Orientation Tensor Research Articles

Late Jurassic syn-extensional sedimentary deposition and Cenozoic basin inversion as recorded in The Girón Formation, northern Andes of Colombia

The Yariguíes Anticlinorium, a regional structure located at the western flank of the Eastern Cordillera of Colombia, includes the thickest record of continental sedimentary rocks accumulated near to the Jurassic-Cretaceous boundary. The sedimentary rocks are lithoarenites and feldspathic arenites, grouped in the Girón Formation, and deposited in a Late Jurassic extensional basin interpreted in this work as a rift basin. We analysed the sedimentologic and compositional characteristics of two sections that accumulated in a complex rift system. We identified important thickness variations, from 3,350 m in the type section to at least 525 m in a reference section in the Zapatoca area, as well as petrographic and lithofacies changes. This led us to confirm that the Girón Formation encompasses all the continental facies, whose source rock correspond mainly to the exhumed blocks of the Santander Massif during the Late Jurassic. The synrift successions were segmented by transverse structures and regional longitudinal faults of the rift-shoulder, as the Suárez Fault. The tectonic frame of the study area shows the relevance of the W-E compressional regimes, explaining the local kinematics as a heritage of the former configuration and tectonic inversion of the basins. However, clockwise rotation of the stress field was detected from the stress tensor analysis. The latest orientation of the stress tensors and shear joints are related to the effect of the transpressional Bucaramanga and Lebrija faults along the study area.

Probing the Rheological Properties of Liquids Under Conditions of Elastohydrodynamic Lubrication Using Simulations and Machine Learning

In elastohydrodynamic lubrication (EHL), the lubricant experiences pressures in excess of 500 MPa and strain rates larger than 10^5 text{s}^{-1}. The high pressures lead to a dramatic rise in the Newtonian viscosity and the high rates lead to large shear stresses and pronounced shear thinning. The extraction of accurate rheological properties using non-equilibrium molecular dynamics simulations (NEMD) has played a key role in improving our understanding of lubricant flow in EHL conditions. However, the high dimensionality of the output data generated by NEMD simulations often makes a deeper interrogation of the link between molecular-scale features and rheological properties challenging. In this paper, we explore the use of machine learning to analyze and visualize the high-dimensional output data generated in typical NEMD simulations. We show that dimension reduction of NEMD simulation data describing the shear flow of squalane enables a clear visualization of the transition from Newtonian to non-Newtonian shear thinning with increasing shear rate and provides a reliable assessment of the correlation between shear thinning and the evolution in molecular alignment. The end-to-end atom pairs dominate the largest variations in pair orientation tensor components for low-pressure systems (0.1, 100 MPa) and provide the clearest separation of the orientation tensors with rate. On the other hand, the side atom pairs dominate the largest variation in the tensor components for the high-pressure systems (Pge 400 MPa) which exhibit an overall limited evolution in orientation tensors as a function of rate. Dimension reduction using all the six components of the orientation tensors of all 435 pairs associated with a squalane molecule shows that the decrease in viscosity with rate for low pressures is strongly correlated with changes in molecular alignment. However, for high pressures, shear thinning occurs at saturated orientational order.

Effect of gas pressure on the microstructure of parts foamed with the novel microcellular injection molding technology Ku‐Fizz™

AbstractThe increasing demand for lightweight and economical automotive components boosts investigation of advanced materials and new lightweighting technologies. This work employs the novel microcellular injection molding technology Ku‐Fizz™. The process introduces gas with granulates at moderate low pressures into the feed zone of the injection molding machine. Ku‐Fizz is controlled by gas pressure; thus, a simple plate geometry was molded and the effect of various gas contents on the microstructure was analyzed. The material used was a chemically coupled glass fiber‐reinforced polypropylene compound. Optical microscopy was employed to measure the foam microstructure. Microcomputed tomography was used to quantify the fiber volume fraction and the orientation tensors. Results of the fully characterized microstructure showed cell density increasing and cell size decreasing with gas pressure and melt flow direction. Fiber length increased with gas content. Cell growth displaced fibers from the center of the part towards the mold surface, changing the fiber concentration and global fiber orientation.

Pairwise Rigid Registration Based on Riemannian Geometry and Lie Structures of Orientation Tensors

Pairwise Rigid Registration Based on Riemannian Geometry and Lie Structures of Orientation Tensors

Magnetic Anisotropy Trends along a Full 4f-Series: The fn+7 Effect.

The combined experimental and computational study of the 13 magnetic complexes belonging to the Na[LnDOTA(H2O)] (H4DOTA = tetraazacyclododecane-N,N′,N″,N‴-tetraacetic acid and Ln = Ce–Yb) family allowed us to identify a new trend: the orientation of the magnetic anisotropy tensors of derivatives differing by seven f electrons practically coincide. We name this trend the fn+7 effect. Experiments and theory fully agree on the match between the magnetic reference frames (e.g., the easy, intermediate, and hard direction). The shape of the magnetic anisotropy of some couples of ions differing by seven f electrons might seem instead different at first look, but our analysis explains a hidden similarity. We thus pave the way toward a reliable predictivity of the magnetic anisotropy of lanthanide complexes with a consequent reduced need of computational and synthetical efforts. We also offer a way to gain information on ions with a relatively small total angular momentum (i.e., Sm3+ and Eu3+) and on the radioactive Pm3+, which are difficult to investigate experimentally.

A Fully Coupled Simulation of Planar Deposition Flow and Fiber Orientation in Polymer Composites Additive Manufacturing.

Numerical studies for polymer composites deposition additive manufacturing have provided significant insight promoting the rapid development of the technology. However, little of existing literature addresses the complex yet important polymer composite melt flow–fiber orientation coupling during deposition. This paper explores the effect of flow–fiber interaction for polymer deposition of 13 wt.% Carbon Fiber filled Acrylonitrile Butadiene Styrene (CF/ABS) composites through a finite-element-based numerical approach. The molten composite flow in the extrusion die plus a strand of the deposited bead contacting the deposition substrate is modelled using a 2D isothermal and incompressible Newtonian planar flow model, where the material deposition rate is ~110 mm/s simulating a large scale additive manufacturing process. The Folgar–Tucker model associated with the Advani–Tucker orientation tensor approach is adopted for the evaluation of the fiber orientation state, where the orthotropic fitted closure is applied. By comparing the computed results between the uncoupled and fully coupled solutions, it is found that the flow-orientation effects are mostly seen in the nozzle convergence zone and the extrusion-deposition transition zone of the flow domain. Further, the fully coupled fiber orientation solution is highly sensitive to the choice of the fiber–fiber interaction coefficient , e.g., assigning as 0.01 and 0.001 results in a 23% partial relative difference in the predicted elastic modulus along deposition direction. In addition, Structural properties of deposited CF/ABS beads based on our predicted fiber orientation results show favorable agreements with related experimental studies.

Theoretical approximation of hydrodynamic and fiber-fiber interaction forces for macroscopic simulations of polymer flow process with fiber orientation tensors

Flow processes of discontinuous fiber reinforced polymers (FRPs) are the essence of several polymer-based manufacturing processes. FRPs show a transient chemo-thermomechanical matrix behavior and fiber-induced anisotropic physical properties. Therefore, they are one of the most complex materials used in volume production. The general flow behavior is influenced by fibers and their interactions with the matrix and other fibers. The consideration of individual fibers is numerically not capable for process simulation of FRP parts. Therefore, orientation tensors are used in macroscopic simulations, leading to a loss of information about the fiber network. Within this work, novel approximation schemes are presented to determine hydrodynamic and fiber-fiber contact forces with information provided by the second order fiber orientation tensor. Approximation of these forces can henceforth facilitate fiber breakage modeling in macroscopic process simulations. The results are verified by numerical simulations with individual fibers of different orientation states and lengths, showing good agreement with the verification results.

Molecular-statistical theory of elasticity in nematic liquid crystals composed of polar and nonpolar molecules.

A molecular-statistical theory of the orientational elasticity of nematic liquid crystals has been developed employing the orientational deformation tensor which describes the rotation of the director. An explicit expression for the general elasticity tensor of the nematic phase has been obtained and the Frank elastic constants are expressed in terms of the three independent parameters of this tensor. Explicit expressions for the Frank elastic constants have been derived in the molecular field approximation in terms of the orientational order parameters and the corresponding coefficients of expansion of the intermolecular potential in spherical invariants. Frank elastic constants have been calculated numerically for nematic liquid crystals composed of both polar and nonpolar molecules together with the orientational order parameters using the classical Gay-Berne model interaction potential and the two of its popular modifications. The polarity of the uniaxial molecular shape has been directly introduced into the model potential by modifying the distance of closest approach. The elastic constants are presented as functions of temperature for different values of the molecular elongation, the anisotropy of the potential well and the molecular shape polarity. It has been shown that the elastic constants are much more sensitive to the details of the intermolecular interaction potential in comparison with the orientational order parameters. In particular, a relatively weak polarity of the molecular shape may result in an unusual decrease of the splay constant K_{11} which may vanish at some temperature leading to the instability of the homogeneous nematic phase. This may represent a mechanism of the formation of the splay-bend phase.

An improved seismic data completion algorithm using low-rank tensor optimization: Cost reduction and optimal data orientation

Seismic data are often incomplete due to equipment malfunction, limited source and receiver placement at near and far offsets, and missing crossline data. Seismic data contain redundancies because they are repeatedly recorded over the same or adjacent subsurface regions, causing the data to have a low-rank structure. To recover missing data, one can organize the data into a multidimensional array or tensor and apply a tensor completion method. We can increase the effectiveness and efficiency of low-rank data reconstruction based on tensor singular value decomposition (tSVD) by analyzing the effect of tensor orientation and exploiting the conjugate symmetry of the multidimensional Fourier transform. In fact, these results can be generalized to any order tensor. Relating the singular values of the tSVD to those of a matrix leads to a simplified analysis, revealing that the most square orientation gives the best data structure for low-rank reconstruction. After the first step of the tSVD, a multidimensional Fourier transform, frontal slices of the tensor form conjugate pairs. For each pair, a singular value decomposition can be replaced with a much cheaper conjugate calculation, allowing for faster computation of the tSVD. Using conjugate symmetry in our improved tSVD algorithm reduces the runtime of the inner loop by 35%–50%. We consider synthetic and real seismic data sets from the Viking Graben Region and the Northwest Shelf of Australia arranged as high-dimensional tensors. We compare the tSVD-based reconstruction with traditional methods, projection onto convex sets and multichannel singular spectrum analysis, and we see that the tSVD-based method gives similar or better accuracy and is more efficient, converging with runtimes that are an order of magnitude faster than the traditional methods. In addition, we verify that the most square orientation improves recovery for these examples by 10%–20% compared with the other orientations.

Finite element modelling of fully-coupled flow/fiber-orientation effects in polymer composite deposition additive manufacturing nozzle-extrudate flow

This paper presents a Finite Element Method (FEM) based algorithm to simulate the mutually dependent effects between non-Newtonian polymer melt flow and fiber orientation in Polymer Composite Deposition Additive Manufacturing (PCDAM). The computational approach is employed to analyze an axisymmetric flow with a free surface that defines the melt extrudate. The non-Newtonian power law model is applied to quantify the shear thinning rheological behavior of the polymer flow. The fiber orientation state of the composite melt is simulated using the Advani-Tucker orientation tensor approach, and a streamline-based remeshing technique is applied to compute die swell of the free extrudate. The non-linear FEM system is solved with the Newton Raphson iteration method. Computed results are compared to those obtained using a flow-fiber one way coupling simulation, where it is shown that the magnitude of flow field along the direction of extrusion, as well as the fiber alignment in the flow direction, both increase when full coupling is used. In addition, the extrudate swell ratio solved by the fully-coupled scheme reduces by roughly a factor of ~2× as compared to the weakly-coupled flow solution.

The use of the empirical crack orientation tensor to characterize the damage anisotropy

In practice, a dominant failure mode of brittle materials, such as fiber-reinforced thermosets is the initiation and propagation of cracks under cyclic loading. In general, the damage in composites with irregular microstructure do not occur in regular patterns. There are several state-of-the-art continuum mechanical models which take the anisotropic damage for predicting the material behavior into account. Since damage generally occurs in an anisotropic way, methods that experimentally characterize the damage anisotropy are needed.Micro-Computed Tomography systems (μCT) acquire volumetric images in a non-destructive way. By combining μCT scanning and mechanical in-situ testing, detailed microstructure data of specimens under load are generated. Based on image processing methods, the damage propagation from crack initiation to fracture is analyzed. In practice, cyclic load is a common load case for many components. Consequently, fatigue and cycle load tests are essential for a comprehensive material characterization.In this contribution interrupted in-situ μCT tests with cyclic tensile load are performed on Sheet Molding Compounds (SMC), a discontinuous glass fiber-reinforced thermset composite. Image processing methods are introduced for the experimental determination of the anisotropic damage characteristic based on volumetric images. The methods enable analyzing the spatial crack orientation distribution. In order to quantify the damage anisotropy, empirical formulations of the crack density distribution and second-order crack orientation tensor are applied. The presented work in this contribution extends the results of preliminary experimental damage investigations. In addition to previous studies, the damage anisotropy is quantified and analyzed.

Hasdrubal Field, Tunisia: geomechanical integrity study

Hasdrubal is a naturally fractured carbonate reservoir field located in offshore Tunisia. Over the last decade, the field has manifested serious integrity and water coning production issues. The extended network of discontinuities in addition to the impact of reservoir depletion renders the stability of the reservoir a major concern for the field operator. An integrity study of the field was necessary to accurately determine the ever-changing stress settings (magnitudes and orientation of stresses tensors) in order to accordingly adjust the design of well trajectory while properly assimilate their impact on the production trend. An elaborated workflow was initiated to fine-tune mechanical properties of rock basing on geological information, drilling event, and field logs. The one-dimensional mechanical earth model (MEM) was then built to validate wellbore failure and explain drilling incidences reported. The stress regime was also confirmed and matches the geological history of the area with an alteration between normal faulting and strike-slip regimes. The mechanical earth model was in position to explain the drilling events for all the vertical wells and so providing reasonable guide design for the wells under development. The shear stability of faults encountered by horizontal well Hasdrubal-A1 was also appraised using the Fracture Stability Advisor software. The results show that at initial reservoir pressures, the fractures in Hasdrubal field are stable and do not exceed the failure criterion. Previous interpretation is applicable to any major discrete discontinuity that is present in the same stress field and depicts similar rock-related properties strength. A predictive and robust three-dimensional model to represent the complex environment of reservoir is necessary to explain production profile induced from pressure depletion, especially alteration at fractures and faults network, and so improving well planning and long-term field development. The mechanical earth model described herewith has represented an indispensable foundation of the three-dimensional model that has been built to address the classical 1D-MEM limitations and so to properly assimilate the presence of fractures and their impacts on the geomechanical behaviour of the field.

Paleostress reconstruction of faults recorded in the Nied\u017awiedzia Cave (Sudetes): insights into Alpine intraplate tectonic of NE Bohemian Massif

Brittle structures identified within the largest karstic cave of the Sudetes (the Niedźwiedzia Cave) were studied to reconstruct the paleostress driving post-Variscan tectonic activity in the NE Bohemian Massif. Individual fault population datasets, including local strike and dip of fault planes, striations, and Riedel shear, enabled us to discuss the orientation of the principal stresses tensor. The (meso) fault-slip data analysis performed both with Dihedra and an inverse method revealed two possible main opposing compressional regimes: (1) NE–SW compression with the formation of strike-slip (transpressional) faults and (2) WNW–ESE horizontal compression related to fault-block tectonics. The (older) NE-SW compression was most probably associated with the Late Cretaceous–Paleogene pan-regional basin inversion throughout Central Europe, as a reaction to ongoing African-Iberian-European convergence. Second WNW–ESE compression was active as of the Middle Miocene, at the latest, and might represent the Neogene–Quaternary tectonic regime of the NE Bohemian Massif. Exposed fault plane surfaces in a dissolution-collapse marble cave system provided insights into the Meso-Cenozoic tectonic history of the Earth’s uppermost crust in Central Europe, and were also identified as important guiding structures controlling the origin of the Niedźwiedzia Cave and the evolution of subsequent karstic conduits during the Late Cenozoic.

Porous materials reinforced with short fibers: Unbiased full-field assessment of several homogenization strategies in elasticity

This work is concerned with the micromechanical modeling of porous short fiber-reinforced composites considered as three-phase microstructures: cavities and short fibers embedded in a matrix phase. Several homogenization strategies are evaluated in isothermal linear elasticity: two-level, two-step and direct Mori-Tanaka (MT) models. Unbiased evaluation of the methods is conducted based on full-field finite element (FE) analyses. No Eshelby-based analytical mean-field models are used. A parametric study for a porous thermoplastic polymer matrix reinforced with short glass fibers is carried out, for both fixed and distributed fiber orientations. The predictions of the various homogenization strategies are compared against reference FE results of the original three-phase composites. The reported numerical simulations are in 2D plane stress, but provide nevertheless insight into 3D situations. There are three main findings. (1) The best predictions are obtained with a two-level strategy, where in the lower level the actual porous matrix is homogenized, and in the upper level, fibers are embedded in the homogenized matrix. (2) The direct MT model can generate nonphysical predictions: effective properties outside the Voigt and Reuss estimates, and non-symmetric effective stiffness matrix. (3) For misaligned fibers, two-step homogenization methods can be used at the upper level in combination with the recommended two-level strategy. Acronyms and abbreviations: FE: finite element, BC: boundary condition, PBC: periodic BC, MF: mean-field, MT: Mori-Tanaka, ODF: orientation distribution function, OT: orientation tensor, RVE: representative volume element, SFRC: short fiber-reinforced composite, UC: unit cell, UD: unidirectional.

Evaluating the Taylor hardening model in polycrystalline Ti using high energy X-ray diffraction microscopy

High energy X-ray diffraction microscopy (HEDM) was employed to index nearly 1000 grains in a polycrystalline Ti specimen and characterize their deformation during an incremental tensile test. For each grain, the positions of its associated diffraction peaks were used for analyzing its evolving crystal orientation and stress tensor. The azimuthal breadth of each peak at different load steps was measured, allowing measurement of initial yielding and providing an estimate of the dislocation density evolution in each grain. The Taylor hardening model was evaluated grain by grain using the above data, indicating that it can represent hardening in most grains. The yield stress and the strain hardening coefficient for all grains were statistically analyzed with respect to grain orientation, grain size, slip systems, and the surrounding neighborhood to examine how the yield stress and hardening are correlated.

Directional dark matter detection in anisotropic Dirac materials

Dirac materials, because of their small ${\cal O}(\mbox{meV})$ band gap, are a promising target for dark photon-mediated scattering and absorption of light dark matter. In this paper, we characterize the daily modulation rate of dark matter interacting with a Dirac material due to anisotropies in their crystal structure. We show that daily modulation is an ${\cal O}(1)$ fraction of the total rate for dark matter scattering in the Dirac material ZrTe$_5$. When present, the modulation is dominated by the orientation of the material's dielectric tensor with respect to the dark matter wind, and is maximized when the crystal is oriented such that the dark matter wind is completely aligned with the largest and smallest components of the dielectric tensor at two different times of the day. Because of the large modulation, any putative dark matter scattering signal could be rapidly verified or ruled out by changing the orientation of the crystal with respect to the wind and observing how the daily modulation pattern changes.

White matter alterations and cognitive outcomes in children born very low birth weight

BackgroundVery low birth weight (VLBW) infants are at risk for disrupted white matter maturation, yet little is known about the contributing factors, particularly at preschool-age when cognitive difficulties begin to emerge. We examined white matter microstructure in five-year-old VLBW and full-term (FT) children, and its association with cognitive outcomes and birth weight. MethodsMulti-shell diffusion and MR images were obtained for 41 VLBW (mean birth weight: 1028.6 ± 256.8 g) and 26 FT (3295.4 ± 493.9 g) children. Fractional anisotropy (FA), radial diffusivity (RD), neurite orientation dispersion index (ODI) and density index (NDI) were estimated using diffusion tensor and neurite orientation dispersion and density imaging models. Between-group analyses used a general linear model with group and sex as explanatory variables. Within-group associations between white matter microstructure, cognitive outcomes and birth weight were also investigated. ResultsVLBW compared to FT children showed lower FA and NDI across widespread white matter regions. Smaller clusters of atypical ODI were also found in VLBW children. Within-group analyses in FT children revealed that lower RD and higher NDI were associated with vocabulary acquisition and working memory. In VLBW children, higher FA and NDI, and lower RD and ODI, were associated with improved processing speed. In both groups, FA was positively associated with birth weight. ConclusionsOur findings demonstrate white matter alterations in young VLBW children, including widespread reductions in axon density that may reflect sustained myelination disruptions. The associations with cognitive outcomes may also highlight which of the VLBW children are at higher risk for later cognitive difficulties.

Numerical investigation on the influence of fiber orientation mapping procedure to the mechanical response of short-fiber reinforced composites using Moldflow, Digimat and Ansys software

Within this paper, a numerical study was performed, aiming to assess the influence of fiber orientation on the mechanical properties of tensile specimens, by using the finite element method. The specimen, designed according to ISO-527-2, is type 1BA and consists of a reinforced polyamide with 30% glass fiber (PA66 GF30). The specimens were extracted from 2 mm thickness plates, for which the fiber orientation tensor was determined using the dedicated Moldflow software for injection molding. The composite material was modelled using Digimat mean-field homogenization tool. The mechanical evaluation was performed in Ansys finite element software by coupling it with Digimat and thus considering the anisotropic behavior of the material. Different mapping procedures and mesh sizes for the Moldflow model and Ansys model were considered.

Comparison of diffusion MRI and CLARITY fiber orientation estimates in both gray and white matter regions of human and primate brain

Diffusion MRI (dMRI) represents one of the few methods for mapping brain fiber orientations non-invasively. Unfortunately, dMRI fiber mapping is an indirect method that relies on inference from measured diffusion patterns. Comparing dMRI results with other modalities is a way to improve the interpretation of dMRI data and help advance dMRI technologies. Here, we present methods for comparing dMRI fiber orientation estimates with optical imaging of fluorescently labeled neurofilaments and vasculature in 3D human and primate brain tissue cuboids cleared using CLARITY. The recent advancements in tissue clearing provide a new opportunity to histologically map fibers projecting in 3D, which represents a captivating complement to dMRI measurements. In this work, we demonstrate the capability to directly compare dMRI and CLARITY in the same human brain tissue and assess multiple approaches for extracting fiber orientation estimates from CLARITY data. We estimate the three-dimensional neuronal fiber and vasculature orientations from neurofilament and vasculature stained CLARITY images by calculating the tertiary eigenvector of structure tensors. We then extend CLARITY orientation estimates to an orientation distribution function (ODF) formalism by summing multiple sub-voxel structure tensor orientation estimates. In a sample containing part of the human thalamus, there is a mean angular difference of 19o±15o between the primary eigenvectors of the dMRI tensors and the tertiary eigenvectors from the CLARITY neurofilament stain. We also demonstrate evidence that vascular compartments do not affect the dMRI orientation estimates by showing an apparent lack of correspondence (mean angular difference = 49o±23o) between the orientation of the dMRI tensors and the structure tensors in the vasculature stained CLARITY images. In a macaque brain dataset, we examine how the CLARITY feature extraction depends on the chosen feature extraction parameters. By varying the volume of tissue over which the structure tensor estimates are derived, we show that orientation estimates are noisier with more spurious ODF peaks for sub-voxels below 30 µm3 and that, for our data, the optimal gray matter sub-voxel size is between 62.5 µm3 and 125 µm3. The example experiments presented here represent an important advancement towards robust multi-modal MRI-CLARITY comparisons.

General liquid-crystal theory for anisotropically shaped molecules: Symmetry, orientational order parameters, and system free energy.

A general theory of liquid crystals is presented, starting from the group-theory symmetry analysis of the constituting molecules. A particular attention is paid to the type of elastic free-energies and their relationships with the molecular symmetries. The orientational order-parameter tensors are identified for each molecular symmetry, in a consideration of consistently keeping the leading, characteristic elastic free energies in a model. The order parameters are expressed in terms of symmetric traceless tensors, some of high orders, for all major molecular symmetries, including seven groups of axial symmetries and seven groups of polyhedral symmetries. For spatially inhomogeneous liquid crystals, the couplings of these tensors in the elastic energies are derived by expanding the interaction energies between these molecules. The aim is to provide a general view of the molecular symmetries of individual molecules, orientational order parameters characterizing the orientational distribution functions, and the elastic free energies, all under one single group-theory approach.