620 Ingenieurwissenschaften
Refine
Document Type
- Doctoral Thesis (27) (remove)
Institute
- Institut für Strukturmechanik (ISM) (12)
- F. A. Finger-Institut für Baustoffkunde (FIB) (5)
- Professur Baubetrieb und Bauverfahren (3)
- Graduiertenkolleg 1462 (1)
- Professur Abfallwirtschaft (1)
- Professur Bauchemie und Polymere Werkstoffe (1)
- Professur Grundbau (1)
- Professur Raumplanung und Raumforschung (1)
- Professur Verkehrssystemplanung (1)
- Professur Werkstoffe des Bauens (1)
Keywords
- Beton (3)
- Finite-Elemente-Methode (3)
- Strukturmechanik (3)
- Bruch (2)
- Bruchverhalten (2)
- Building Information Modeling (2)
- Rice husk ash (2)
- Werkstoffkunde (2)
- crack (2)
- Abbiegespur (1)
Die fortschreitende Digitalisierung lässt innovative bauprojekt- und unternehmensinterne Workflows sowie Organisationssysteme entstehen. In diesem Zusammenhang ist die digitale Fortentwicklung durch Building Information Modeling [BIM] als Veränderungsprozess zu definieren, der Organisationsstrukturen nachhaltig umformen wird. BIM ist die führende digitale Arbeitsmethodik im Bauwesen, die entwurfs-, ausführungs- und bauprojektbezogenen Belangen gerecht werden kann. Die deutsche Bauwirtschaft ist im Vergleich zu anderen Branchen jedoch als digital rückständig zu betrachten. Sie ist durch einen Markt gekennzeichnet, an dem kleine und mittelständische Unternehmen [KMU] in hoher Zahl vertreten sind. Aufgrund von Anwendungsunkenntnis der kleinen und mittelständischen Unternehmen fehlt der flächendeckende und durchgängige BIM-Einsatz in Projekten. Mit dem Fokus auf dem Bauprojekt als temporärer Organisation adressiert der vorliegende Forschungsschwerpunkt die Schaffung eines realistischen Abbilds erprobter BIM-Anwendungsfälle in Modellprojekten. Herausgearbeitet werden derzeit bestehende BIM-Herausforderungen für Erstanwender, die die durchgängige BIM-Anwendung in Deutschland bisher hemmen.
Die Forschungsarbeit fokussiert sich auf die Evaluation erfolgskritischer Faktoren [ekF] in BIM-Anwendungsfällen [AWF] im Rahmen einer qualitativen Inhaltsanalyse. Die digitale Transformation birgt strukturrelevante Veränderungsdeterminanten für Organisationen durch die BIM-Anwendung und außerdem Herausforderungen, die in der Anwendungsfallforschung betrachtet werden.
Die Zielstellung ist dreiteilig. Ein entwickeltes BIM-Strukturmodell erfasst die aktuelle Richtlinienarbeit sowie Standardisierung und stellt dadurch den Rahmen notwendiger BIM-Strukturen im Bauprojekt auf. Aus dem Strukturmodell ist ein Modell zur Prüfung von Anwendungsfallrisiken abgeleitet worden. Dieses wird auf gezielt recherchierte BIM-Modellprojekte in Deutschland angewendet, um aus den erfolgskritischen Faktoren der darin praktizierten BIM-Anwendungsfälle eine ekF-Risikomatrix abzuleiten. Daraus geht ein unterstützendes BIM-Anwendungsinstrument in Form von BPMN-Abläufen für KMU hervor. Resultierend aus der Verbindung des BIM-Strukturmodels und der Anwendungsfallanalyse wird in den einzelnen Ablaufübersichten eine Risikoverortung je Anwendungsfall kenntlich gemacht. Unternehmen ohne BIM-Anwendungsexpertise in Bauprojektorganisationen erhalten auf diese Weise einen instrumentellen und niederschwelligen Zugang zu BIM, um die kollaborativen und wirtschaftlichen Vorteile der digitalen Arbeitsmethodik nutzen zu können.
Modell bedarfsorientierter Leistungserbringung im FM auf Grundlage von Sensortechnologien und BIM
(2023)
Während der Digitalisierung im Bauwesen insbesondere im Bereich der Planungs- und Errichtungsphase von Bauwerken immer größere Aufmerksamkeit zuteilwird, ist das digitale Potenzial im Facility Management weit weniger ausgeschöpft, als dies möglich wäre. Vor dem Hintergrund, dass die Bewirtschaftung von Gebäuden jedoch einen wesentlichen Kostenanteil im Lebenszyklus darstellt, ist eine Fokussierung auf digitale Prozesse im Gebäudebetrieb erforderlich. Im Facility Management werden Dienstleistungen häufig verrichtungsorientiert, d. h. nach statischen Intervallen, oder bedarfsorientiert erbracht. Beide Arten der Leistungserbringung weisen Defizite auf, beispielweise weil Tätigkeiten auf Basis definierter Intervalle erbracht werden, ohne dass eine Notwendigkeit besteht oder weil bestehende Bedarfe mangels Möglichkeiten der Bedarfsermittlung nicht identifiziert werden. Speziell die Definition und Ermittlung eines Bedarfs zur Leistungserbringung ist häufig subjektiv geprägt. Auch sind Dienstleister oft nicht in frühen Phasen der Gebäudeplanung involviert und erhalten für ihre Dienstleistungen notwendige Daten und Informationen erst kurz vor Inbetriebnahme des zu betreibenden Gebäudes.
Aktuelle Ansätze des Building Information Modeling (BIM) und die zunehmende Verfügbarkeit von Sensortechnologien in Gebäuden bieten Chancen, die o. g. Defizite zu beheben.
In der vorliegenden Arbeit werden deshalb Datenmodelle und Methoden entwickelt, die mithilfe von BIM-basierten Datenbankstrukturen sowie Auswertungs- und Entscheidungsmethodiken Dienstleistungen der Gebäudebewirtschaftung objektiviert und automatisiert auslösen können. Der Fokus der Arbeit liegt dabei auf dem Facility Service der Reinigungs- und Pflegedienste des infrastrukturellen Facility Managements.
Eine umfangreiche Recherche etablierter Normen und Standards sowie öffentlich zugänglicher Leistungsausschreibungen bilden die Grundlage der Definition erforderlicher Informationen zur Leistungserbringung. Die identifizierten statischen Gebäude- und Prozessinformationen werden in einem relationalen Datenbankmodell strukturiert, das nach einer Darstellung von Messgrößen und der Beschreibung des Vorgehens zur Auswahl geeigneter Sensoren für die Erfassung von Bedarfen, um Sensorinformationen erweitert wird. Um Messwerte verschiedener und bereits in Gebäuden existenten Sensoren für die Leistungsauslösung verwenden zu können, erfolgt die Implementierung einer Normierungsmethodik in das Datenbankmodell. Auf diese Weise kann der Bedarf zur Leistungserbringung ausgehend von Grenzwerten ermitteln werden. Auch sind Verknüpfungsmethoden zur Kombination verschiedener Anwendungen in dem Datenbankmodell integriert. Zusätzlich zur direkten Auslösung erforderlicher Aktivitäten ermöglicht das entwickelte Modell eine opportune Auslösung von Leistungen, d. h. eine Leistungserbringung vor dem eigentlich bestehenden Bedarf. Auf diese Weise können tätigkeitsähnliche oder räumlich nah beieinander liegende Tätigkeiten sinnvoll vorzeitig erbracht werden, um für den Dienstleister eine Wegstreckeneinsparung zu ermöglichen. Die Arbeit beschreibt zudem die für die Auswertung, Entscheidungsfindung und Auftragsüberwachung benötigen Algorithmen.
Die Validierung des entwickelten Modells bedarfsorientierter Leistungserbringung erfolgt in einer relationalen Datenbank und zeigt simulativ für unterschiedliche Szenarien des Gebäudebetriebs, dass Bedarfsermittlungen auf Grundlage von Sensortechnologien erfolgen und Leistungen opportun ausgelöst, beauftragt und dokumentiert werden können.
Encapsulation-based self-healing concrete (SHC) is the most promising technique for providing a self-healing mechanism to concrete. This is due to its capacity to heal fractures effectively without human interventions, extending the operational life and lowering maintenance costs. The healing mechanism is created by embedding capsules containing the healing agent inside the concrete. The healing agent will be released once the capsules are fractured and the healing occurs in the vicinity of the damaged part. The healing efficiency of the SHC is still not clear and depends on several factors; in the case of microcapsules SHC the fracture of microcapsules is the most important aspect to release the healing agents and hence heal the cracks. This study contributes to verifying the healing efficiency of SHC and the fracture mechanism of the microcapsules. Extended finite element method (XFEM) is a flexible, and powerful discrete crack method that allows crack propagation without the requirement for re-meshing and has been shown high accuracy for modeling fracture in concrete. In this thesis, a computational fracture modeling approach of Encapsulation-based SHC is proposed based on the XFEM and cohesive surface technique (CS) to study the healing efficiency and the potential of fracture and debonding of the microcapsules or the solidified healing agents from the concrete matrix as well. The concrete matrix and a microcapsule shell both are modeled by the XFEM and combined together by CS. The effects of the healed-crack length, the interfacial fracture properties, and microcapsule size on the load carrying capability and fracture pattern of the SHC have been studied. The obtained results are compared to those obtained from the zero thickness cohesive element approach to demonstrate the significant accuracy and the validity of the proposed simulation. The present fracture simulation is developed to study the influence of the capsular clustering on the fracture mechanism by varying the contact surface area of the CS between the microcapsule shell and the concrete matrix. The proposed fracture simulation is expanded to 3D simulations to validate the 2D computational simulations and to estimate the accuracy difference ratio between 2D and 3D simulations. In addition, a proposed design method is developed to design the size of the microcapsules consideration of a sufficient volume of healing agent to heal the expected crack width. This method is based on the configuration of the unit cell (UC), Representative Volume Element (RVE), Periodic Boundary Conditions (PBC), and associated them to the volume fraction (Vf) and the crack width as variables. The proposed microcapsule design is verified through computational fracture simulations.
Encapsulation-based self-healing concrete has received a lot of attention nowadays in civil engineering field. These capsules are embedded in the cementitious matrix during concrete mixing. When the cracks appear, the embedded capsules which are placed along the path of incoming crack are fractured and then release of healing agents in the vicinity of damage. The materials of capsules need to be designed in a way that they should be able to break with small deformation, so the internal fluid can be released to seal the crack. This study focuses on computational modeling of fracture in encapsulation-based selfhealing concrete. The numerical model of 2D and 3D with randomly packed aggreates and capsules have been developed to analyze fracture mechanism that plays a significant role in the fracture probability of capsules and consequently the self-healing process. The capsules are assumed to be made of Poly Methyl Methacrylate (PMMA) and the potential cracks are represented by pre-inserted cohesive elements with tension and shear softening laws along the element boundaries of the mortar matrix, aggregates, capsules, and at the interfaces between these phases. The effects of volume fraction, core-wall thickness ratio, and mismatch fracture properties of capsules on the load carrying capacity of self-healing concrete and fracture probability of the capsules are investigated. The output of this study will become valuable tool to assist not only the experimentalists but also the manufacturers in designing an appropriate capsule material for self-healing concrete.
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.
Die Gase Sauerstoff und Stickstoff werden für eine Vielzahl an technischen, industriellen, biologischen und medizinischen Einsatzzwecken benötigt. So liegen Anwendungsgebiete dieser Gase neben der klassischen metallverarbeitenden und der chemischen Industrie bei Sauerstoff vor allem in der Medizin, Verbrennungs- und Kläranlagenoptimierung sowie der Fischzucht und bei Stickstoff als Schutz- beziehungsweise Inertgas in der Kunststoffindustrie, der Luft- und Raumfahrt sowie dem Brandschutz.
Die Bereitstellung der Gase Sauerstoff und Stickstoff wird nahezu ausschließlich durch die Abtrennung aus der Umgebungsluft realisiert, welche aus ca. 78 Vol.-% Stickstoff, 21 Vol.-% Sauerstoff und 1 Vol.-% Spurengasen (Ar, CO2, Ne, He, ...) besteht. Am Markt etablierte Verfahren der Luftzerlegung sind das Linde-, das PSA- (pressure swing adsorption/Druckwechseladsorption) oder verschiedene Membran-Verfahren. Hierdurch werden die benötigten Gase entweder direkt vor Ort beim Verbraucher erzeugt (PSA- und Polymer-Membranverfahren: geringe Reinheiten) oder zentral in großen Anlagen hergestellt (Linde-Verfahren: hohe Reinheiten) und anschließend zum Verbraucher in Form von Flaschen- oder Tankgasen geliefert (Tansportkosten).
Für kleinere Verbraucher mit hohen Ansprüchen an die Reinheit des benötigten Sauerstoffs beziehungsweise Stickstoffs ergibt sich nur die Möglichkeit, die Gase als kostenintensive Transportgase zentraler Gaseversorger zu beziehen und sich somit in eine Abhängigkeit (Lieferverträge, Flaschen-/Tankmieten, ...) zu diesen zu begeben sowie eine eigene Lagerhaltung für die benötigten Gase (Mehraufwand, Lagerkosten, Platzbedarf) zu betreiben.
Ziel dieser Arbeit ist es, keramische Material-Systeme auf Basis chemischer Hochtemperatur-Reaktionen als Reaktive Oxidkeramiken zu entwickeln und diese hinsichtlich eines möglichen Einsatzes für die Sauerstoffseparation in neuartigen Luftzerlegungsanlagen zu untersuchen.
Derartige Anlagen sollen in ihrem Prinzip an die regenerative Sauerstoffseparation angelehnt sein und in ihren Reaktoren die Reaktiven Oxidkeramiken als Festbett-Material abwechselnd mit Luft be- und Vakuum oder O2-armen Atmosphären entladen.
Die Verwendung Reaktiver Oxidkeramiken, welche im Vergleich zu den bisherigen Materialien höhere Sauerstoffaustauschmengen und -raten bei gleichzeitig hoher Lebensdauer und Korrosionsbeständigkeit sowie relativ einfacher Handhabe aufweisen würden, soll ein Schritt in Richtung einer effizienten alternativen Luftzerlegungstechnologie sein.
Mit den Reaktiven Oxidkeramiken in einer Luftzerlegungsanlage sollte es im besten Fall möglich sein, in kleinen Anlagen sehr reinen Sauerstoff und zugleich sauerstofffreies Inertgas zu erzeugen sowie eine Sauerstoffan- oder -abreicherung von Luft, Prozess- oder Abgasen zu generieren.
Somit besäße eine solche, auf Reaktiven Oxidkeramiken basierende Technologie sehr weit gefächerte Einsatzgebiete und demzufolge ein enormes wirtschaftliches Potential.
Turbomachinery plays an important role in many cases of energy generation or conversion. Therefore, turbomachinery is a promising approaching point for optimization in order to increase the efficiency of energy use. In recent years, the use of automated optimization strategies in combination with numerical simulation has become increasingly popular in many fields of engineering. The complex interactions between fluid and solid mechanics encountered in turbomachines on the one hand and the high computational expense needed to calculate the performance on the other hand, have, however, prevented a widespread use of these techniques in this field of engineering. The objective of this work was the development of a strategy for efficient metamodel based optimization of centrifugal compressor impellers. In this context, the main focus is the reduction of the required numerical expense. The central idea followed in this research was the incorporation of preliminary information acquired from low-fidelity computation methods and empirical correlations into the sampling process to identify promising regions of the parameter space. This information was then used to concentrate the numerically expensive high-fidelity computations of the fluid dynamic and structure mechanic performance of the impeller in these regions while still maintaining a good coverage of the whole parameter space. The development of the optimization strategy can be divided into three main tasks. Firstly, the available preliminary information had to be researched and rated. This research identified loss models based on one dimensional flow physics and empirical correlations as the best suited method to predict the aerodynamic performance. The loss models were calibrated using available performance data to obtain a high prediction quality. As no sufficiently exact models for the prediction of the mechanical loading of the impellercould be identified, a metamodel based on finite element computations was chosen for this estimation. The second task was the development of a sampling method which concentrates samples in regions of the parameter space where high quality designs are predicted by the preliminary information while maintaining a good overall coverage. As available methods like rejection sampling or Markov-chain Monte-Carlo methods did not meet the requirements in terms of sample distribution and input correlation, a new multi-fidelity sampling method called “Filtered Sampling“has been developed. The last task was the development of an automated computational workflow. This workflow encompasses geometry parametrization, geometry generation, grid generation and computation of the aerodynamic performance and the structure mechanic loading. Special emphasis was put into the development of a geometry parametrization strategy based on fluid mechanic considerations to prevent the generation of physically inexpedient designs. Finally, the optimization strategy, which utilizes the previously developed tools, was successfully employed to carry out three optimization tasks. The efficiency of the method was proven by the first and second testcase where an existing compressor design was optimized by the presented method. The results were comparable to optimizations which did not take preliminary information into account, while the required computational expense cloud be halved. In the third testcase, the method was applied to generate a new impeller design. In contrast to the previous examples, this optimization featuredlargervariationsoftheimpellerdesigns. Therefore, theapplicability of the method to parameter spaces with significantly varying designs could be proven, too.
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.
Matrix-free voxel-based finite element method for materials with heterogeneous microstructures
(2019)
Modern image detection techniques such as micro computer tomography
(μCT), magnetic resonance imaging (MRI) and scanning electron microscopy (SEM) provide us with high resolution images of the microstructure of materials in a non-invasive and convenient way. They form the basis for the geometrical models of high-resolution analysis, so called image-based analysis.
However especially in 3D, discretizations of these models reach easily the size of 100 Mill. degrees of freedoms and require extensive hardware resources in terms of main memory and computing power to solve the numerical model. Consequently, the focus of this work is to combine and adapt numerical solution methods to reduce the memory demand first and then the computation time and therewith enable an execution of the image-based analysis on modern computer desktops. Hence, the numerical model is a straightforward grid discretization of the voxel-based (pixels with a third dimension) geometry which omits the boundary detection algorithms and allows reduced storage of the finite element data structure and a matrix-free solution algorithm.
This in turn reduce the effort of almost all applied grid-based solution techniques and results in memory efficient and numerically stable algorithms for the microstructural models. Two variants of the matrix-free algorithm are presented. The efficient iterative solution method of conjugate gradients is used with matrix-free applicable preconditioners such as the Jacobi and the especially suited multigrid method. The jagged material boundaries of the voxel-based mesh are smoothed through embedded boundary elements which contain different material information at the integration point and are integrated sub-cell wise though without additional boundary detection. The efficiency of the matrix-free methods can be retained.