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Simulation-driven product development is nowadays an essential part in the industrial digitalization. Notably, there is an increasing interest in realistic high-fidelity simulation methods in the fast-growing field of additive and ablative manufacturing processes. Thanks to their flexibility, meshfree solution methods are particularly suitable for simulating the stated processes, often accompanied by large deformations, variable discontinuities, or phase changes. Furthermore, in the industrial domain, the meshing of complex geometries represents a significant workload, which is usually minor for meshfree methods. Over the years, several meshfree schemes have been developed. Nevertheless, along with their flexibility in discretization, meshfree methods often endure a decrease in accuracy, efficiency and stability or suffer from a significantly increased computation time. Peridynamics is an alternative theory to local continuum mechanics for describing partial differential equations in a non-local integro-differential form. The combination of the so-called peridynamic correspondence formulation with a particle discretization yields a flexible meshfree simulation method, though does not lead to reliable results without further treatment.\newline In order to develop a reliable, robust and still flexible meshfree simulation method, the classical correspondence formulation is generalized into the Peridynamic Galerkin (PG) methods in this work. On this basis, conditions on the meshfree shape functions of virtual and actual displacement are presented, which allow an accurate imposition of force and displacement boundary conditions and lead to stability and optimal convergence rates. Based on Taylor expansions moving with the evaluation point, special shape functions are introduced that satisfy all the previously mentioned requirements employing correction schemes. In addition to displacement-based formulations, a variety of stabilized, mixed and enriched variants are develo

The large flexibility of meshfree solution schemes makes them attractive for many kinds of engineering applications, like Additive Manufacturing or cutting processes. While numerous meshfree methods were developed over the years, the accuracy and robustness are still challenging and critical issues. Stabilization techniques of various kinds are typically used to overcome these problems, but often require the tuning of unphysical parameters. The Peridynamic Petrov–Galerkin method is a generalization of the peridynamic theory of correspondence materials and offers a stable and robust alternative. In this work, the stabilization free approach is extended to three dimensional problems of finite elasticity. Locking-free mixed formulations for nearly incompressible and incompressible materials are developed and investigated in convergence studies. In general, an efficient implicit quasi-static framework based on Automatic Differentiation is presented. The numerical examples highlight the convergence properties and robustness of the proposed formulations. © 2020, The Author(s).

Selective Laser Melting (SLM) is a 3D printing technology which is suited for additively manufacturing of metals and polymers. The main barriers of this process are the lack of reproducibility and the control of the influence of the process parameters, like laser power, scan rate, layer height and particle distribution for instance. A high fidelity simulation scheme for SLM processes can not only give an insight into the physical behaviour during the process, but can also help to control the whole 3D printing process in order to guarantee the reproducibility of the desired final product properties. However many challenges have to be overcome in order to guarantee a high fidelity simulation, like modelling the heat source or the phase change for instance. In this work the modelling of the heat source is addressed. A Ray Tracing algorithm should be implemented into the existing thermomechanical Optimal Transportation Meshfree (OTM) code. A Ray Tracing algorithm for the simulation of laser processes is investigated in combination with the Discrete Element Method in the literature. Therefore in a first step this algorithm should be recoded in order to benchmark the implemented Ray Tracing algorithm. In the next step this algorithm has to be implemented into the OTM code. An investigation by means of some examples should demonstrate the influence of the Ray Tracing algorithm on the fusion of two metal particles.

Die Finite Element Methode (FEM) hat sich im Ingenieurwesen aufgrund seiner stabilen und numerisch genauen Approximation der Lösung von partiellen Differenzialgleichungen als Simulationswerkzeug bewährt. Aufgrund der Unterteilung des Lösungsgebiets in feste Elemente sind bei sehr großen Deformationen zusätzliche Algorithmen von Nöten, die meist die Stabilität und Genauigkeit negativ beeinflussen. Netzfreie Simulationsverfahren, wie die ”Optimal Transportation Meshfree“ (OTM) Methode, bestechen gerade hierbei durch Flexibilität, da keine feste Konnektivität zwischen einzelnen Knoten benötigt wird. Anstatt fester Elemente wird die Anzahl von Knoten, die den jeweiligen Materialpunkt beeinflusst, in jedem Zeitpunkt durch einen Suchalgorithmus neu bestimmt. Dieser Bereich wird dabei als Einflussgebiet des Materialpunkts bezeichnet. Auf der anderen Seite sind netzfreie Verfahren von Haus aus nicht stabil. Einer der Hauptgründe ist die Unterintegration in den Einflussgebieten der Materialpunkte. Daher soll im Rahmen dieser Studienarbeit die OTM Methode dahingehend erweitert werden, dass zusätzliche Integrationspunkte in das Einflussgebiet des jeweiligen Materialpunkts gelegt wird. Besonderer Fokus soll dabei auf die benötigte Anzahl von Integrationspunkten und die Kopplung zu ”Mean Value“ Ansatzfunktionen gelegt werden. Aufgrund der dadurch entstehenden Nähe zum Ablaufschema der FEM, soll dieses Verfahren als flexible Finite Element Methode bezeichnet werden. Nach der Implementation des neuen Algorithmus soll des Weiteren der Vorteil der neuen Methode anhand von Beispielen untersucht werden.

A novel, ultra low background contacting technique for large mass HPGe detectors was developed for the neutrinoless double beta decay experiment GERDA. This technique was applied for all 40 detectors of the currently running GERDA Phase II which, also thanks to the results of this work, will reach an unprecedented half-life sensitivity of 1026 yr. A full overview of the contacting technique development is presented. A first data analysis of Phase II is discussed with focus on possible contaminations related to the contacting method., Eine neuartige, mit extrem niedrigem Untergrund behaftete Methode um Germanium-Detektoren zu kontaktieren, wurde im Rahmen des neutrinolosen Doppel-Beta Zerfallsexperiments GERDA entwickelt und in der jetzt laufenden Phase II bei allen 40 Detektoren angewandt. Diese Phase II wird, auch Dank der in dieser Arbeit detailliert vorgestellten Kontaktierungsmethode, auf Zerfalls-Halbwertszeiten von bis zu 1026 a sensitiv sein. Eine erste Analyse der Phase II Daten mit Fokus auf eine mögliche zusätzliche Kontamination durch die Kontaktierung wird präsentiert.