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A nonlinear multiscale finite element model for comb-like sandwich panels

Heller, Dominik (2015):
A nonlinear multiscale finite element model for comb-like sandwich panels.
Darmstadt, Technische Universität Darmstadt, [Online-Edition: http://tuprints.ulb.tu-darmstadt.de/5288],
[Ph.D. Thesis]

Abstract

Modern composite materials and lightweight construction elements are increasingly replacing classic materials in practical applications of mechanical and civil engineering. Their high prevalence creates a demand for calculation methods which can accurately describe the mechanical behavior of a composite structure, while at the same time preserving moderate requirements in terms of numerical cost. Modeling the full microstructure of a composite by means of the classical finite element method quickly exceeds the capabilities of today’s hardware. The resulting equation systems would be extremely large and unsuitable for solution due to their enormous calculation times and memory requirements. Homogenization methods have been developed as a remedy to this issue, in which the complex microstructure is replaced by a homogeneous material using averaged mechanical properties that are determined via experiments or by analytical or numerical investigation. However, classical homogenization methods usually fail as soon as nonlinear system behavior is introduced and the effective properties, which are presumed to be constant, begin to change during the course of a simulation. In this work, a coupled global-local method will be presented specifically for sandwich panels with axially stiffened or honeycomb cores. Herein, a global model, in which the complete structure is discretized with standard shell elements, is coupled with multiple local models, describing the microstructure of the sandwich throughout the full thickness coordinate and using shell elements for discretization as well. The local formulation is implemented by means of a constitutive law for the global model, so that one local boundary value problem is evaluated in each integration point of the global structure. By reevaluating the local models in every iteration step in a nonlinear simulation, physical and geometrical nonlinearity can be described. For instance, it will be shown in numerical examples that elasto-plastic material behavior and pre- and postcritical buckling behavior can be described, contrary to most classical homogenization methods. Next to the derivation of theoretical fundamentals and the introduction of the coupled method as well as several numerical examples, additional chapters are detailing some issues concerning mesh generation and the implementation of a high-bandwidth data interface between global and local models.

Item Type: Ph.D. Thesis
Erschienen: 2015
Creators: Heller, Dominik
Title: A nonlinear multiscale finite element model for comb-like sandwich panels
Language: English
Abstract:

Modern composite materials and lightweight construction elements are increasingly replacing classic materials in practical applications of mechanical and civil engineering. Their high prevalence creates a demand for calculation methods which can accurately describe the mechanical behavior of a composite structure, while at the same time preserving moderate requirements in terms of numerical cost. Modeling the full microstructure of a composite by means of the classical finite element method quickly exceeds the capabilities of today’s hardware. The resulting equation systems would be extremely large and unsuitable for solution due to their enormous calculation times and memory requirements. Homogenization methods have been developed as a remedy to this issue, in which the complex microstructure is replaced by a homogeneous material using averaged mechanical properties that are determined via experiments or by analytical or numerical investigation. However, classical homogenization methods usually fail as soon as nonlinear system behavior is introduced and the effective properties, which are presumed to be constant, begin to change during the course of a simulation. In this work, a coupled global-local method will be presented specifically for sandwich panels with axially stiffened or honeycomb cores. Herein, a global model, in which the complete structure is discretized with standard shell elements, is coupled with multiple local models, describing the microstructure of the sandwich throughout the full thickness coordinate and using shell elements for discretization as well. The local formulation is implemented by means of a constitutive law for the global model, so that one local boundary value problem is evaluated in each integration point of the global structure. By reevaluating the local models in every iteration step in a nonlinear simulation, physical and geometrical nonlinearity can be described. For instance, it will be shown in numerical examples that elasto-plastic material behavior and pre- and postcritical buckling behavior can be described, contrary to most classical homogenization methods. Next to the derivation of theoretical fundamentals and the introduction of the coupled method as well as several numerical examples, additional chapters are detailing some issues concerning mesh generation and the implementation of a high-bandwidth data interface between global and local models.

Place of Publication: Darmstadt
Divisions: 13 Department of Civil and Environmental Engineering Sciences > Mechanics > Solid Body Mechanics
13 Department of Civil and Environmental Engineering Sciences > Mechanics
13 Department of Civil and Environmental Engineering Sciences
Date Deposited: 01 May 2016 19:55
Official URL: http://tuprints.ulb.tu-darmstadt.de/5288
URN: urn:nbn:de:tuda-tuprints-52889
Referees: Gruttmann, Prof. Friedrich and Wagner, Prof. Werner
Refereed / Verteidigung / mdl. Prüfung: 27 November 2015
Alternative Abstract:
Alternative abstract Language
Moderne Kompositwerkstoffe und Leichtbauteile ersetzen in der Praxis im Maschinenbau und Bauwesen zunehmend klassische Materialien. Durch die hohe Verbreitung entsteht ein Bedarf an Berechnungsmethoden, die das mechanische Verhalten dieser Bauteile akkurat beschreiben können, gleichzeitig aber eine zumutbare Rechenzeit gewährleisten. Eine klassische Finite-Element-Modellierung gerät im Hinblick auf Kompositwerkstoffe und Sandwichstrukturen an ihre Grenzen, da durch die vollständige Modellierung der Mikrostruktur enorm große FE-Modelle entstehen. Deren Anforderungen im Sinne von Rechenzeit und Speicherbedarf übersteigen die Rechenkapazität heutiger Computer in vielen Fällen bei weitem. Sogenannte Homogenisierungsverfahren ersetzen die vollständige Modellierung einer Mikrostruktur durch die Betrachtung eines homogenen Materials mit gemittelten Eigenschaften, die auf experimentelle, analytische oder numerische Art gewonnen werden können. Klassische Homogenisierungsmethoden scheitern jedoch in der Regel bei der Beschreibung nichtlinearen Systemverhaltens, da die effektiven Eigenschaften im Laufe einer Simulation als konstant angenommen werden. In dieser Arbeit wird ein gekoppeltes global-lokales Verfahren speziell für Sandwichstrukturen mit wabenförmigem oder axial verstärktem Kern vorgestellt. Hierbei wird ein globales Modell, in dem die vollständige zu untersuchende Struktur mit herkömmlichen Schalenelementen diskretisiert wird, mit mehreren lokalen Modellen gekoppelt, welche die Sandwich-Mikrostruktur durch den gesamten Dickenverlauf nachbilden und ebenfalls mit Schalenelementen vernetzt sind. Die lokale Formulierung wird dabei als Materialgesetz für das globale Modell implementiert, so dass in jedem Integrationspunkt der globalen Struktur ein lokales Randwertproblem ausgewertet wird. Durch die erneute Auswertung der lokalen Modelle in jedem Iterationsschritt einer nichtlinearen Simulation können physikalisch und geometrisch nichtlineare Effekte abgebildet werden. Anhand einiger Beispiele wird gezeigt, dass es im Gegensatz zu klassischen Homogenisierungsmethoden beispielsweise möglich ist elasto-plastisches Materialverhalten oder prä- und postkritisches Beulverhalten zu beschreiben. Neben der Herleitung der theoretischen Grundlagen und der Vorstellung der gekoppelten Methode sowie von Beispielen wird zudem auf einige Details der Netzgenerierung und auf die Implementierung einer Datenschnittstelle mit hoher Bandbreite zwischen globalen und lokalen Modellen eingegangen.German
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