW - Muscle model KW - FEM KW - Biomechanics KW - Incompressibility KW - Thorax Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20201211-43002 ER - TY - THES A1 - Luther, Torsten T1 - Adaptation of atomistic and continuum methods for multiscale simulation of quasi-brittle intergranular damage N2 - 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. N2 - Strukturmechanische Ermüdungs- und Lebensdaueranalysen basieren meist auf der Anwendung phänomenologischer Modelle der Schädigungs- und Bruchmechanik zur numerischen Simulationen des makroskopischen Schädigungsverhaltens. Ausgehend von einer definierten Anfangsschädigung sind diese Modelle nicht in der Lage, die tatsächlichen Vorgänge der Rissinitiierung und unterschiedlichen Rissausbreitung zu erfassen. Eine physikalische Interpretation der phänomenologisch eingeführten Schädigungsparameter ist oftmals nicht möglich und deren experimentelle Bestimmung schwierig. Die Berücksichtigung des mikrostrukturellen Aufbaus von Materialien in numerischen Modellen der Schädigungs- und Bruchmechanik bietet neue Möglichkeiten, die für die Rissinitiierung und Rissausbreitung ursächlichen physikalischen Phänomene abzubilden. Zunehmende Erkenntnisse über gleichzeitig auftretende Mikro- und Makroschädigungsvorgänge resultieren in verbesserten numerischen Modellen, mit denen aufwändige und kostenintensive Experimente in der Materialentwicklung zum Teil ersetzt werden können. In Kenntnis einer Vielfalt von unterschiedlichen Schädigungsphänomenen in technischen Materialien fokussiert die vorliegende Dissertation auf die Entwicklung und Verbesserung numerischer Methoden der Atomistik und der Kontinuumsmechanik zur Mehrskalenuntersuchung quasi-spröder Korngrenzenschädigung in polykristallinen Werkstoffen, z.B. Aluminium. Die kombinierte Anwendung dieser Methoden ist Teil eines hierarchischen Mehrskalenansatzes zur Integration des physikalisch beschriebenen Materialverhaltens der Atomistik in ein ingenieurmäßiges Kontinuumsschädigungsmodell. Ziel der Dissertation ist die Entwicklung einer Methodik, die es erlaubt, den Verlust atomarer Bindungen als physikalische Ursache spröder Schädigung zu simulieren und Ergebnisse aus diesen atomistischen Mikroskalen-Simulationen zur Parametrisierung von kohäsiven Materialmodellen der Kontinuumsmechanik zu nutzen. Diese beschreiben den intergranularen Sprödbruch in heterogenen Polykristallmodellen der Mesoskala. Der Einfluss der Heterogenität wird in nichtlinearen Finite-Elemente-Simulationen durch explizite Abbildung der Kornstruktur im mesoskopischen Polykristallmodell berücksichtigt. Durch den Einsatz des kohäsiven Interface-Gesetzes erlaubt das auf der Mesoskala angewandte Kontinuumsmodell die Simulation spröder Korngrenzenschädigung in statisch belasteten 2D und 3D Modellen ohne die Notwendigkeit der Definition einer Anfangsschädigung, wie dies in klassischen Modellen der linear-elastischen Bruchmechanik notwendig ist. Zur effizienten Realisierung der atomistischen Mikroskalen-Simulationen wird eine Implementation der nichtlokalen 3D Quasikontinuumsmethode angewandt. Diese Methode basiert auf einem atomistischen Ansatz und beschreibt das Materialverhalten auf Grundlage atomarer Bindungskräfte. In Modellgebieten mit gleichmäßigem Verformungsfeld werden kinematische Kopplungen atomarer Freiheitsgrade eingeführt, sodass sich die Zahl unabhängiger Freiheitsgrade stark reduziert. Deren effizienter Einsatz erlaubt Simulationen an größeren Modellen ohne Kopplung mit kontinuumsmechanischen Methoden. Eine verbesserte Vernetzung, ein robuster Optimierungsalgorithmus und die vorgenommene Parallelisierung machen die implementierte nichtlokale 3D Quasikontinuumsmethode zu einem effizienten Werkzeug für die robuste Simulation von physikalischen Schädigungsphänomenen in beliebigen atomistischen Konfigurationen. In quasistatischen Simulationen wird eine deutliche Beschleunigung gegenüber der Methode der Gitterstatik bei vergleichbarer Qualität der Ergebnisse erreicht. T2 - Weiterentwicklung numerischer Methoden der Atomistik und Kontinuumsmechanik zur Multiskalen-Simulation quasi-spröder intergranularer Schädigung T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2010,2 KW - Mechanik KW - Computersimulation KW - Mikro-Scale KW - Meso-Scale KW - Polykristall KW - intergranular damage KW - atomistic simulation methods KW - continuum mechanics KW - quasicontinuum method KW - scale transition Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20101101-15245 ER - TY - CHAP A1 - Pham, Hoang Anh ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - ADAPTIVE EXCITATION FOR SELECTIVE SENSITIVITY-BASED STRUCTURAL IDENTIFICATION N2 - Major problems of applying selective sensitivity to system identification are requirement of precise knowledge about the system parameters and realization of the required system of forces. This work presents a procedure which is able to deriving selectively sensitive excitation by iterative experiments. The first step is to determine the selectively sensitive displacement and selectively sensitive force patterns. These values are obtained by introducing the prior information of system parameters into an optimization which minimizes the sensitivities of the structure response with respect to the unselected parameters while keeping the sensitivities with respect to the selected parameters as a constant. In a second step the force pattern is used to derive dynamic loads on the tested structure and measurements are carried out. An automatic control ensures the required excitation forces. In a third step, measured outputs are employed to update the prior information. The strategy is to minimize the difference between a predicted displacement response, formulated as function of the unknown parameters and the measured displacements, and the selectively sensitive displacement calculated in the first step. With the updated values of the parameters a re-analysis of selective sensitivity is performed and the experiment is repeated until the displacement response of the model and the actual structure are conformed. As an illustration a simply supported beam made of steel, vibrated by harmonic excitation is investigated, thereby demonstrating that the adaptive excitation can be obtained efficiently. KW - Architektur KW - CAD KW - Computerunterstütztes Verfahren Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-30015 UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html ER - TY - THES A1 - Eckardt, Stefan T1 - Adaptive heterogeneous multiscale models for the nonlinear simulation of concrete N2 - 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. N2 - Das nichtlineare Materialverhalten von Beton ist durch die Entwicklung von Mikrorissen innerhalb der heterogenen Materialstruktur gekennzeichnet. In dieser Arbeit wird ein Mesoskalenmodell entwickelt, welches die einzelnen Bestandteile der Materialstruktur explizit auflöst und somit die Simulation dieser Mikrorisse erlaubt. Dadurch können die wirklichen physikalischen Vorgänge, welche das komplexe nichtlineare Verhalten von Beton verursachen, durch relativ einfache Materialformulierungen abgebildet werden. Für Beton wird auf der Mesoskala ein 3-Phasenmodell vorgeschlagen, bestehend aus groben Zuschlägen, Mörtelmatrix und Übergangszone zwischen Zuschlag und Matrix. In diesem Zusammenhang wird ein effizienter Algorithmus vorgestellt, welcher ausgehend von einer gegebenen Sieblinie dreidimensionale Kornstrukturen mittels Ellipsoiden simuliert. Im Mesoskalenmodell wird das Zugversagen der Mörtelmatrix durch einen Kontinuumsansatz beschrieben. Um Netzabhängigkeiten, welche durch das Entfestigungsverhalten des Materials hervorgerufen werden, zu reduzieren, kommen nichtlokale Materialformulierungen zum Einsatz. Risse innerhalb der Übergangszone zwischen Zuschlag und Matrix werden, basierend auf einem kohäsiven Modell, mittels eines diskreten Rissansatzes abgebildet. Die Verwendung einer neuen Nebenbedingung innerhalb der Last-Verschiebungs-Zwangsmethode führt zu einer Stabilisierung des iterativen Lösungverfahrens, so dass eine effiziente Simulation von Snap-back Phänomenen möglich wird. Anhand von Beispielen wird gezeigt, dass Mesoskalenmodelle die stochastische Streuung von Ergebnissen und Maßstabseffekte abbilden können. Da auf der Mesoskala die Diskretisierung der inneren Materialstruktur erforderlich ist, steigt im Vergleich zu Simulationen auf der Makroskala der numerische Aufwand erheblich. Aufgrund der Komplexität des numerischen Modells sind Mesoskalensimulationen in der Regel auf kleine Probekörper beschränkt. In dieser Arbeit wird ein adaptiver heterogener Mehrskalenansatz vorgestellt, welcher die Verwendung von Mesoskalenmodellen in nichtlinearen Simulationen von Betonstrukturen erlaubt. In heterogenen Mehrskalenmodellen werden nur kritische Bereiche auf der Mesoskala aufgelöst, während ungeschädigte Bereiche auf der Makroskala abgebildet werden. Ein wichtiger Aspekt in Simulationen mit heterogenen Mehrskalenmodellen ist die Kopplung der auf unterschiedlichen Längenskalen diskretisierten Teilgebiete. Diese unterscheiden sich nicht nur in der Größe der finiten Elemente sondern auch in der Beschreibung des Materials. Verschiedene Methoden zur Kopplung nicht übereinstimmender Vernetzungen - Kopplungsgleichungen, die Mortar-Methode und die Arlequin-Methode - werden untersucht und ihre Anwendung in heterogenen Mehrskalenmodellen wird gezeigt. Ein weiterer wichtiger Aspekt ist die Bestimmung kritischer Regionen. Eine adaptive Lösungsstrategie wird entwickelt, welche die Umwandlung von Makroskalengebieten auf die Mesoskala erlaubt. In diesem Zusammenhang werden Indikatoren vorgestellt, die eine Modellanpassung auslösen. Anhand nichtlinearer Simulationen von Betonstrukturen wird die Anwendung des vorgestellten adaptiven heterogenen Mehrskalenansatzes demonstriert. T2 - Adaptive heterogene Mehrskalenmodelle zur nichtlinearen Simulation von Beton T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2010,1 KW - Beton KW - Mehrskalenanalyse KW - Finite-Elemente-Methode KW - Nichtlineare Finite-Elemente-Methode KW - Schadensmechanik KW - Mehrskalenmodell KW - Adaptives Verfahren KW - concrete KW - multiscale method KW - finite element method KW - continuum damage mechanics KW - adaptive simulation Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20100317-15023 ER -