Universität Stuttgart
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Item Open Access On the computational modeling of micromechanical phenomena in solid materials(2013) Linder, Christian; Miehe, Christian (Prof. Dr.-Ing. habil.)This work aims to contribute to the research on the constitutive modeling of solid materials, by investigating three particular micromechanical phenomena on three different length scales. The first microscopic phenomenon to be considered on the macroscopic scale is the process of failure in solid materials. Its characteristic non-smoothness in the displacement field results in the need for sophisticated numerical techniques in case one aims to capture those failure zones in a discrete way. One of the few finite element based methods successfully applied to such challenging problems is the so called strong discontinuity approach, for which failure can be described within the individual finite elements. To avoid stress locking, a higher order approximation of the resulting strong discontinuities is developed in the first part of this work for both, purely mechanical as well as electromechanical coupled materials. A sophisticated crack propagation concept relying on a combination of the widely used global tracking algorithm and the computer graphics based marching cubes algorithm is employed to obtain realistic crack paths in three dimensional simulations. Secondly, materials with an inherent network microstructures such as elastomers, hydrogels, non-woven fabrics or biological tissues are considered. The development of advanced homogenization principles accounting for such microstructures is the main focus in the second part of this work to better understand the mechanical and time-dependent effects displayed by such soft materials. Finally, the incorporation of wave functions into finite element based electronic structure calculations at the microscopic scale aims to account for the fact that the properties of condensed matter as for example electric conductivity, magnetism as well as the mechanical response upon external excitations are determined by the electronic structure of a material.Item Open Access Tackling coupled problems in porous media : development of numerical models and an open source simulator(2013) Flemisch, Bernd; Helmig, Rainer (Prof. Dr.-Ing.)Flow and transport processes in porous media are the governing processes in a large variety of geological, technical and biological systems. For many interesting and important applications, these processes cannot be treated in an isolated manner or adequately described by means of a single-scale, single-physics mathematical model, and the coupling of two or more models is required. The development of coupled numerical models poses severe challenges on the conceptual, analytical and computational level. This habilitation thesis aims to describe a number of these challenges and solve some of the problems they pose. It is divided into three parts: Part A "Model Coupling" deals with uncoupled and coupled porous-media models in general and describes some of these models in detail. "Locally Conservative Discretization Methods," as treated in Part B, are a fundamental ingredient of reasonable numerical models for porous media flow and transport processes. A numerical model is realized by its implementation in the form of computer code. Part C "Open-Source Porous-Media Simulation" deals with the idea of developing such a computer code by means of open-source development techniques.