Fiber Orientation Tensors and Mean Field Homogenization: Application to Sheet Molding Compound

Effective mechanical properties of fiber-reinforced composites strongly depend on the microstructure, including the fibers\u27 orientation. Studying this dependency, we identify the variety of fiber orientation tensors up to fourth-order using irreducible tensors and material symmetry. The case of planar fiber orientation tensors, relevant for sheet molding compound, is presented completely. Consequences for the reconstruction of fiber distributions and mean field homogenization are presented

On the dependence of orientation averaging mean field homogenization on planar fourth-order fiber orientation tensors

A comprehensive study on the influence of planar fourth-order fiber orientation tensors on effective linear elastic stiffnesses predicted by orientation averaging mean field homogenization is given. Fiber orientation states of sheet molding compound (SMC) are identified to be in most cases approximately planar. In the planar case, all possible fourth-order fiber orientation tensors are given by a minimal invariant set of structurally differing planar fourth-order fiber orientation tensors. This set defines a three-dimensional body and forms the basis for a comprehensive study on the influence of a fiber orientation distribution in terms of a fourth-order tensor on homogenized stiffnesses. The methodology of this study is the main contribution of this work and can be adopted to analyze the orientation dependence of any quantity which is a function of a planar fourth-order fiber orientation tensor. At specific points inside the set of planar fiber orientation tensors, effective stiffnesses are calculated with selected mean field homogenization schemes. These schemes are based on orientation averaging of transversely isotropic elasticity tensors following Advani and Tucker (1987), which is explicitly recast as linear invariant composition in the fiber orientation tensors of second and fourth order of Kanatani third kind. A maximum entropy reconstruction of a fiber orientation distribution function based on leading fiber orientation tensors, enables a new numerical formulation of the Advani and Tucker average for the special planar case. Polar plots of Young’s modulus and generalized bulk modulus obtained by selected homogenization schemes are arranged on two-dimensional slices within the body of admissible fiber orientation tensors, visualizing the influence of the orientation tensor on the stiffness tensor. The orientation-dependence of the generalized bulk modulus differs significantly between selected homogenizations. Restrictions on the effective anisotropic material response caused by orthotropy of closure approximations are discussed

Variety of fiber orientation tensors

Fiber orientation tensors are established descriptors of fiber orientation states in (thermo-)mechanical material models for fiber-reinforced composites. In this paper, the variety of fourth-order orientation tensors is analyzed and specified by parameterizations and admissible parameter ranges. The combination of parameterizations and admissible parameter ranges allows for studies on the mechanical response of different fiber architectures. Linear invariant decomposition with focus on index symmetry leads to a novel compact hierarchical parameterization, which highlights the central role of the isotropic state. Deviation from the isotropic state is given by a triclinic harmonic tensor with simplified structure in the orientation coordinate system, which is spanned by the second-order orientation tensor. Material symmetries reduce the number of independent parameters. The requirement of positive-semi-definiteness defines admissible ranges of independent parameters. Admissible parameter ranges for transversely isotropic and planar cases are given in a compact closed form and the orthotropic variety is visualized and discussed in detail. Sets of discrete unit vectors, leading to selected orientation states, are given

Fiber orientation distributions based on planar fiber orientation tensors of fourth order

Fiber orientation tensors represent averaged measures of fiber orientations inside a microstructure. Although, orientation-dependent material models are commonly used to describe the mechanical properties of representative microstructure, the influence of changing or differing microstructure on the material response is rarely investigated systematically for directional measures which are more precise than second-order fiber orientation tensors. For the special case of planar orientation distributions, a set of admissible fiber orientation tensors of fourth-order is known. Fiber orientation distributions reconstructed from given orientation tensors are of interest both for numerical averaging schemes in material models and visualization of the directional information itself. Focusing on the special case of planar orientations, this paper draws the geometric picture of fiber orientation distribution functions reconstructed from fourth-order fiber orientation tensors. The developed methodology can be adopted to study the dependence of material models on planar fourth-order fiber orientation tensors. Within the set of admissible fiber orientation tensors, a subset of distinct tensors is identified. Advantages and disadvantages of the description of planar orientation states in two- or three-dimensional tensor frameworks are demonstrated. Reconstruction of fiber orientation distributions is performed by truncated Fourier series and additionally by deploying a maximum entropy method. The combination of the set of admissible and distinct fiber orientation tensors and reconstruction methods leads to the variety of reconstructed fiber orientation distributions. This variety is visualized by arrangements of polar plots within the parameter space of fiber orientation tensors. This visualization shows the influence of averaged orientation measures on reconstructed orientation distributions and can be used to study any simulation method or quantity which is defined as a function of planar fourth-order fiber orientation tensors

Side differences of upper quarter Y balance test performance in sub-elite young male and female handball players with different ages

Background Handball is characterised by repetitive passing and shooting actions mainly performed with the throwing arm. This can lead to side differences (inter-limb asymmetry) in upper quarter mobility/stability between the throwing and non-throwing arm, which could even increase with advancing age (i.e., playing experience). However, side differences in upper quarter mobility/stability is associated with an increased musculoskeletal injury risk. Therefore, we assessed side differences in upper quarter mobility/stability in young handball players at different ages using a cross-sectional study design. Methods Upper Quarter Y Balance test performance of the throwing and non-throwing arm was assessed in 190 sub-elite young female and male handball players (13–18 years). Per arm, relative maximal reach distances (% arm length) for all three directions (i.e., medial, inferolateral, superolateral) and the composite score (CS) were calculated and used for an age × side analysis of variance. Additionally, partial eta-squared (ηp2) was calculated as an effect size measure. Results Irrespective of measure, statistically significant main effects of age (except for the composite score) and side but no statistically significant age × side interaction effects were detected. Further, limb asymmetry in the inferolateral reach direction was above the injury-related cut-off value (i.e., ≥ 7.75% arm length) in 13- and 14-year-olds but not in the older players. Conclusion The detection of limb asymmetry above the proposed injury-related cut-off value in younger players (13- and 14-year-olds) but not in older players (15- to 18-year-olds) may be indicative for an increased injury risk for the younger age group. Thus, prevention programs should be implemented in the handball training routine, especially for the younger ones

Collective rearrangement at the onset of flow of a polycrystalline hexagonal columnar phase

Creep experiments on polycrystalline surfactant hexagonal columnar phases show a power law regime, followed by a drastic fluidization before reaching a final stationary flow. The scaling of the fluidization time with the shear modulus of the sample and stress applied suggests that the onset of flow involves a bulk reorganization of the material. This is confirmed by X-ray scattering under stress coupled to \textit{in situ} rheology experiments, which show a collective reorientation of all crystallites at the onset of flow. The analogy with the fracture of heterogeneous materials is discussed.Comment: to appear in Phys. Rev. Let

On the Phase Space of Fourth-Order Fiber-Orientation Tensors

Fiber-orientation tensors describe the relevant features of the fiber-orientation distribution compactly and are thus ubiquitous in injection-molding simulations and subsequent mechanical analyses. In engineering applications to date, the second-order fiber-orientation tensor is the basic quantity of interest, and the fourth-order fiber-orientation tensor is obtained via a closure approximation. Unfortunately, such a description limits the predictive capabilities of the modeling process significantly, because the wealth of possible fourth-order fiber-orientation tensors is not exploited by such closures, and the restriction to second-order fiber-orientation tensors implies artifacts. Closures based on the second-order fiber-orientation tensor face a fundamental problem – which fourth-order fiber-orientation tensors can be realized? In the literature, only necessary conditions for a fiber-orientation tensor to be connected to a fiber-orientation distribution are found. In this article, we show that the typically considered necessary conditions, positive semidefiniteness and a trace condition, are also sufficient for being a fourth-order fiber-orientation tensor in the physically relevant case of two and three spatial dimensions. Moreover, we show that these conditions are not sufficient in higher dimensions. The argument is based on convex duality and a celebrated theorem of D. Hilbert (1888) on the decomposability of positive and homogeneous polynomials of degree four. The result has numerous implications for modeling the flow and the resulting microstructures of fiber-reinforced composites, in particular for the effective elastic constants of such materials. Based on our findings, we show how to connect optimization problems on fourth-order fiber-orientation tensors to semi-definite programming. The proposed formulation permits to encode symmetries of the fiber-orientation tensor naturally. As an application, we look at the differences between orthotropic and general, i.e., triclinic, fiber-orientation tensors of fourth order in two and three spatial dimensions, revealing the severe limitations inherent to orthotropic closure approximations

Design und Implementierung eines Identity and Access Management Reporting Moduls basierend auf Metriken

In den letzten Jahren stieg die Anzahl an erfolgreichen Cyberangriffen gegen Organisationen kontinuierlich an [BS21]. Gleichzeitig haben sich die Ausgaben zur Abwehr dieser stetig erhöht [Bit22]. Die Organisationen stehen hier vor der Herausforderung, die Performance der implementierten Informationstechnologie-(IT-)Sicherheitsmaßnahmen zu quantifizieren, um fundierte Entscheidungen treffen zu können. Durch Bildung von Metriken, die auf Messwerten aus verschiedenen Systemen und Datenquellen aufbauen, werden die Performance und der Reifegrad von der IT-Sicherheit in Organisationen bestimmt. Um diese Metriken nachhaltig zu ermitteln und bereitzustellen, ist ein adäquates IT-System einzusetzen. Im Rahmen der vorliegenden Arbeit wird untersucht, wie im Identity and Access Management (IAM) – ein Teilgebiet von IT-Sicherheit – die Performance mithilfe eines Tools – namens IAM Reporting Modul – basierend auf Metriken ermittelt und berichtet werden kann. Das Vorgehen ist dabei angelehnt an die Design Science Research (DSR) Methodologie nach Hevner [HMPR04]. Ziel ist es, die Anforderungen an ein IAM Reporting Modul zu untersuchen, ein Konzept für ein solches Tool zu entwerfen und auf Grundlage des Konzepts einen Prototyp des IAM Reporting Moduls zu implementieren. Abschließend sind aus den gewonnenen Erkenntnissen Gestaltungsprinzipien abzuleiten. Bei den abgeleiteten Gestaltungsprinzipien handelt es sich um die regelmäßige Berechnung und Ermittlung der Metriken und der Messwerte, um den Prozess zur Konfiguration von den Metriken und den Messwerten und um die zusätzlich benötigten Informationen über den Messwert je nach Typ der Datenquelle sowie um das konzipierte Datenmodell für Reporting Module

A SOA Repository with Advanced Analysis Capabilities - Improving the Maintenance and Flexibility of Service-Oriented Applications

a service-oriented architecture (SOA), a change or shutdown of a particular service might have a significant impact on its consumers (e.g., IT systems). To effectively cope with such situations, the IT systems affected by a service change should be identified before actually applying the latter. For this purpose, a SOA repository with advanced analysis capabilities is needed. However, due to the numerous complex inter-dependencies between service providers and consumers, it is a challenging task to figure out which IT systems might be directly or indirectly affected by a service change and for which period of time this applies. The paper tackles this challenge and presents the design of an advanced SOA repository enriched with analysis capabilities. In particular, this repository enables automatic analyses to detect already existing problems (as-is analyses) as well as problems that might occur due to future service changes (what-if analyses). Respective analyses will foster the development of robust service-oriented applications

Determining the Quality of Product Data Integration

To meet customer demands, companies must manage numerous variants and versions of their products. Since product-related data (e.g., requirements' specifications, geometric models, and source code, or test cases) are usually scattered over a large number of heterogeneous, autonomous information systems, their integration becomes crucial when developing complex products on one hand and aiming at reduced development costs on the other. In general, product data are created in different stages of the product development process. Furthermore, they should be integrated in a complete and consistent way at certain milestones during process development (e.g., prototype construction). Usually, this data integration process is accomplished manually, which is both costly and error prone. Instead semi-automated product data integration is required meeting the data quality requirements of the various stages during product development. In turn, this necessitates a close monitoring of the progress of the data integration process based on proper metrics. Contemporary approaches solely focus on metrics assessing schema integration, while not measuring the quality and progress of data integration. This paper elicits fundamental requirements relevant in this context. Based on them, we develop appropriate metrics for measuring product data quality and apply them in a case study we conducted at an automotive original equipment manufacturer