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A Multiscale Finite Element Model for Damage Simulations in Fiber-Reinforced Composites

Maaß, Jan Grischa (2017)
A Multiscale Finite Element Model for Damage Simulations in Fiber-Reinforced Composites.
Book, Primary publication

Abstract

Fiber-reinforced plastics are of increasing relevance in a broad variety of engineering applications. Developments in E-Mobility and ever-increasing demands on materials guarantee that this trend will continue. The increasing use and importance of FRP will in turn increase demand for appropriate methodologies for describing the complex mechanical properties of these materials. This thesis contributes to this end to the theoretical development and implementation of damage models. These models build on the so called smeared crack approach, whereby the damage in the material is assumed to have a continuous distribution. With the help of damage models, maximum bearing load computations can be performed and the damage initiation and propagation can be precisely followed. A variety of approaches are used in this thesis: firstly, a macroscopic view of anisotropic damage models is presented. The model utilizes either Hashin's failure criterion or Cuntze's failure mode concept to determine damage initiation. At the onset of damage, a linear degradation model is used, the path of which is determined by the critical energy release rate. In conjunction with the characteristic element length, an accurate calculation of the dissipated energy in the finite element model is assured. A second approach is based on a coupled multi-scaled finite element model. The model presented here is a two-scale model consisting of a micro scale and a macro scale. The distortions in the macro scale are mapped onto the micro scale using appropriate boundary conditions. In the micro scale, the modeling of the damage is carried out separately on the individual fiber and polymer components. The nonlinear micro model is solved by means of Newton-Raphson method before the homogenized stresses and material tangents are delivered to the macro system. This process is repeated until global equilibrium is achieved. The micro scale model utilizes an exponential degradation law, which lacks an elastic initial region and has proven to be especially robust. The multi scale model affects damage at locations where it actually occurs, giving it a significant advantage over macroscopic models. The use of costly failure criterion is spared in this approach. Furthermore, use of the multi scale approach allows detailed observations of the failure in the material, and failure modes such as fiber-polymer separation can easily be implemented. The counter-argument to this approach is the significant computational cost, caused by the necessity of a complete iteration loop in the micro system for every integration point in the global system. However, the structure of the models makes them especially suitable for simultaneous parallel processing, so that it can be expected that they supersede macroscopic models in the mid term future.

Item Type: Book
Erschienen: 2017
Creators: Maaß, Jan Grischa
Type of entry: Primary publication
Title: A Multiscale Finite Element Model for Damage Simulations in Fiber-Reinforced Composites
Language: English
Referees: Gruttmann, Prof. Dr. Friedrich ; Gross, Prof. Dr. Dietmar
Date: January 2017
Place of Publication: Darmstadt
Publisher: Studienbereich Mechanik
Refereed: 20 October 2016
URL / URN: http://tuprints.ulb.tu-darmstadt.de/5957
Abstract:

Fiber-reinforced plastics are of increasing relevance in a broad variety of engineering applications. Developments in E-Mobility and ever-increasing demands on materials guarantee that this trend will continue. The increasing use and importance of FRP will in turn increase demand for appropriate methodologies for describing the complex mechanical properties of these materials. This thesis contributes to this end to the theoretical development and implementation of damage models. These models build on the so called smeared crack approach, whereby the damage in the material is assumed to have a continuous distribution. With the help of damage models, maximum bearing load computations can be performed and the damage initiation and propagation can be precisely followed. A variety of approaches are used in this thesis: firstly, a macroscopic view of anisotropic damage models is presented. The model utilizes either Hashin's failure criterion or Cuntze's failure mode concept to determine damage initiation. At the onset of damage, a linear degradation model is used, the path of which is determined by the critical energy release rate. In conjunction with the characteristic element length, an accurate calculation of the dissipated energy in the finite element model is assured. A second approach is based on a coupled multi-scaled finite element model. The model presented here is a two-scale model consisting of a micro scale and a macro scale. The distortions in the macro scale are mapped onto the micro scale using appropriate boundary conditions. In the micro scale, the modeling of the damage is carried out separately on the individual fiber and polymer components. The nonlinear micro model is solved by means of Newton-Raphson method before the homogenized stresses and material tangents are delivered to the macro system. This process is repeated until global equilibrium is achieved. The micro scale model utilizes an exponential degradation law, which lacks an elastic initial region and has proven to be especially robust. The multi scale model affects damage at locations where it actually occurs, giving it a significant advantage over macroscopic models. The use of costly failure criterion is spared in this approach. Furthermore, use of the multi scale approach allows detailed observations of the failure in the material, and failure modes such as fiber-polymer separation can easily be implemented. The counter-argument to this approach is the significant computational cost, caused by the necessity of a complete iteration loop in the micro system for every integration point in the global system. However, the structure of the models makes them especially suitable for simultaneous parallel processing, so that it can be expected that they supersede macroscopic models in the mid term future.

Alternative Abstract:
Alternative abstract Language

Faserverbundwerkstoffe gewinnen in den verschiedensten Ingenieurwissenschaften immer mehr an Bedeutung. Dieser Trend wird sich in den nächsten Jahren, gerade im Hinblick auf E-Mobilty und immer höheren Materialanforderungen, noch verstärken. Mit der zunehmenden Verwendung wird auch die Nachfrage nach geeigneten Berechnungsverfahren zur Beschreibung des komplexen mechanischen Verhaltens dieser Werkstoffe immer größer. Diese Arbeit leistet einen Beitrag zur theoretischen Entwicklung und Implementierung von Schädigungsmodellen. Mit Hilfe von Schädigungsmodellen kann der Beginn der Schädigung lokalisiert, der Verlauf durch die Struktur verfolgt sowie deren Traglast bestimmt werden. In der vorliegenden Arbeit werden verschiedene Modellansätze verfolgt, die auf einem sogenannten Smeared-Crack-Ansatz basieren. Dabei wird die Schädigung im Material als kontinuierlich verteilt angenommen. Vorgestellt wird ein auf makroskopischer Betrachtung basierendes anisotropes Schädigungsmodell, das wahlweise das Bruchkriterium nach Hashin oder das Failure Mode Concept nach Cuntze zur Bestimmung des Schädigungsbeginns verwendet. Der Verlauf der Schädigung wird durch ein lineares Degradationsmodell beschrieben, dessen Steigung von der kritischen Energiefreisetzungsrate bestimmt wird. Um die dissipierte Energie in Finite-Elemente-Modellen korrekt zu berechnen, wird die charakteristische Elementlänge als zusätzlicher Parameter eingeführt. Mit den gewonnenen Erkenntnissen wird dann ein zweiter Ansatz verfolgt, der auf einem zweiskaligen Finite-Elemente-Modell basiert, das aus einem Mikromodell und einem Makromodell besteht. Hierbei werden die Verzerrungen des Makromodells als Verschiebungsrandbedingungen auf das Mikromodell aufgebracht. In dem Mikromodell wird die Beschreibung der Schädigung separat auf den einzelnen Faser- und Matrixanteilen durchgeführt. Die endgültigen inneren Verschiebungen des Mikrosystems werden mit dem Newton-Raphson-Verfahren bestimmt und die homogenisierten Spannungen und die Materialtangente werden an das Makrosystem zurückgegeben. Die Schädigung im verwendeten Mikromodell wird durch ein exponentielles Degradationsgesetz ohne elastische Anfangsregion beschrieben, das sich als besonders robust erwiesen hat. Ein Gegenargument zur Verwendung von Mehrskalenmodellen ist die erhebliche Rechenzeit, da in jedem Integrationspunkt des globalen Systems ein komplettes Mikrosystem gelöst werden muss. Da sich aber Mehrskalenmodelle, aufgrund ihrer Struktur, besonders zur simultanen parallelen Berechnung eignen, ist zu ist zu erwarten, dass sie mittelfristig die makroskopischen Modelle ersetzen werden.

German
URN: urn:nbn:de:tuda-tuprints-59575
Classification DDC: 600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
Divisions: 13 Department of Civil and Environmental Engineering Sciences
13 Department of Civil and Environmental Engineering Sciences > Mechanics
13 Department of Civil and Environmental Engineering Sciences > Mechanics > Solid Body Mechanics
Date Deposited: 05 Feb 2017 20:55
Last Modified: 03 Jun 2018 21:28
PPN:
Referees: Gruttmann, Prof. Dr. Friedrich ; Gross, Prof. Dr. Dietmar
Refereed / Verteidigung / mdl. Prüfung: 20 October 2016
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