principal axes
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Abstract Determination of permeability of thick-section glass fabric preforms with fabric layers of different architectures is critical for manufacturing large, thick composite structures with complex geometry, such as wind turbine blades. The thick-section reinforcement permeability is inherently three-dimensional and needs to be obtained for accurate composite processing modeling and analysis. Numerical simulation of the liquid stage of vacuum-assisted resin infusion molding (VARIM) is important to advance the composite manufacturing process and reduce processing-induced defects. In this research, the 3D permeability of thick-section E-glass fabric reinforcement preforms is determined and the results are validated by a comparison between flow front progressions from experiments and from numerical simulations using ANSYS Fluent software. The orientation of the principal permeability axes were unknown prior to experiments. The approach used in this research differs from those in literature in that the through-thickness permeability is determined as a function of flow front positions along the principal axes and the in-plane permeabilities and is not dependent on the inlet radius. The approach was tested on reinforcements with fabric architectures which vary through-the-thickness direction, such as those in a spar cap of a wind turbine blade. The computational simulations of the flow-front progression through-the-thickness were consistent with experimental observations.

Abstract The propagation of electromagnetic waves in a medium with electrical and magnetic anisotropy is a subject that is not usually handled in conventional optics and electromagnetism books. During this work, we try to give a pedagogical approach to the subject, using tools that are accessible to an average physics student. In this article, we obtain the Fresnel relation in a media with electromagnetic anisotropy, which corresponds to a quartic equation in the refraction index, assuming only that the principal axes of the electric and magnetic tensors coincide. Additionally, we find the geometric location related to the different situations the discriminant of the quartic equation provides. In order to illustrate our findings, we determine the refractive index together with the plane wave equations for certain values of the parameters that meet the established conditions. The target readers of the paper are students pursuing physics at the intermediate undergraduate level.

Abstract Background A complete definition of anatomical reference systems (ARS) for all bones of the foot and ankle complex is lacking. Using a morphological approach, we propose new ARS for these bones with the aim of being highly repeatable, consistent among individuals, clinically interpretable, and also suited for a sound kinematic description. Methods Three specimens from healthy donors and three patients with flat feet were scanned in weight-bearing CT. The foot bones were segmented and ARS defined according to the proposed approach. To assess repeatability, intra class coefficients (ICC) were computed both intra- and inter-operator. Consistency was evaluated as the mean of the standard deviations of the ARS position and orientation, both within normal and flat feet. Clinical interpretability was evaluated by providing a quantification of the curvature variation in the medial-longitudinal and transverse arches and computing the Djiann-Annonier angle for normal and flat feet from these new ARS axes. To test the capability to also provide a sound description of the foot kinematics, the alignment between mean helical axes (MHA) and ARS axes was quantified. Results ICC was 0.99 both inter- and intra-operator. Rotational consistency was 4.7 ± 3.5 ° and 6.2 ± 4.4° for the normal and flat feet, respectively; translational consistency was 4.4 ± 4.0 mm and 5.4 ± 2.9 mm for the normal and flat feet, respectively. In both these cases, the consistency was better than what was achieved by using principal axes of inertia. Curvature variation in the arches were well described and the measurements of the Djiann-Annoier angles from both normal and flat feet matched corresponding clinical observations. The angle between tibio-talar MHA and ARS mediolateral axis in the talus was 12.3 ± 6.0, while the angle between talo-calcaneal MHA and ARS anteroposterior axis in the calcaneus was 17.2 ± 5.6, suggesting good capability to represent joint kinematics. Conclusions The proposed ARS definitions are robust and provide a solid base for the 3-dimensional description of posture and motion of the foot and ankle complex from medical imaging.

AbstractSpontaneous symmetry breaking in crystalline solid often produces exotic nonreciprocal phenomena. As one such example, the unconventional optical rotation with nonreciprocity, which is termed gyrotropic birefringence, is expected to emerge from the magnetoelectric coupling. However, the fundamental nature of gyrotropic birefringence remains to be examined. Here w`e demonstrate the gyrotropic birefringence enhanced by the dynamical magnetoelectric coupling on the electrically active magnon resonance, i.e. electromagnon, in a multiferroic helimagnet. The helical spin order having both polarity and chirality is found to cause the giant gyrotropic birefringence in addition to the conventional gyrotropy, i.e. natural optical activity. It is demonstrated that the optical rotation of gyrotropic birefringence can be viewed as the nonreciprocal rotation of the optical principal axes, while the crystallographic and magnetic anisotropies are intact. The independent control of the nonreciprocal linear (gyrotropic birefringence) and circular (natural optical activity) birefringence/dichroism paves a way for the optically active devices.

Studying different types of tooth movements can help us to better understand the force systems used for tooth position correction in orthodontic treatments. This study considers a more realistic force system in tooth movement modeling across different patients and investigates the effect of the couple force direction on the position of the center of rotation (CRot). The finite-element (FE) models of human mandibles from three patients are used to investigate the position of the CRots for different patients’ teeth in 3D space. The CRot is considered a single point in a 3D coordinate system and is obtained by choosing the closest point on the axis of rotation to the center of resistance (CRes). A force system, consisting of a constant load and a couple (pair of forces), is applied to each tooth, and the corresponding CRot trajectories are examined across different patients. To perform a consistent inter-patient analysis, different patients’ teeth are registered to the corresponding reference teeth using an affine transformation. The selected directions and applied points of force on the reference teeth are then transformed into the registered teeth domains. The effect of the direction of the couple on the location of the CRot is also studied by rotating the couples about the three principal axes of a patient’s premolar. Our results indicate that similar patterns can be obtained for the CRot positions of different patients and teeth if the same load conditions are used. Moreover, equally rotating the direction of the couple about the three principal axes results in different patterns for the CRot positions, especially in labiolingual direction. The CRot trajectories follow similar patterns in the corresponding teeth, but any changes in the direction of the force and couple cause misalignment of the CRot trajectories, seen as rotations about the long axis of the tooth.

Abstract In this study, moisture dependent shear moduli in Scots pine (Pinus sylvestris L.) wood were determined by a 45° off-axis (longitudinal, radial, and tangential) compression test and ultrasonic transverse wave propagation. Finite element modeling was performed to ascertain how the results agree with the numerical method. Ultrasonic transverse wave velocities on the LR, LT, and RT planes were decreased from 1347, 1323, and 589 m × s-1 to 1286, 1269, and 561 m × s-1 when relative humidity increased from 45 % to 85 % at a constant temperature of 20 ± 1 °C, respectively. The dynamic and static shear modulus on the LR, LT, and RT planes were decreased from 988, 953, and 189, and 966, 914, and 182 MPa to 927, 903, and 176, and 845, 784, and 154 MPa when relative humidity increased from 45 % to 85 % at a constant temperature of 20 ± 1 °C, respectively. Therefore, both velocity and modulus values at all principal axes and planes were decreased with an increase in moisture. Maximum (15.2 %) and minimum (2.3 %) differences between dynamic and the static shear modulus were observed for GLT at 85 % and GLR at 45 % relative humidity, respectively. Coefficients of determinations between the dynamic and static shear moduli were ranged from 0.68 (GLR at 65 % RH) to 0.97 (GLR at 85 % RH). Finite element analysis, only for 65 % RH values, was performed using Solid 45 element, and, according to results, load-deformation curves created by linear orthotropic material properties, are well-matched with the static curves.

Plastic anisotropy significantly influences the behavior of structures subjected to various loading conditions. The extremum principles in the theory of rigid plastic solids are convenient and reliable tools for plastic design. The present paper combines the upper bound theorem and Hill’s quadratic yield criterion for orthotropic materials to evaluate the plastic collapse load of a highly undermatched welded tensile panel with a crack in the weld. The base material is supposed to be rigid. The shape of the crack is quite arbitrary. The orientation of the principal axes of anisotropy varies through the thickness of the weld. The upper bound solution is based on an exact solution for a layer of an anisotropic material. This feature of the upper bound solution is advantageous for increasing its accuracy. A numerical treatment is only necessary to find the solution for the uncracked specimen. This specimen has two axes of symmetry, which simplifies the solution. Simple analytic formulae transform this solution into a solution for the cracked specimens with one axis of symmetry and no symmetry. It is shown that the through-thickness distribution of anisotropic properties significantly affects the limit load.

On the basis of A. N. Tikhonov's regularization theory, a technique has been developed for solving inverse heat conduction problems of identifying the thermal conductivity tensor in a two-dimensional domain. Such problems are replaced by problems of identifying the principal heat conductivity coefficients and the orientation angle of the principal axes, with the principal coefficients being approximated by Schoenberg’s cubic splines. As a result, the problem is reduced to determining the unknown coefficients in these approximations and the orientation angle of the principal axes. With known boundary and initial conditions, the temperature in the domain will depend only on these coefficients and the orientation angle. If one expresses it by the Taylor formula for two terms of series and substitutes it into the Tikhonov functional, then the determination of the increments of the coefficients and the increment of the orientation angle can be reduced to solving a system of linear equations with respect to these increments. By choosing a certain regularization parameter as well as some functions for the principal thermal conductivity coefficients and the orientation angle as an initial approximation, one can implement an iterative process for determining these coefficients. After obtaining the vectors of the coefficients and the angle of orientation as a result of the converging iterative process, it is possible to determine the root-mean-square discrepancy between the temperature obtained and the temperature measured as a result of the experiment. It remains to choose the regularization parameter in such a way that this discrepancy is within the root-mean-square discrepancy of the measurement error. When checking the efficiency of using the proposed method, a number of two-dimensional test problems for bodies with known thermal conductivity tensors were solved. The influence of random measurement errors on the error in the identification of the thermal conductivity tensor was analyzed.

Abstract Background Dependence of strength and failure behavior of anisotropic ductile metals on loading direction and on stress state has been indicated by many experiments. To realistically predict safety and lifetime of structures these effects must be taken into account in material models and numerical analysis. Objective The influence of stress state and loading direction on damage and failure behavior of the anisotropic aluminum alloy EN AW-2017A is investigated. Methods New biaxial experiments and numerical simulations have been performed with the H-specimen under different load ratios. Digital image correlation shows evolution of strain fields and scanning electron microscopy is used to visualize failure modes on fracture surfaces. Corresponding numerical studies predict stress states to explain damage and fracture processes on the micro-scale. Results The stress state, the load ratio and the loading direction with respect to the principal axes of anisotropy affect the width and orientation of localized strain fields and the formation of damage mechanisms and fracture modes at the micro-level. Conclusions The enhanced experimental program with biaxial tests considering different loading directions and load ratios is suggested for characterization of anisotropic metals.

Accumulating space debris edges the space domain ever closer to cascading Kessler syndrome, a chain reaction of debris generation that could dramatically inhibit the practical use of space. Meanwhile, a growing number of retired satellites, particularly in higher orbits like geostationary orbit, remain nearly functional except for minor but critical malfunctions or fuel depletion. Servicing these ailing satellites and cleaning up “high-value” space debris remains a formidable challenge, but active interception of these targets with autonomous repair and deorbit spacecraft is inching closer toward reality as shown through a variety of rendezvous demonstration missions. However, some practical challenges are still unsolved and undemonstrated. Devoid of station-keeping ability, space debris and fuel-depleted satellites often enter uncontrolled tumbles on-orbit. In order to perform on-orbit servicing or active debris removal, docking spacecraft (the “Chaser”) must account for the tumbling motion of these targets (the “Target”), which is oftentimes not known a priori. Accounting for the tumbling dynamics of the Target, the Chaser spacecraft must have an algorithmic approach to identifying the state of the Target’s tumble, then use this information to produce useful motion planning and control. Furthermore, careful consideration of the inherent uncertainty of any maneuvers must be accounted for in order to provide guarantees on system performance. This study proposes the complete pipeline of rendezvous with such a Target, starting from a standoff estimation point to a mating point fixed in the rotating Target’s body frame. A novel visual estimation algorithm is applied using a 3D time-of-flight camera to perform remote standoff estimation of the Target’s rotational state and its principal axes of rotation. A novel motion planning algorithm is employed, making use of offline simulation of potential Target tumble types to produce a look-up table that is parsed on-orbit using the estimation data. This nonlinear programming-based algorithm accounts for known Target geometry and important practical constraints such as field of view requirements, producing a motion plan in the Target’s rotating body frame. Meanwhile, an uncertainty characterization method is demonstrated which propagates uncertainty in the Target’s tumble uncertainty to provide disturbance bounds on the motion plan’s reference trajectory in the inertial frame. Finally, this uncertainty bound is provided to a robust tube model predictive controller, which provides tube-based robustness guarantees on the system’s ability to follow the reference trajectory translationally. The combination and interfaces of these methods are shown, and some of the practical implications of their use on a planned demonstration on NASA’s Astrobee free-flyer are additionally discussed. Simulation results of each of the components individually and in a complete case study example of the full pipeline are presented as the study prepares to move toward demonstration on the International Space Station.