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.

The Myosin Myocardial Mesh Interpreted as a Biological Analogous of Nematic Chiral Liquid Crystals

There are still grey areas in the understanding of the myoarchitecture of the ventricular mass. This is despite the progress of investigation methods since the beginning of the 21st century (diffusion tensor magnetic resonance imaging, microcomputed tomography, and polarised light imaging). The objective of this article is to highlight the specificities and the limitations of polarised light imaging (PLI) of the unstained myocardium embedded in methyl methacrylate (MMA). Thus, to better differentiate our method from other PLI modes, we will refer to it by the acronym PLI-MMA. PLI-MMA shows that the myosin mesh of the compact left ventricular wall behaves like a biological analogous of a nematic chiral liquid crystal. Results obtained by PLI-MMA are: the main direction of the myosin molecules contained in an imaged voxel, the crystal liquid director n, and a regional isotropy index RI that is an orientation tensor, the equivalent of the crystal liquid order parameter. The vector n is collinear with the first eigenvector of diffusion tensor imaging (DTI-MRI). The RI has not been confounded with the diffusion tensor of DTI that gives information about the three eigenvectors of the ellipsoid of diffusion. PLI-MMA gives no information about the collagen network. The physics of soft matter has allowed the revisiting of Streeter’s conjecture on the myoarchitecture of the compact left ventricular wall: “geodesics on a nested set of toroidal surfaces”. Once the torus topology is understood, this characterisation of the myoarchitecture is more accurate and parsimonious than former descriptions. Finally, this article aims to be an enthusiastic invitation to a transdisciplinary approach between physicists of liquid crystals, anatomists, and specialists of imaging.

Polarimetric radar reveals the spatial distribution of ice fabric at domes in East Antarctica

Ice crystals are mechanically and dielectrically anisotropic. They progressively align under cumulative deformation, forming an ice crystal orientation fabric that, in turn, impacts ice deformation. However, almost all the observations of fabric are from ice core analysis and its interplay with the flow is unclear. Here, we present a non-linear inverse approach that combines radar polarimetry with vertical changes in anisotropic reflection to extract, for the first time, the full orientation tensor. The orientation tensor is routinely used to synthesize fabric information and it is used in anisotropic ice flow models. We validate our approach at two Antarctic ice-core sites (EDC and EDML) in contrasting flow regimes. Spatial variability of ice-fabric characteristics in the dome-to-flank transition near Dome C is quantified with 20 more sites located along a 36 km long cross-section. Local horizontal anisotropy increases under the dome summit and decreases away from the dome summit. We suggest that this is a consequence of the non-linear rheology of ice also known as Raymond effect. On larger spatial scales, horizontal anisotropy increases with increasing distance from the dome. At most of the sites, the main driver of ice-fabric evolution is vertical compression, yet our data show that ice fabric horizontal distribution is consistent with the present horizontal flow. Our method, which uses co- and cross polarimetric radar data suitable for profiling radar applications, can constrain ice-fabric distribution on a spatial scale comparable to ice flow observations and models.

Investigation on the Coupling Effects between Flow and Fibers on Fiber-Reinforced Plastic (FRP) Injection Parts

Glass or carbon fibers have been verified that can enhance the mechanical properties of the polymeric composite injection molding parts due to their orientation distribution. However, the interaction between flow and fiber is still not fully understood yet, especially for the flow–fiber coupling effect. In this study, we have tried to investigate the flow–fiber coupling effect on fiber reinforced plastics (FRP) injection parts utilizing a more complicated geometry system with three ASTM D638 specimens. The study methods include both numerical simulation and experimental observation. Results showed that in the presence of flow–fiber coupling effect, the melt flow front advancement presents some variation, specifically the “convex-flat-flat” pattern will change to a “convex-flat-concave” pattern. Furthermore, through the fiber orientation distribution (FOD) study, the flow–fiber coupling effect is not significant at the near gate region (RG). It might result from the strong shear force to repress the appearance of the flow–fiber interaction. However, at the end of filling region (ER), the flow–fiber coupling effect tries to diminish the flow direction orientation tensor component A11 and enhance the cross-flow orientation tensor component A22 simultaneously. It results in the dominance in the cross-flow direction at the ER. This orientation distribution behavior variation has been verified using a micro-computerized tomography (micro-CT) scan and image analysis technology.

Integrated Prediction of Mechanical Behavior for the Non-Aligned Fiber Composites With Experimental Validation

This paper aims to present an integrated multi-scale method for predicting the anisotropic and nonlinear elasto-plastic behavior of short glass fiber-reinforced polymer (GFRP) materials typically produced by injection molding. The proposed method combines injection molding and microstructure together, with considering the nonaligned fibers and their corresponding anisotropy, to semi-analytically estimate the local effective mechanical properties at every point of GFRP. Micro-computed tomography measurement and injection molding simulation are used to obtain the fiber orientation tensor. The two-step mean-field homogenization method is applied to calculate the mechanical behaviors of the PA66GF30 GFRP with distributed-orientation fibers based on the fiber orientation tensor. Reverse engineering is used to obtain the optimized parameters of J2-plasticity and Tsai-Hill three-dimensional transversely isotropic stain-based failure criterion. Moreover, the integral mapping method can complete the transformation of the fiber orientation tensor from injection simulation to structure simulation model. The proposed integrated approach with the optimized parameters is verified by predicting the ring samples’ behavior from injection plates. The results from this investigation are expected to provide some design guidelines for GFRP composites.

Investigation on the Fiber Orientation Distributions and Their Influence on the Mechanical Property of the Co-Injection Molding Products

In recent years, due to the rapid development of industrial lightweight technology, composite materials based on fiber reinforced plastics (FRP) have been widely used in the industry. However, the environmental impact of the FRPs is higher each year. To overcome this impact, co-injection molding could be one of the good solutions. But how to make the suitable control on the skin/core ratio and how to manage the glass fiber orientation features are still significant challenges. In this study, we have applied both computer-aided engineering (CAE) simulation and experimental methods to investigate the fiber feature in a co-injection system. Specifically, the fiber orientation distributions and their influence on the tensile properties for the single-shot and co-injection molding have been discovered. Results show that based on the 60:40 of skin/core ratio and same materials, the tensile properties of the co-injection system, including tensile stress and modulus, are a little weaker than that of the single-shot system. This is due to the overall fiber orientation tensor at flow direction (A11) of the co-injection system being lower than that of the single-shot system. Moreover, to discover and verify the influence of the fiber orientation features, the fiber orientation distributions (FOD) of both the co-injection and single-shot systems have been observed using micro-computerized tomography (μ-CT) technology to scan the internal structures. The scanned images were further utilizing Avizo software to perform image analyses to rebuild the fiber structure. Specifically, the fiber orientation tensor at flow direction (A11) of the co-injection system is about 89% of that of the single-shot system in the testing conditions. This is because the co-injection part has lower tensile properties. Furthermore, the difference of the fiber orientation tensor at flow direction (A11) between the co-injection and the single-shot systems is further verified based on the fiber morphology of the μ-CT scanned image. The observed result is consistent with that of the FOD estimation using μ-CT scan plus image analysis.