1,692 research outputs found

    Multiscale Modeling of Curing and Crack Propagation in Fiber-Reinforced Thermosets

    Get PDF
    Aufgrund ihres Leichtbaupotenzials bei relativ geringen Kosten gewinnen glasfaserverstärkte Polymere in industriellen Anwendungen zunehmend an Bedeutung. Sie verbinden die hohe Festigkeit von Glasfasern mit der Beständigkeit von z.B. duroplastischen Harzen. Bei der Verarbeitung von faserverstärkten Duroplasten kommt es zu einer chemischen Reaktion des Harzes. Die chemische Reaktion geht mit einer chemischen Schrumpfung einher. In Verbindung mit der thermischen Ausdehnung kann das Material bereits beim Herstellungsprozess beschädigt werden. Auch wenn das Komposit nicht vollständig versagt, kann es zu Mikrorissbildung kommen. Diese Schäden können die Blastbarkeit des Bauteils und damit seine Lebensdauer beeinträchtigen. Faserverstärkte Duroplaste enthalten Strukturen auf verschiedenen Längenskalen, die das Verhalten des Gesamtbauteils beeinflussen und daher für eine genaue Vorhersage der Rissbildung berücksichtigt werden müssen. Das Verständnis der Mechanismen der Rissbildung auf den verschiedenen Längenskalaen ist daher von großem Interesse. Auf der Grundlage von Molekulardynamiksimulationen wird ein Harzsystem zusammen mit einer Faseroberfläche und einer Schlichte auf der Nanoskala betrachtet und ein systematisches Verfahren für die Entwicklung eines ausgehärteten Systems vorgestellt. Eine zweistufige Reaktion, eine Polyurethanreaktion und eine radikale Polymerisation, wird auf der Grundlage eines etablierten Ansatzes modelliert. Anhand des fertig ausgehärteten Systems werden Auswertungen über gemittelte Größen und entlang der Normalenrichtung der Faseroberfläche durchgeführt, was eine räumliche Analyse der Faser-Schlichtharz-Grenzfläche erlaubt. Auf der Mikrolängenskala werden die einzelnen Fasern räumlich aufgelöst. Mit Hilfe der Kontinuumsmechanik und der Phasenfeldmethode wird das Versagen während des Aushärtungsprozesses auf dieser Längenskala untersucht. In der Materialwissenschaft wird die Phasenfeldmethode häufig zur Modellierung der Rissausbreitung verwendet. Sie ist in der Lage, das komplexe Bruchverhalten zu beschreiben und zeigt eine gute Übereinstimmung mit analytischen Lösungen. Dennoch sind die meisten Modelle auf homogene Systeme beschränkt, und nur wenige Ansätze für heterogene Systeme existieren. Es werden bestehende Modelle diskutiert und ein neues Modell für heterogene Systeme abgeleitet, das auf einem etablierten Phasenfeldansatz zur Rissausbreitung basiert. Das neue Modell mit mehreren Rissordnungsparametern ist in der Lage, quantitatives Risswachstum vorherzusagen, wo die etablierten Modelle eine analytische Lösung nicht reproduzieren können. Darüber hinaus wird ein verbessertes Homogenisierungsschema, das auf der mechanischen Sprungbedingung basiert, auf das neuartige Modell angewandt, was zu einer Verbesserung der Rissvorhersage selbst bei unterschiedlichen Steifigkeiten und Risswiderständen der betrachteten Materialien führt. Zudem wird zur Erzeugung digitaler Mikrostrukturen, die für Aushärtungssimulationen im Mikrobereich verwendet werden, ein Generator für gekrümmte Faserstrukturen eingeführt. Anschließend wird die Verteilung mechanischer und thermischer Größen für verschiedene Abstraktionsebenen der realen Mikrostruktur sowie für verschiedene Faservolumenanteile verglichen. Schließlich wird das neue Rissausbreitungsmodell mit dem Aushärtungsmodell kombiniert, was die Vorhersage der Mikrorissbildung während des Aushärtungsprozesses von glasfaserverstärktem UPPH-Harz ermöglicht

    Development, Implementation, and Optimization of a Modern, Subsonic/Supersonic Panel Method

    Get PDF
    In the early stages of aircraft design, engineers consider many different design concepts, examining the trade-offs between different component arrangements and sizes, thrust and power requirements, etc. Because so many different designs are considered, it is best in the early stages of design to use simulation tools that are fast; accuracy is secondary. A common simulation tool for early design and analysis is the panel method. Panel methods were first developed in the 1950s and 1960s with the advent of modern computers. Despite being reasonably accurate and very fast, their development was abandoned in the late 1980s in favor of more complex and accurate simulation methods. The panel methods developed in the 1980s are still in use by aircraft designers today because of their accuracy and speed. However, they are cumbersome to use and limited in applicability. The purpose of this work is to reexamine panel methods in a modern context. In particular, this work focuses on the application of panel methods to supersonic aircraft (a supersonic aircraft is one that flies faster than the speed of sound). Various aspects of the panel method, including the distributions of the unknown flow variables on the surface of the aircraft and efficiently solving for these unknowns, are discussed. Trade-offs between alternative formulations are examined and recommendations given. This work also serves to bring together, clarify, and condense much of the literature previously published regarding panel methods so as to assist future developers of panel methods

    Level-Set Mass-Conservative Front-Tracking Technique for Multistep Simulations of In-Flight Ice Accretion

    Get PDF
    This paper presents a novel level-set-based approach to model evolving boundary problems for in-flight ice accretion. No partial differential equations are solved as in the standard level-set formulation, but simple geometrical quantities are employed to provide an implicit discretization of the updated boundary. This method avoids mesh entanglements and grid intersections typical of algebraic and mesh deforming techniques, making it suitable for generating a body-fitted discretization of arbitrarily complex geometries as in-flight ice shapes, including the collision of separate ice fronts. Moreover, this paper presents a local ice thickness correction, which accounts for the body's curvature, to conserve the prescribed iced mass locally. The verification includes ice accretion over an ellipse and a manufactured example to show the proposed strategy's advantages and robustness compared to standard algebraic methods. Finally, the method is applied to ice accretion problems. A temporal and grid convergence study is presented for automatic multistep in-flight simulations over a NACA0012 airfoil in rime, glaze, and mixed ice conditions

    New hybrid quadrature schemes for weakly singular kernels applied to isogeometric boundary elements for 3D Stokes flow

    Full text link
    This work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for several partial differential equations including the Stokes equation for viscous flow and the Helmholtz equation for acoustics. The proposed quadrature schemes apply a Duffy transform-based quadrature rule to surface elements containing the singularity and classical Gaussian quadrature to the remaining elements. Two of the four schemes additionally consider a special treatment for elements near to the singularity, where refined Gaussian quadrature and a new moment-fitting quadrature rule are used. The hybrid quadrature schemes are systematically studied on flat B-spline patches and on NURBS spheres considering two different sphere discretizations: An exact single-patch sphere with degenerate control points at the poles and an approximate discretization that consist of six patches with regular elements. The efficiency of the quadrature schemes is further demonstrated in boundary element analysis for Stokes flow, where steady problems with rotating and translating curved objects are investigated in convergence studies for both, mesh and quadrature refinement. Much higher convergence rates are observed for the proposed new schemes in comparison to classical schemes

    Analiza progresivnog loma kompozitnih laminata u uslovima prostornog stanja napona primenom slojevitih konačnih elemenata

    Get PDF
    Laminar composites are extensively used in civil engendering due to their exceptional strength, stiffness, corrosion resistance, and cost-effectiveness. They are ideal for high-reliability applications. The 21st century’s focus on environmental protection has led to increased use of natural-based materials like cross-laminated timber (CLT) in building construction. CLT panels have a high stiffness-to-weight ratio, making them well-suited as load-bearing elements, such as walls and floors. The optimal design of laminar composites is often hindered by uncertainties in failure prediction and the computational costs associated with progressive failure analysis (PFA), particularly for larger structures. This study introduces a novel prediction model that combines the smeared crack band (SCB) damage model with the full layerwise theory (FLWT). The aim is to enhance the computational efficiency of PFA in laminar composites while maintaining the accuracy of 3D finite element models. The SCB model accurately captures the response of damaged lamina in both fiber and matrix directions using distinct strain-softening curves, ensuring a precise representation of post-failure behaviour. The damage law is derived based on the assumption that the total energy required to cause failure in an element (released strain energy) is equivalent to the energy necessary to create a crack passing through it. To alleviate mesh dependency, the fracture energy is scaled by a characteristic element length. Failure initiation and modes are determined using the Hashin failure criterion. Furthermore, the model is extended to consider different failure behaviour of timber in tension and compression. This extension enhances the computational framework’s applicability to the field of computational mechanics for bio-based composites, such as CLT. The validity of the model is then confirmed through an extensive experimental program carried out at the Faculty of Civil Engineering, University of Belgrade. Application of layered finite elements for continuum damage modelling in laminar composites remains largely unexplored in literature, particularly when combined with the SCB damage model. The FLWT-based model accurately captures the 3D stress state within each lamina, including continuous transverse stresses between adjacent layers, crucial for accurate prediction of failure initiation. Furthermore, the FLWT demonstrates a weak correlation between the size of the considered domain and the mesh, presenting a notable difference from standard finite element models. The developed FLWT-SCB prediction model is integrated into an original FLWTFEM framework, offering a user-friendly graphical environment for easy visualization of input and output data. The proposed model’s efficiency has been verified using numerous benchmark examples during progressive failure analyses of laminar composites and CLT panels with arbitrary geometries, loading and boudary conditions and stacking sequences. The model has demonstrated its accuracy in predicting the response of both intact and damaged laminar composites, and valuable recommendations for future research in this field are included.Zbog svojih izuzetnih materijalnih karakteristika u pogledu čvrstoće i krutosti, male sopstvene težine, otpornosti na koroziju i niskih troškova održavanja, kompozitni laminati imaju potencijal za upotrebu u građevinarstvu. Sa porastom svesti o zaštiti životne sredine u 21. veku, sve je češća upotreba prirodnih materijala. U skladu sa tim, u građevinarstvu sve veću popularnost stiče kompozitni laminat na bazi drveta - unakrsno-lamelirano drvo (CLT). Zbog visokog odnosa krutosti i sopstvene težine CLT-a, moguće je projektovati elemente male težine i velikog raspona. Nepouzdanost u predviđanju ponašanja oštećenih kompozitnih laminata, kao i kompleksnost proračuna progresivnog loma znatno otežavaju njihovo projektovanje. U okviru ove disertacije je razvijen numerički model za analizu progresivnog loma kompozitnih laminata, koristeći model razmazane pukotine (eng. "smeared crack band" - SCB) i slojevitu teoriju ploča. Model poseduje kapacitet trodimenzionalnih numeričkih modela uz smanjeno trajanje proračuna, čime se povećava efikasnost numeričke analize. Kod SCB modela, ponašanje oštećene lamine je opisano različitim krivama loma u naponsko-deformacijskom prostoru, kako bi se u makroskopskom pogledu opisala propagacija oštećenja koje nastaje usled kidanja vlakana i matrice, respektivno. Zakon omekšavanja materijala je određen na osnovu pretpostavke da je oslobođena energija deformacije jednaka energiji potrebnoj da dođe do loma vlakana, odnosno kidanja matrice. Inicijacija i oblici loma su određeni primenom Hashin-ovog kriterijuma loma. Nakon toga, izvršena je modifikacija modela kako bi se opisalo različito ponašanje drveta pri zatezanju i pritisku. Na taj način, mogućnosti razvijenog numeričkog modela su proširene i na analizu progresivnog loma prirodnih kompozitnih laminata, kao što je CLT. Validnost predloženog modela je potvrđena kroz detaljna eksperimentalna ispitivanja na Građevinskom fakultetu Univerziteta u Beogradu. Upotreba slojevitih konačnih elemenata u analizi progresivnog loma je u velikoj meri neistražena u literaturi, posebno u kombinaciji sa SCB degradacijskim modelima, gde slojeviti model ploče treba objediniti sa fenomenima mehanike loma. Numerički model, zasnovan na slojevitoj teoriji ploča, omogućava precizno određivanje prostornog stanja napona, zadovoljavajući uslove ravnoteže međulaminarnih napona, što je veoma bitno prilikom predviđanja inicijacije loma. Takođe, pri modeliranju većih konstrukcija, primenom slojevite teorije ploča omogućava se znatno smanjenje broja konačnih elemenata u poređenju sa postojećim numeričkim modelima. Razvijeni numerički model je implementiran u FLWTFEM kod, čime je obezbeđeno puno grafičko okruženje, pogodno za vizualizaciju ulaznih podataka i rezultata proračuna. Efikasnost predloženog modela je verifikovana korišćenjem brojnih referentnih numeričkih primera, prilikom analize progresivnog loma kompozitnih laminata i CLT panela sa proizvoljnom geometrijom, opterećenjem, graničnim uslovima i orijentacijom slojeva. Potvrđena je tačnost predloženog modela u predviđanju odgovora kako neoštećenih tako i oštećenih kompozitnih laminata, a date su i važne preporuke za buduća istraživanja u ovoj oblasti

    Drift-diffusion models for innovative semiconductor devices and their numerical solution

    Get PDF
    We present charge transport models for novel semiconductor devices which may include ionic species as well as their thermodynamically consistent finite volume discretization

    Integration of Polynomials Times Double Step Function in Quadrilateral Domains for XFEM Analysis

    Get PDF
    The numerical integration of discontinuous functions is an abiding problem addressed by various authors. This subject gained even more attention in the context of the extended finite element method (XFEM), in which the exact integration of discontinuous functions is crucial to obtaining reliable results. In this scope, equivalent polynomials represent an effective method to circumvent the problem while exploiting the standard Gauss quadrature rule to exactly integrate polynomials times step function. Certain scenarios, however, might require the integration of polynomials times two step functions (i.e., problems in which branching cracks, kinking cracks or crack junctions within a single finite element occur). In this context, the use of equivalent polynomials has been investigated by the authors, and an algorithm to exactly integrate arbitrary polynomials times two Heaviside step functions in quadrilateral domains has been developed and is presented in this paper. Moreover, the algorithm has also been implemented into a software library (DD_EQP) to prove its precision and effectiveness and also the proposed method’s ease of implementation into any existing computational software or framework. The presented algorithm is the first step towards the numerical integration of an arbitrary number of discontinuities in quadrilateral domains. Both the algorithm and the library have a wide application range, in addition to fracture mechanics, from mathematical computing of complex geometric regions, to computer graphics and computational mechanics

    Model order reduction for seismic waveform modelling: inspiration from normal modes

    Get PDF
    The computational cost of full waveform simulation in seismological contexts is known to be expensive and generally requires large clusters of computers working in parallel. Although there have been many methods proposed over recent years to reduce this burden, in this work, we focus on a particular method called model order reduction (MOR) whereby a full waveform system of equations is projected onto a lower dimensional space to reduce computational and memory requirements at the cost of introducing approximation errors. In this paper, inspired by normal mode (NM) theory, we use the eigenmodes of the seismic wave equation to span this lower dimensional space. From this we argue that NM theory can be seen as an early form of MOR. Using this as inspiration, we demonstrate how free body oscillations and a form of Petrov–Galerkin projection can be applied in regional scale problems utilizing recent advanced eigensolvers to create a MOR scheme. We also demonstrate how this can be applied to inverse problems. We further conjecture that MOR will have an important role to play in future full waveform applications, particularly those of a time-critical nature such as seismic hazard monitoring

    Multi-adaptive spatial discretization of bond-based peridynamics

    Get PDF
    Peridynamic (PD) models are commonly implemented by exploiting a particle-based method referred to as standard scheme. Compared to numerical methods based on classical theories (e.g., the finite element method), PD models using the meshfree standard scheme are typically computationally more expensive mainly for two reasons. First, the nonlocal nature of PD requires advanced quadrature schemes. Second, non-uniform discretizations of the standard scheme are inaccurate and thus typically avoided. Hence, very fine uniform discretizations are applied in the whole domain even in cases where a fine resolution is per se required only in a small part of it (e.g., close to discontinuities and interfaces). In the present study, a new framework is devised to enhance the computational performance of PD models substantially. It applies the standard scheme only to localized regions where discontinuities and interfaces emerge, and a less demanding quadrature scheme to the rest of the domain. Moreover, it uses a multi-grid approach with a fine grid spacing only in critical regions. Because these regions are identified dynamically over time, our framework is referred to as multi-adaptive. The performance of the proposed approach is examined by means of two real world problems, the Kalthoff-Winkler experiment and the bio-degradation of a magnesium-based bone implant screw. It is demonstrated that our novel framework can vastly reduce the computational cost (for given accuracy requirements) compared to a simple application of the standard scheme
    corecore