Visual Analysis of Second and Third Order Tensor Fields in Structural Mechanics

This work presents four new methods for the analysis and visualization of tensor fields. The focus is on tensor fields which arise in the context of structural mechanics simulations. The first method deals with the design of components made of short fiber reinforced polymers using injection molding. The stability of such components depends on the fiber orientations, which are affected by the production process. For this reason, the stresses under load as well as the fiber orientations are analyzed. The stresses and fiber orientations are each given as tensor fields. For the analysis four features are defined. The features indicate if the component will resist the load or not, and if the respective behavior depends on the fiber orientation or not. For an in depth analysis a glyph was developed, which shows the admissible fiber orientations as well as the given fiber orientation. With these visualizations the engineer can rate a given fiber orientation and gets hints for improving the fiber orientation. The second method depicts gradients of stress tensors using glyphs. A thorough understanding of the stress gradient is desirable, since there is some evidence that not only the stress but also its gradient influences the stability of a material. Gradients of stress tensors are third order tensors, the visualization is therefore a great challenge and there is very little research on this subject so far. The objective of the third method is to analyse the complete invariant part of the tensor field. Scalar invariants play an important role in many applications, but proper selection of such invariants is often difficult. For the analysis of the complete invariant part the notion of 'extremal point' is introduced. An extremal point is characterized by the fact that there is a scalar invariant which has a critical point at this position. Moreover it will be shown that the extrema of several common invariants are contained in the set of critical points. The fourth method presented in this work uses the Heat Kernel Signature (HKS) for the visualization of tensor fields. The HKS is computed from the heat kernel and was originally developed for surfaces. It characterizes the metric of the surface under weak assumptions. i.e. the shape of the surfaces is determined up to isometric deformations. The fact that every positive definite tensor field can be considered as the metric of a Riemannian manifold allows to apply the HKS on tensor fields

Gestaltung von Formschlussverbindungen in Thermoplast-CFK-Metall-Hybriden auf verschiedenen Skalenebenen

In der Automobilindustrie werden Leichtbaukonzepte metallischer Werkstoffe weiterentwickelt und mit faserverstärkten Kunststoffen im Multimaterialverbund kombiniert. Dabei führen Verbindungen artfremder Materialien zu werkstoffspezifischen sowie konstruktiven Herausforderungen, zu denen die mechanische Gestaltung eines Anbindungssystems und dessen Grenzflächen zählen. In dieser Arbeit wird der Einfluss der Oberflächengestaltung auf die Verbundfestigkeit und das Schädigungsverhalten derartiger Verbindungen untersucht. In simulativen Studien wird die Funktion von mesoskaligen, formschlüssigen Pin-Strukturen analysiert und die Wirkungsweise der Geometrie und Anordnung der Pins unter Beachtung der Wechselwirkung mit adhäsiven Grenzflächenhafteigenschaften beschrieben. In quasistatischen und dynamischen Experimenten werden Einflüsse und Funktionen von Formschlussüberlagerung mehrerer Skalenebenen erforscht. Dabei werden der Rauheitseinfluss auf der Mikroskala, die Pin-Strukturen auf der Mesoskala und das Einlegerdesign auf der Makroskala und deren Zusammenwirken analysiert. Die Entwicklung eines geeigneten Prüfkörpers dient als Basis für die Untersuchung von lastpfadorientierten Pin-Strukturen und deren Auswirkung auf die Verbundfestigkeit und das Schadensverhalten in Abhängigkeit zur Grenzflächenhaftfestigkeit des Hybridverbunds. Die Erkenntnisse werden in Gestaltungshinweisen für Thermoplast-CFK-Metall-Hybridgrenzflächen zusammengefasst.In the automotive industry, lightweight construction concepts of metallic materials are expanded and combined with fibre-reinforced plastics in multi-material composites. Thereby, connections of dissimilar materials lead to material-specific as well as constructive challenges including the mechanical design of a connection system and its interfaces. The influence of surface design on joint strength and damage behavior is the focus of this investigation. Simulation studies are conducted to analyze the functionality of interlocking mesoscale pin structures and to describe how the geometry and arrangement of pins interact with adhesive bond strengths. In quasi-static and dynamic experiments, influences and functions of interlocking superposition on several scale levels are explored. This includes the influence of surface roughness on the microscale, the pin structures on the mesoscale and the inserter design on the macroscale as well as their interactions. The development of a specific test specimen enables the investigation of load-path oriented pin structures and their effect on the bond strength and damage behavior. The influence of the interfacial adhesion strength on these properties is considered in the experimental set-up. The findings are summarized in design instructions for thermoplastic-CFRP-metal hybrid interfaces

Tensor Visualization Driven Mechanical Component Design

This paper is the result of a close collaboration of mechanical en- gineers and visualization researchers. It showcases how interdisci- plinary work can lead to new insight and progress in both fields. Our case is concerned with one step in the product development process. Its goal is the design of mechanical parts that are func- tional, meet required quality measures and can be manufactured with standard production methods. The collaboration started with unspecific goals and first experiments with the available data and vi- sualization methods. During the course of the collaboration many concrete questions arose and in the end a hypothesis was developed which will be discussed and evaluated in this paper. We facilitate a case study to validate our hypothesis. For the case study we con- sider the design of a reinforcement structure of a brake lever, a plas- tic ribbing. Three new lever geometries are developed on basis of our hypothesis and are compared against each other and against a reference model. The validation comprises standard numerical and experimental tests. In our case, all new structures outperform the reference geometry. The results are very promising and suggest potential to impact the product development process also for more complex scenarios