Ein Finite-Elemente-Modell zur Analyse des Verhaltens von Formgedächtnisfaserkompositen mit beliebiger Mikrostruktur

Kohlhaas, Benedikt; Wagner, Werner (Thesis advisor); Klinkel, Sven (Thesis advisor)

Aachen (2016)
Book, Dissertation / PhD Thesis

In: Schriftenreihe des Lehrstuhls für Baustatik und Baudynamik 05 (2015)
Page(s)/Article-Nr.: 1 Online-Ressource (IV, 185 Seiten) : Illustrationen, Diagramme

Abstract

This thesis provides numerical methods for the analysis of shape memory fiber composites. In detail, this includes the formulation of a one-dimensional material model for shape memory alloys (SMA), the description of a three dimensional inelastic material model for large strains, the finite element implementation for two structural elements together with appropriate meshing algorithms and a multi-scale approach for a coupled homogenization framework.Shape memory alloys are materials with unique properties. They can be applied in a broad technical field. Particularly, they can be used for damping, self-healing, prestressing etc. A huge disadvantage is their extraordinary cost. This prevents broader application. Therefore, this thesis proposes the use of shape memory fiber composites according to certain literature sources. The material costs can be reduced to few percentages. Nevertheless, the fiber composites retain the characteristic properties of the shape memory alloys. Additionaly, the feebleness of the matrix material may be overcome.Four mile-stones are defined for the efficient numerical representation of shape memory fiber composites. First, the material model for the shape memory alloy has to be able to model the most important material phenomena. These are pseudoplasticity, pseudoelasticity, superelasticity and all shape memory effects. Next, the matrix material should be valid in the context of large strains. It is needed to represent the material behavior of many materials which are suitable for the use in composite structures. Third, the finite element method is an adequate tool for the analysis of composite structures. Due to the lack of experimental data, two different structural elements are derived. It is shown that they yield equivalent results. A truss element with linear ansatz functions is compared to a hexahedral brick element with linear and quadratic ansatz functions. Both elements require performant mesh-generators which are capable of creating the complex micro-structure and discretizing it for the finite element method. However, the calculation of complete structures only becomes possible when an FE2-approach is introduced. Fourth, a representative volume element (RVE) is attached to each Gauß point of the macroscopic structure. The desired effective material parameters are derived on RVE level and are transferred back to the macro-structure. The realisation of the described mile-stones creates a framework for the numerical analysis of shape memory fiber composites with arbitrary micro-structure. The simulation complements expensive experiments reasonably and information about the complex mechanisms and the load-bearing behavior on the micro-structure can be yielded. The proposed homogenization process allows for the economical use of hardware capacities. Thus, the analysis of whole structures becomes possible. Not least, the usage of SMA as fiber reinforcement spares expensive material.

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