# Entwicklung eines adaptiven $FE^{2}$ Ansatzes zur Simulation von thermomechanisch beanspruchten Faser-Matrix-Kompositen

• Development of an adaptive $FE^{2}$ approach for the simulation of thermomechanically exposed fiber-matrix composites

Aachen : Rheinisch-Westfälische Technische Hochschule Aachen, Fakultät für Bauingenieurwesen, Lehrstuhl für Baustatik und Baudynamik (2020)
Book, Dissertation / PhD Thesis

In: Schriftenreihe des Lehrstuhls für Baustatik und Baudynamik der RWTH Aachen University 09 (2020)
Page(s)/Article-Nr.: 1 Online-Ressource (X, 162 Seiten) : Illustrationen, Diagramme

Dissertation, RWTH Aachen University, 2020

Abstract

This thesis focuses on a method for the coupled homogenization of heterogeneous composite materials which are subjected to thermo-mechanical loading. The advantages of an FE2 method, such as the determination of the material behaviour of complex microstructures without knowledge of the phenomenological behaviour, the knowledge of detailed processes on the micro level or the general applicability for arbitrary microstructures are decisive and will lead to a steadily growing application of the method in the future. However, there are currently still serious disadvantages which limit the use of the method, especially on desktop PCs. The key factors here are the high costs in terms of computational time and memory resources. This thesis tries to eliminate these deﬁciencies. For this purpose, indicators are formulated which are able to predict the nonlinear behaviour on the material level. The FE2 method determines effective material parameters in each Gaussian point by means of an accompanying homogenization at the representative volume element (RVE). However, for those areas of a structure where linear material behavior is observed, it is sufﬁcient to know the effective linear material parameters in advance. The indicator is used to determine whether a linear response can be expected and thus the previously determine deffective material parameters are sufﬁcient for the calculation, or whether the microstructure is responding non-linearly and thus a detailed analysis on the microscale is necessary. In the scope of the work, two types of ﬁbres are distinguished, elasto-plastic ﬁbres on the one hand and shape memory alloys on the other hand. Individual indicators are formulated for both materials, whereby the temperature-dependent material parameters play a signiﬁcant role, especially in the case of shape memory alloys. The performance of the new adaptive FE2 method is demonstrated by means of relevant examples. The result is a comprehensive, economic concept for the analysis of complex, highly temperature-dependent ﬁber-matrix composites with arbitrary microstructure. The speed of the method by saving many scale transitions underlines the effectiveness.