Generation of Initial Fiber Orientation States for Long Fiber Reinforced Thermoplastic Compression Molding Simulation

The prediction of the fiber orientation state (FOS) is of utmost interest for compression molded long fiber reinforced thermoplastics as the part\u27s properties strongly depend on it. Besides the position of the initial plastificate in the mold cavity and the process settings, detailed knowledge of the initial FOS is essential. During compounding, the fibers align depending on the extruder screw configuration yielding a non-uniform local FOS. For process simulation, a common approach is to neglect this effect and assume an isotropic or planar-isotropic FOS of the initial plastificate. A more sophisticated approach consists of micro-computed tomography (µCT-) scans of slices of the initial plastificate and the derivation of the initial FOS from the three-dimensional image data. This approach can yield accurate predictions but is quite cumbersome and expensive. In this paper, we present a novel approach to account for the FOS of the initial plastificate. The approach is motivated by experimental observations and based on geometric assumptions. Depending on the extruder type and the dimensions of the initial plastificate, the developed tool generates a three-dimensional data set containing the mesh information alongside the initial FOS in a tensorial representation. To investigate the influence of the initial FOS for different flow regimes, we conducted compression molding simulations on a planar part

Application of a Tensor Interpolation Method on the Determination of Fiber Orientation Tensors From Computed Tomography Images

When investigating the mechanical behavior of fiber-reinforced polymers, fiber orientation plays a decisive role concerning anisotropy. Fiber orientation distributions are typically measured in the form of fiber orientation tensors. In order to measure orientation tensors, computed tomography scans and consecutive image processing methods have become one of the leading non-destructive testing methods. The conflict between scan resolution and sample size limits the volume that can be scanned. To obtain the fiber orientation behavior across an entire plate, a direct interpolation of orientation tensors computed from CT scans of smaller volumes at selected coordinates of the plate is implemented. Rather than a component-based interpolation, the authors chose a decomposition and reassembly method interpolating shape and orientation of the tensors separately. While this approach has been implemented and used for e.g. diffusion tensors in medical imaging, the authors consider the application to sparse but measured CT-based data to be a novelty

Assessing the usability of tile-based interfaces to visually navigate 3-D parameter domains

Navigating 3-D parameter domains, such as color and orientation of an object, is a common task performed in most computer graphics applications. Although 1-D sliders are the most common interface for browsing such domains, they provide a tedious and difficult user experience that hampers finding desirable visual solutions. We present the Rhomb-i slider, a novel and visually enriching tile-based interface to navigate arbitrary 3-D parameter domains. Contrary to 1-D sliders, the Rhomb-i slider supports a sketch-based interface that gives simultaneous access to up to two parameters. We conducted a usability study to ascertain whether the proposed Rhomb-i slider is a more natural interface compared to 1-D sliders and other commonly used widgets for different 3-D parameter domains: HSV color space, super-shape curves, and rotation of a 3-D object. On the one hand, qualitative feedback and performance measures reveal that Rhomb-i sliders have similar results when compared to conventional HSV color interfaces, and are the preferred interface to efficiently explore the super-shapes parameter domain. On the other hand, Rhomb-i revealed to be a less efficient and effective interface to rotate a 3D object, thus paving the way to new design explorations regarding this tile-based interface

Visual analytics methods for shape analysis of biomedical images exemplified on rodent skull morphology

In morphometrics and its application fields like medicine and biology experts are interested in causal relations of variation in organismic shape to phylogenetic, ecological, geographical, epidemiological or disease factors - or put more succinctly by Fred L. Bookstein, morphometrics is "the study of covariances of biological form". In order to reveal causes for shape variability, targeted statistical analysis correlating shape features against external and internal factors is necessary but due to the complexity of the problem often not feasible in an automated way. Therefore, a visual analytics approach is proposed in this thesis that couples interactive visualizations with automated statistical analyses in order to stimulate generation and qualitative assessment of hypotheses on relevant shape features and their potentially affecting factors. To this end long established morphometric techniques are combined with recent shape modeling approaches from geometry processing and medical imaging, leading to novel visual analytics methods for shape analysis. When used in concert these methods facilitate targeted analysis of characteristic shape differences between groups, co-variation between different structures on the same anatomy and correlation of shape to extrinsic attributes. Here a special focus is put on accurate modeling and interactive rendering of image deformations at high spatial resolution, because that allows for faithful representation and communication of diminutive shape features, large shape differences and volumetric structures. The utility of the presented methods is demonstrated in case studies conducted together with a collaborating morphometrics expert. As exemplary model structure serves the rodent skull and its mandible that are assessed via computed tomography scans

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

Identifying Changes of Functional Brain Networks using Graph Theory

This thesis gives an overview on how to estimate changes in functional brain networks using graph theoretical measures. It explains the assessment and definition of functional brain networks derived from fMRI data. More explicitly, this thesis provides examples and newly developed methods on the measurement and visualization of changes due to pathology, external electrical stimulation or ongoing internal thought processes. These changes can occur on long as well as on short time scales and might be a key to understanding brain pathologies and their development. Furthermore, this thesis describes new methods to investigate and visualize these changes on both time scales and provides a more complete picture of the brain as a dynamic and constantly changing network.:1 Introduction 1.1 General Introduction 1.2 Functional Magnetic Resonance Imaging 1.3 Resting-state fMRI 1.4 Brain Networks and Graph Theory 1.5 White-Matter Lesions and Small Vessel Disease 1.6 Transcranial Direct Current Stimulation 1.7 Dynamic Functional Connectivity 2 Publications 2.1 Resting developments: a review of fMRI post-processing methodologies for spontaneous brain activity 2.2 Early small vessel disease affects fronto-parietal and cerebellar hubs in close correlation with clinical symptoms - A resting-state fMRI study 2.3 Dynamic modulation of intrinsic functional connectivity by transcranial direct current stimulation 2.4 Three-dimensional mean-shift edge bundling for the visualization of functional connectivity in the brain 2.5 Dynamic network participation of functional connectivity hubs assessed by resting-state fMRI 3 Summary 4 Bibliography 5. Appendix 5.1 Erklärung über die eigenständige Abfassung der Arbeit 5.2 Curriculum vitae 5.3 Publications 5.4 Acknowledgement