Symmetric Deformation Research Articles

Symmetric Piecewise Developable Approximations

AbstractWe propose a novel method for generating symmetric piecewise developable approximations for shapes in approximately global reflectional or rotational symmetry. Given a shape and its symmetry constraint, the algorithm contains two crucial steps: (i) a symmetric deformation to achieve a nearly developable model and (ii) a symmetric segmentation aided by the deformed shape. The key to the deformation step is the use of the symmetric implicit neural representations of the shape and the deformation field. A new mesh extraction from the implicit function is introduced to construct a strictly symmetric mesh for the subsequent segmentation. The symmetry constraint is carefully integrated into the partition to achieve the symmetric piecewise developable approximation. We demonstrate the effectiveness of our algorithm over various meshes.

Achieving strength-ductility balance in AZ31-WE43 Mg alloys by symmetric extrusion-shear process at various temperatures

The development of composites that simultaneously improve strength and plasticity is a challenging task, especially in Mg alloys. The focus of this study is to create a novel multiscale gradient structure (GS) in Mg laminates to exhibit optimal strength-plasticity synergies through a temperature-controlled extrusion shear (TCES) and extrusion composite process with preset grain sizes. Initially, the gradient structure is formed by a short extrusion process, leading to an increase in the average grain size of the elongated coarse grains from the middle layer of the equiaxed fine grain zone to the elongated coarse grain surface layer. The resulting gradient structure improves the material synergy. The microstructure evolution mechanism of the alloy during symmetric plastic deformation was analyzed. The initial grains underwent DDRX, CDRX, and shear deformation-induced dynamic recrystallization (SDDRX) during the RZ extrusion stage, the grains were significantly refined, and the basal texture intensity was significantly weakened during the SD extrusion stage. The effect of extrusion temperature (400 °C, 450 °C, 500 °C) on the alloys in the forming zone after ES extrusion was further investigated. Tensile tests on Mg laminates prepared by the extrusion method showed that the ultimate tensile strength (UTS) of the samples prepared at 450 °C was 265 MPa and the elongation (EL) was 23.8 %. The significant improvement in the yield tensile strength (YTS) of the composite Mg alloys post-ES processing is primarily attributed to the fine-grained (FG) interior, while the increase in elongation is due to the coarse-grained (CG) exterior. This study presents a novel approach to enhancing the mechanical properties of Mg alloys, offering a promising direction for the development of advanced materials with superior strength and ductility.

TECHNOLOGY OF MINIMALLY INVASIVE SURGICAL CORRECTION FUNNEL-SHAPED DEFORMATION OF THE CHEST IN CHILDREN

The most common method surgical treatment of pectus excavatum (PE) is thoracoplasty according by D.Nuss at the moment. But serious complications associated with trauma to the pericardium, blood vessels, and bleeding are known. Objective. Development of a modified technology surgical correction of pectus excavatum, which involves exclusively extrapleural passage of the plate, according to the individual size and shape of the deformation of the patient’s chest, in order to prevent intraoperative complications. Methods. 81 patients aged 10 to 17 years were involved in the study. A modified technology of extrapleural surgical correction of PE was performed. The plate was carried level of the VI–VII sternocostal joints through the formed through submuscular-extrapleural retrosternal tunnel from right to left under control of right-sided thoracoscopy. The plate was modeled according by individual deformation parameters chest. The analysis was carried out according to the following criteria: age, gender, type of deformity, Haller index, duration of surgery, intraoperative and early postoperative complications according by Clavien–Dindo classification. Results. The median age of patients was (13.8 ± 1.9) years, of which there were 65 (85.25 %) boys, 16 (19.75 %) girls. 48 (59.3 %) children were diagnosed with type I (symmetric) deformity, and 33 (40.7 %) with type II (asymmetric) according to the classification. The median Haller was (4.07 ± 0.62), which corresponds to 2–3 degrees. Differences in the degree of deformation in children of different sexes were not determined (р = 0.828). Impaired lung function was d iagnosed i n 55.55 % (n = 45), i mpaired h eart f unction — 40.74 % (n = 33). T he d uration of the o peration was on a verage (70.6 ± 15.4) minutes, from 50 to 110 minutes. Early postoperative complications were found in 5 (6.17 %) patients classified as grade I (mild) according to the Clavien–Dindo classification, which did not require additional medical or surgical correction. After the operation, the correction of chest deformation was on average (2.35 ± 0.22) according by Haller index, which was statistically significantly (р = 0.001) different from the initial level. Conclusions. The use of modified technology surgical correction of PE meets safety requirements and minimizes postoperative complications.

Ginzburg-Landau description for multicritical Yang-Lee models

We revisit and extend Fisher’s argument for a Ginzburg-Landau description of multicritical Yang-Lee models in terms of a single boson Lagrangian with potential φ2(iφ)n. We explicitly study the cases of n = 1, 2 by a Truncated Hamiltonian Approach based on the free massive boson perturbed by PT symmetric deformations, providing clear evidence of the spontaneous breaking of PT symmetry. For n = 1, the symmetric and the broken phases are separated by the critical point corresponding to the minimal model M25\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M}\\left(2,5\\right) $$\\end{document}, while for n = 2, they are separated by a critical manifold corresponding to the minimal model M25\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M}\\left(2,5\\right) $$\\end{document} with M27\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M}\\left(2,7\\right) $$\\end{document} on its boundary. Our numerical analysis strongly supports our Ginzburg-Landau descriptions for multicritical Yang-Lee models.

Clinical characteristics and early results of the modified abramson technique to treat pectus carinatum at Viet Đuc Hospital from 2020-2023

Pectus carinatum is the second most common congenital anterior chest wall deformity. This study describe the clinical, paraclinical characteristics and evaluate the early results of the modified Abramson technique to treat pectus carinatum at Viet Duc Hospital. This is a retrospective descriptive study, in all cases diagnosed with pectus carinatum and underwent surgery according to the modified Abramson technique at Viet Duc Hospital from 1/2020 to 12/2023. In 134 patients, 131 were male, the mean age 13.6 ± 1.98 years. All patients presented with cosmetic complaints, and 85.2% patients have BMI <18.5. 94/134 cases (70.2%) had symmetrical deformities, 37/134 cases (27.6%) had asymmetrical deformities, and 3 cases (2.2%) had mixed pectus deformities. The average Haller index is 2.1 ± 0.3. All patients were operated using a bar, fixed at both ends with steel thread. Operative time was 33.6 ± 7.76 minutes, and hospital stay was 5.3 ± 0.76 days (4–7 days). There was no significant early postoperative complications. Conclusion: clinical examination and computed tomography play an important role in diagnosing pectus carinatum. The modified Abramson technique is a minimally invasive surgical method for pectus carinatum patients with short operative time, hospital stay, and the first step gives good treatment results. TRANSLATE with x English Arabic Hebrew Polish Bulgarian Hindi Portuguese Catalan Hmong Daw Romanian Chinese Simplified Hungarian Russian Chinese Traditional Indonesian Slovak Czech Italian Slovenian Danish Japanese Spanish Dutch Klingon Swedish English Korean Thai Estonian Latvian Turkish Finnish Lithuanian Ukrainian French Malay Urdu German Maltese Vietnamese Greek Norwegian Welsh Haitian Creole Persian TRANSLATE with COPY THE URL BELOW Back EMBED THE SNIPPET BELOW IN YOUR SITE Enable collaborative features and customize widget: Bing Webmaster Portal Back

Information geometry of Wasserstein statistics on shapes and affine deformations

AbstractInformation geometry and Wasserstein geometry are two main structures introduced in a manifold of probability distributions, and they capture its different characteristics. We study characteristics of Wasserstein geometry in the framework of [32] for the affine deformation statistical model, which is a multi-dimensional generalization of the location-scale model. We compare merits and demerits of estimators based on information geometry and Wasserstein geometry. The shape of a probability distribution and its affine deformation are separated in the Wasserstein geometry, showing its robustness against the waveform perturbation in exchange for the loss in Fisher efficiency. We show that the Wasserstein estimator is the moment estimator in the case of the elliptically symmetric affine deformation model. It coincides with the information-geometrical estimator (maximum-likelihood estimator) when the waveform is Gaussian. The role of the Wasserstein efficiency is elucidated in terms of robustness against waveform change.

Size and kinematics of the C IV broad emission line region from microlensing-induced line profile distortions in two gravitationally lensed quasars

Microlensing of the broad emission line region (BLR) in gravitationally lensed quasars produces line profile distortions that can be used to probe the BLR size, geometry, and kinematics. Based on single-epoch spectroscopic data, we analyzed the C IV line profile distortions due to microlensing in two quasars, SDSS J133907.13+131039.6 (J1339) and SDSS J113803.73+031457.7 (J1138), complementing previous studies of microlensing in the quasars Q2237+0305 and J1004+4112. J1339 shows a strong, asymmetric line profile deformation, while J1138 shows a more modest, symmetric deformation, confirming the rich diversity of microlensing-induced spectral line deformations. To probe the C IV BLR, we compared the observed line profile deformations to simulated ones. The simulations are based on three simple BLR models, a Keplerian disk (KD), an equatorial wind (EW), and a polar wind (PW), of various sizes, inclinations, and emissivities. These models were convolved with microlensing magnification maps specific to the microlensed quasar images, which produced a large number of distorted line profiles. The models that best reproduce the observed line profile deformations were then identified using a Bayesian probabilistic approach. We find that the line profile deformations can be reproduced with the simple BLR models under consideration, with no need for more complex geometries or kinematics. The models with disk geometries (KD and EW) are preferred, while the PW model is definitely less likely. In J1339, the EW model is favored, while the KD model is preferred in Q2237+0305, suggesting that various kinematical models can dominate the C IV BLR. For J1339, we find the C IV BLR half-light radii to be r1/2 = 5.1−2.9+4.6 light-days and r1/2 = 6.7−3.8+6.0 light-days from spectra obtained in 2014 and 2017, respectively. They do agree within uncertainties. For J1138, the amplitude of microlensing is smaller and more dependent on the macro-magnification factor. From spectra obtained in 2005 (single epoch), we find r1/2 = 4.9−2.7+4.9 light-days and r1/2 = 12−8+13 light-days for two extreme values of the macro-magnification factor. Combining these new measurements with those previously obtained for the quasars Q2237+0305 and J1004+4112, we show that the BLR radii estimated from microlensing do follow the C IV radius–luminosity relation obtained from reverberation mapping, although the microlensing radii seem to be systematically smaller, which could indicate either a selection bias or a real offset.

Research on Foot Contact State Detection Technology of Wheel-Legged Robot.

The accurate perception of external environment information through the robot foot is crucial for the mobile robot to evaluate its ability to traverse terrain. Adequate foot-end contact signals can provide robust support for robot motion control and decision-making processes. The shape and uncertain rotation of the wheel-legged robot foot end represent a significant challenge to sensing the robot foot-end contact state, which current foot-end sensing schemes cannot solve. This paper presents a sensing method for the tire stress field of wheel-legged robots. A finite element analysis was conducted to study the deformation characteristics of the foot-end tire under force. Based on this analysis, a heuristic contact position estimator was designed that utilizes symmetrical deformation characteristics. Strain sensors, arranged in an array, extract the deformation information on the inner surface of the tire at a frequency of 200 Hz. The contact position estimator reduces the dimensionality of the data and fits the eigenvalues to the estimated contact position. Using support vector regression, the force estimator utilizes the estimated contact position and sensor signal to estimate the normal reaction force, designated as FZ. The sensing system is capable of detecting the contact position on the wheel circumference (with a root mean square error of 1.150°), as well as the normal force of 160 N on the Z axis (with a root mean square error of 6.04%). To validate the efficacy of the sensor detection method, a series of randomized and repeated experiments were conducted on a self-constructed test platform. This novel approach offers a promising avenue for perceiving contact states in wheel-legged robots.

Asymmetric electronic deformation in graphene molecular capacitors

AbstractAsymmetric deformation density analysis is applied on bilayer graphene flakes as molecular capacitors to identify the extent of asymmetric distribution of electrons and holes when exposed to bias voltage. Three triangular, orthorhombic, and hexagonal symmetries for graphene flakes are considered in two sizes and electric field potential is applied along the vector perpendicular to graphene flakes' plane to simulate 1–4 V as the bias voltage applied to molecular‐scale capacitors The number of electrons responsible for asymmetric distribution of electrons and holes, and occupied to virtual transfer are calculated, and electric field deformation density analysis is also performed that shows distributions of electrons and holes are quite asymmetric for the orthorhombic symmetry, while for the other symmetries, they are almost image of each other. It was found that isosurfaces of deformation density distribution possess a multilayer structure and accretion and depletion of electrons can be taken place between flakes or outside the parallel flakes, and it is shown that bias voltage is able to significantly remove symmetry of electrons and holes distribution. Inspection of molecular orbitals showed that electric field could change the energetic order of molecular orbitals, so that occupancy inversion is occurred for the orthorhombic systems that is responsible for their extraordinary properties.

Aerial imagery reveals abnormal stingrays, Taeniura lymma (Myliobatiformes: Dasyatidae), in the central Red Sea.

While morphological abnormalities have been widely reported in batomorphs, ontogenetic deformities of the posterior pectoral fin are rare. In this paper, we present two individuals of the bluespotted ribbontail ray, Taeniura lymma (Forsskål, 1775), with symmetrically deformed posterior pectoral fins. Both individuals were observed through aerial imagery on a coastal sandflat in the central Red Sea (22.30° N, 39.09° E). The similarity of this symmetrical deformity in both individuals indicates it likely has a genetic base. However, lacking access to the specimens, the ultimate cause of the abnormality remains uncertain. The incomplete disk closure did not seem to affect survival, as both individuals had reached a disk width of 22 cm, well above the typical birth size of the species. Our observations constitute both the first report of a morphological abnormality in T. lymma and the first record of a batomorph with a symmetrically deformed posterior pectoral fin.

Effects of differential hardening on energy absorption prediction of AA6061-T6 thin-walled rectangular tube

In this study, the energy absorption characteristics and deformation modes of AA6061-T6 thin-walled rectangular tube are investigated experimentally and numerically under different crushing conditions, including axial crushing, three-point bending and oblique crushing. Mechanical tests are carried out on four specimens of uniaxial tension, uniaxial compression, shear and plane strain tension along different loading directions for AA6061-T6. Besides, the effect of differential hardening behavior on the energy absorption prediction of AA6061-T6 rectangular tubes is illustrated by comparing Lou2022, von Mises and SY2009 functions. The mechanical experiment results indicate that AA6061-T6 shows obvious anisotropy, differential hardening behavior and tension-compression asymmetry, and its plastic evolution is accurately characterized by the Lou2022 model. The axial crushing properties show that the AA6061-T6 thin-walled rectangular tube undergoes the progressive symmetrical folding deformation mode. The introduction of geometric discontinuity can obviously reduce the peak force and improve the crashworthiness performances under the axial load. The main crushing mode is bending with a small amount of indentation for three-point bending. Moreover, the three-point bending simulation shows that the Lou2022 function considering differential hardening behavior has the highest simulation accuracy. Three different oblique crushing simulations of 10∘, 20∘ and 30∘ illustrate that the AA6061-T6 rectangular tube at 10∘ mainly occurs progressive folding deformation. while the other two oblique crushing angles undergo global buckling deformation. The total energy absorption at 10∘ is 1.87 and 2.43 times of that at 20∘ and 30∘, respectively. The crushing force efficiency of 20∘ and 30∘ is 41.28 % and 31.8 % lower than that of 10∘, respectively. A comprehensive understanding of the energy absorption performance of AA6061-T6 thin-walled rectangular tube under different crushing conditions is helpful to determine its position and shape as a vehicle safety structure, and to exert its optimal plastic deformation potential to dissipate the collision energy and ensure passenger safety.

Electromagnetically driven flow in unsupported electrolyte layers: lubrication theory and linear stability of annular flow

We consider a thin horizontal layer of a non-magnetic electrolyte containing a bulk solution of salt and carrying an electric current. The layer is bounded by two deformable free surfaces loaded with an insoluble surfactant and is placed in a vertical magnetic field. The arising Lorentz force drives the electrolyte in the plane of the layer. We employ the long-wave approximation to derive general two-dimensional hydrodynamic equations describing symmetric pinching-type deformations of the free surfaces. These equations are used to study the azimuthal flow in an annular film spanning the gap between two coaxial cylindrical electrodes. In weakly deformed films, the base azimuthal flow and its linear stability with respect to azimuthally invariant perturbations are studied analytically. For relatively thick layers and weak magnetic fields, the leading mode with the smallest decay rate is found to correspond to a monotonic azimuthal velocity perturbation. The Marangoni effect leads to further stabilisation of the flow while perturbations of the solute concentration in the bulk of the fluid have no influence on the flow stability. In strongly deformed films in the diffusion-dominated regime, the azimuthal flow becomes linearly unstable with respect to an oscillatory mixed mode characterised by the combination of radial and azimuthal velocity perturbations when the voltage applied between electrodes exceeds the critical value.

STUDY OF DEFORMABILITY OF THE LARGE-SPAN ROOF STRUCTURAL SYSTEM IN THE FORM OF AN ASYMMETRICAL SHELL

The scientific article is devoted to a complex study of deformability of saddle-type shell of negative Gaussian curvature of a public object that has been in operation for a long time for further general restoration of the building’s roofing system. The authors have developed a specific algorithm for conducting experimental research, providing additional static load on a shell at the lower point of the gentle axial line of the supporting arches. To smoothly carry out the loading procedure, we mounted containers in barrel form on the roof surface and gradually filled them with water. We carried out an experimental evaluation of the bearing capacity of the shell with the determination of the redistribution of forces along the length of the section in the lower zone of the conventionally outlined arch. The experimental test results revealed that the deformability of the shell surface under short-term loading did not exceed 2.0 mm, and, under long-term loading, it was no more than 4.0 mm. Analysis of the qualitative features of structure deformation shows that the displacement of the roof’s points, located symmetrically to the vertical axis, has the opposite sign to the sign of the displacement of the actual ‘saddle’ point (the case of symmetrical deformation). We conducted a numerical verification of the behaviour of the investigated structure by forming a detailed finite element spatial model of the shell. Comparison of the results of numerical calculation with the results of field tests shows the coincidence of qualitative and quantitative parameters, which, in turn, characterises the developed theoretical model as fully adequate and suitable for analysing the stress-strain state of similar large-span structural systems. Based on the results of comprehensive theoretical and experimental research, we made proposals for the further restoration of the roofing structure with the limitation of the self-weight of the covering to 1 kN/m2. Engineers and scientists can use the research results to reconstruct similar authentic structural systems. Keywords: calculation, restoration, loading, deflection, shell, negative Gaussian curvature.

Gravitational radiation of a spherically symmetric source in f(R)-gravitation

It is shown that Birkhoff’s theorem for the general theory of relativity is overcome in the f(R)-theory of gravitation. That means, the f(R)-theory of gravitation, unlike Einstein’s general theory of relativity, does not forbid gravitational radiation from a spherically symmetric source (whether stationary or non-stationary). As a consequence, in the f(R)-theory a spherically symmetric gravitational deformation (e.g., collapse/expansion or pulsation) could emit gravitational waves (of tensor- and scalar polarization modes), a phenomenon impossible in the general relativity. A test model is examined and it turns out that the gravitational radiation is strongest when the surface of the deforming object is in the vicinity of the (modified) event horizon, even suddenly flares up just outside the latter. In this letter, within the f(R)-theory of gravitation, a gravitational wave equation and a formula for the gravitational emission power are derived. These formulae, along with searching for signals, can be used for the experimental test of the f(R)-theory. In general, including the spherically symmetry case, gravitational radiation of both tensor- and scalar polarization modes are allowed, although under some circumstance the contribution of scalar modes is strongly suppressed.

Stationary dimpled drops under linear flow

The axially symmetric deformation of a drop in a viscous fluid, under the influence of an externally imposed flow having simultaneous rotating and compressional or extensional components, is addressed. In the previous studies, two families of stationary drop shapes were constructed by simulating the dynamics of drop deformation: stable singly connected shapes with respect to axisymmetric disturbances, and unstable toroidal shapes. These two branches coexist at the same flow conditions, but were not connected. In this study, we obtain a new family of branches of unstable highly deformed stationary drops connecting with the stable flattened shapes and the toroidal ones. We use a method based on classical control theory. The controller is designed for a two-state dynamic model of the system and is employed on a high-order nonlinear dynamic model of the drop deformation. Through this feedback-control-centred approach, an extended collection of unstable stationary solutions is constructed, which spans the range from the loss of stability to the dimpled shapes almost collapsed at the centre. In the latter region, which was never obtained in previous studies, a multiplicity of solutions is identified.

Energy absorption capacity under tensile and compressive loads of auxetic metamaterial structures

An auxetic metamaterial is a mechanical metamaterial with a negative Poisson’s ratio. When compressed or stretched in one direction, it contracts or expands in a perpendicular direction. This review paper focuses on the energy absorption of auxetic metamaterial structures and their applications. Starting with the original structure proposed by D. Han et al., another structural model with heuristically enhanced ribs is proposed to suit the structure’s anisotropy, reduce mass, and increase energy absorption. An extension to this is the newly designed MH-1 model, which is lightweight compared to commonly reported auxetic forms. Numerical results show that MH-1 has the best specific energy absorption and exhibits an obvious auxetic effect under tension, with symmetrical and stable deformation modes. Auxetic metamaterials are also progressively finding applications in the biomedical field. One of the most promising applications of auxetic is in the development of new and improved prosthetics and implants.

Application of Homotopy Analysis Transform Method for Solving a Fractional Singular One-Dimensional Thermo-Elasticity Coupled System

This article extends the application of fractional-order time derivatives to replace their integer-order counterparts within a system comprising two singular one-dimensional coupled partial differential equations. The resulting model proves invaluable in representing radially symmetric deformation and temperature distribution within a unit disk. The incorporation of fractional-order derivatives in mathematical models is shown to significantly enhance their capacity for characterizing real-life phenomena in comparison to their integer-order counterparts. To address the studied system numerically, we employ the q-homotopy analysis transform method (q-HATM). We evaluate the efficiency of this method in solving the problem through a series of illustrative examples. The convergence of the derived scheme is assessed visually, and we compare the performance of the q-HATM with that of the Laplace decomposition method (LDM). While both methods excel in resolving the majority of the presented examples, a notable divergence arises in the final example: the numerical solutions obtained using q-HATM converge, whereas those derived from LDM exhibit divergence. This discrepancy underscores the remarkable efficiency of the q-HATM in addressing this specific problem.

Integrated design and additive manufacturing of lattice-filled multi-cell tubes

In this paper, 3D printed lattice-filled multi-cell tubes, fabricated using chopped carbon-fiber-reinforced polyamide, were proposed to modify the deformation modes and improve the crashworthiness. Compression responses and energy absorption characteristics of the multi-cell tubes were investigated by quasi-static compression tests. The deformation and synergistic effect mechanisms of lattice-filled tubes were studied by observing the longitudinal sections of specimens. It was found that filling the lattice into multi-cell tubes exhibited an increase in the number of folds. When the lattice-filled tubes were fabricated integrally, multi-cell tubes changed from an asymmetrical to a symmetrical folding deformation mode due to the stronger and symmetrical interactions from the internal-filled lattice. Under the influence of the synergistic effect, the total energy absorption of the lattice-filled tubes with two different combination strategies presented increases of 55.6% and 83.8% compared with the sum of the empty multi-cell tube and pure lattice. In addition, a theoretical analysis for the mean crushing force of composite lattice-filled tubes was conducted based on simplified super folding element (SSFE) theory and bending deformation mechanism of the struts. The theoretical results were in good agreement with experimental studies and could be extended for lattice-filled tubes with other different filling configurations.

Finite element modeling of spherical indentation behavior of 3D mesh fabric at the yarn level

This paper reports an experimental and numerical study on the spherical indentation behavior of three-dimensional (3D) warp-knitted mesh fabrics. A full-size finite element (FE) model of a typical 3D mesh fabric is established at the yarn level based on the realistic monofilament architecture from micro-computed tomography (μCT) scanning and verified with experiments. The structural change of the fabric in the spherical indentation process is quantitatively analyzed in terms of fabric global deformation, local deformation, mesh deformation, and spacer monofilament deformation from the FE simulation. The numerical results show that the fabric shrinks walewise and expands coursewise from the spherical indentation of the continuous intermeshed monofilament architecture, showing counterintuitive partial auxeticity. The coursewise symmetry and walewise asymmetry of the 3D mesh fabric produce relatively symmetrical coursewise deformation and asymmetrical walewise deformation under spherical indentation. The symmetrical coursewise deformation includes even widening, good fitting of the indenter, and almost identical mesh sizes in the coursewise direction. Walewise asymmetry leads to uneven shortening, inferior fitting of the indenter, and considerably varied mesh sizes in the walewise direction. Spacer monofilaments in different positions relative to the spherical indenter have different deformations. The closer to the indenter, the greater bending and twisting of the spacer monofilament. The spacer monofilament knitted earlier of the tested fabric has smaller deformation than that knitted later due to the walewise asymmetry. The coursewise symmetry and walewise asymmetry of the inhomogeneous 3D mesh fabric structure result in a highly nonlinear spherical indentation behavior.

Speculation of fluid dynamics equations based on Liutex theory and constitutive relation of symmetric shearing deformation

Speculation of fluid dynamics equations based on Liutex theory and constitutive relation of symmetric shearing deformation