Heller, Dominik (2015)
A nonlinear multiscale finite element model for comb-like sandwich panels.
Technische Universität Darmstadt
Dissertation, Erstveröffentlichung

Kurzbeschreibung (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.

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