Geometric Anisotropy Research Articles

Anisotropy, hole, and hybridization influences in polyester polymer composites reinforced by glass and glass/Kevlar

AbstractThis study aimed at determining the mechanical properties, residual properties, and mechanical fracture characteristics of two composite laminates reinforced with different types of fibers, the first using a bidirectional fabric of E‐glass fibers and the second, also bidirectional, a hybrid strand of E‐glass and Kevlar 49 fibers. Both laminates consist of four layers of fabric reinforced with Polilyte 10316‐10 polyester resin. Two types of studies were conducted on the laminates: the presence of a geometric discontinuity (central hole) and anisotropy, that is, different fiber arrangements in relation to the applied load. The directions are 0°/90° and ±45°. Another study was carried out on the hybridization process in the composition of reinforcement fabric strands. In all the studies, the test specimens were submitted to uniaxial tensile testing. The results demonstrate the influence of anisotropy, hybridization, and the presence of a central hole on the mechanical response and fracture characteristics of composite laminates, with the 0°/90° configuration exhibiting greater tensile strength in all the conditions studied.

Exploring geometric anisotropy for point-referenced spatial data

Isotropic covariance functions are routinely adopted in specifying models for point-referenced spatial data but carry the limitation that spatial dependence is not directional. Geometric anisotropic covariance functions offer a class of stationary specifications which incorporate directional dependence through spatial range. They have received modest attention in the literature but can provide flexible and readily interpretable directional dependence. Within a Bayesian framework, this paper attempts to illuminate when and how much such models for random effects in geostatistical settings improve out-of-sample predictive performance. We show that geometric anisotropy yields better predictive performance when the residuals strongly depart from isotropy (anisotropy ratio is much greater than one) and sample size is fairly large. Also, improvement is more prominent when the spatial variance is much greater than the pure error variance. The investigation of predictive performance is illustrated through simulation as well as modeling of real data on PM2.5 monitoring stations.

Shear behaviors of granular mixtures of gravel-shaped coarse and spherical fine particles investigated via discrete element method

The shear behaviors of granular mixtures are studied using the discrete element method. These granular materials contain real gravel-shaped coarse particles and spherical fine particles. Dense samples have been created by the isotropic compression method. The samples are then sheared under drained triaxial compression to a large strain to determine the peak and residual shear strengths. The emphasis of this study is placed on assessing the evolutions of contributions of the coarse-coarse (CC) contacts, coarse-fine (CF) contacts and fine-fine (FF) contacts to the peak and critical deviator stresses. The results are used to classify the structure of granular mixtures. Specifically, the granular mixtures are fine-dominated or coarse-dominated materials when the coarse particle content is <30%–40% or >65%–70%, respectively. A comparison with previous findings suggests that the spherical binary mixtures will become coarse-dominated materials at a relatively larger coarse particle content (i.e., 75%–80%) than this study (i.e., 65%–70%), which is attributed to the particle shape effect of coarse particles. A microscopic analysis of CC, CF and FF contacts at the peak and critical states, including normal contact forces and proportions of strong and weak contacts of each contact type to total contacts, reveals why the contributions of CC, CF and FF contacts to the peak and residual shear strengths are varied. Finally, a detailed analysis of the anisotropies indicates that the increases of peak and residual shear strengths are primarily related to the gradual increases in geometrical anisotropy ac and tangential contact force anisotropy at to compensate for the continuous decrease in normal contact force anisotropy an. Furthermore, it is interesting to note that the branch vector frame provides a better linear relationship between the stress ratio and the geometric anisotropy of the strong and nonsliding subnetwork than the contact frame for the coarse-dominated materials.

STUDY OF STRUCTURAL ORGANIZATION OF SYSTEMS ON BASIS OF p-n-PROPYLOXICINNAMIC ACID AND NONMESOGENES OF Ph–X–Ph TYPE

The variants of structural organization in the systems “mesogen – nonmesogen” are considered. The systems contain p-n-propyloxycinnamic acid (A), as a mesogenic component, and nonmesogenic Ph–X–Ph compounds: phenyl benzoate (B, where X = –COO–), azobenzene (C, where X = –N=N–) and N-benzylideneaniline (D, where X = –CH=N–). Quantum-chemical modeling of possible structural units in such systems has been performed. It was shown that all assumed A∙∙∙X(Ph)2 H-complexes do not have electronic and geometric anisotropy and have a lower intermolecular interaction energy than the cyclic dimer of acid A∙∙∙A. The calculated values of the Gibbs free energy of complexation reactions also indicate a low probability of the formation of A∙∙∙X(Ph)2 type H-complexes. It is noted that the “length” of the A∙∙∙A dimer is comparable with the doubled “length” of Ph–X–Ph molecules, which, like the acid dimer, have a rod-like structure favorable for the formation of nematic and smectic LC phases. Based on the analysis of the quantum chemical calculations, it was assumed that Ph–X–Ph can be embedded between acid cyclic dimers A∙∙∙A and can facilitate reduce intermolecular interactions in the system, which reduces the temperature of Cr–LC transitions. The proposed structural organization of systems A: Ph–X–Ph is confirmed by an experimental IR spectrum for a similar system, in which the bands corresponding to the vibrational frequencies of the acid dimer and to individual molecules of alkyloxy substituted phenyl benzoate B are recorded.

Regulating wrinkling patterns by periodic surface stiffness in film-substrate structures

Surface wrinkling of materials holds promise for important applications in diverse fields such as multifunctional surfaces and biomedical engineering. For these applications, it is of interest to attain various surface wrinkles with tunable wavelengths and amplitudes. Through a combination of experiments and numerical simulations, we here propose a method to regulate the wrinkling patterns in a film-substrate system by introducing periodic surface stiffness, which is generated through sequential specified ultraviolet-ozone (UVO) treatments. Both experiments and numerical simulations demonstrate that the proposed technique can produce various patterns with wide, tunable geometrical features and anisotropy. The effects of surface stiffness distribution, the exposure durations of UVO-treatments, and the loading biaxiality are examined on the generated surface patterns.

Geochemical modelling and mapping of Cu and Fe anomalies in soil using combining sequential Gaussian co-simulation and local singularity analysis: a case study from Dedeyazı (Malatya) region, SE Turkey

Mapping and modelling of the spatial distribution of geochemical anomalies is a key task for geochemical exploration. This case study explores mapping and modelling of Cu and Fe geochemical anomalies combining the Sequential Gaussian Co-simulation (SGCS) method and Local Singularity Analysis (LSA) in the Malatya region, SE Turkey. A total of 652 topsoil samples were collected on a regular grid design from the study area. A cell declustering technique was applied to the raw data. Both geometric and zonal anisotropy exist in the directional variogram of Cu and Fe. SGCS was applied to create maps representing an equally probable spatial distribution of Cu and Fe geochemical anomalies. SGCS results have been validated by a variety of tests including the reproduction of the variograms, histograms, descriptive statistics and contour plots. LSA is based on a sliding window estimation approach applied to the grid data created for SGCS realization. LSA was carried out and mapped via the results of the realization on the same grid layout. Critical anomaly threshold values of the variables were identified using the singularity and quantile plot. Integration of SGCS and LSA results provides quantification of the uncertainty of spatial distribution and determination of Cu and Fe critical thresholds.

Spreading Out: Modeling the Physics of Cell-Substrate Interaction in Cell Spreading and Focal Adhesion Evolution

Cell spread area and focal adhesion (FA) sizes are known to increase with substrate stiffness (Yeung et al., Cell Motil. Cytoskeleton., 2005). Different mathematical models have been developed, some of which can predict increases in cell spread area with substrate stiffness while others can predict increases in only the FA area. Here, we describe a two-dimensional model of an actively spreading cell interacting with a deformable elastic substrate through spring-like FA complexes. The model couples FA evolution, intracellular stress, and active cell spreading. With these three components coupled, we demonstrate the ability of our model to qualitatively reproduce both, the increase in cell spread area and FA area with substrate stiffness that has been observed experimentally, as well as the temporal evolution of cell spread areas. To predict the stiffness dependence and the temporal evolution of cell spreading we find there are three key mechanisms: i) cell substrate attachments at the periphery, ii) attachments in the interior generating retrograde flow, and iii) the resistance to spreading from the tensile forces at the cell periphery due to the membrane. The 2D model allows us to capture the role of spatial localization of these different phenomena and the sensitivity of these mechanisms in enabling the observed global behaviors. Using this model, we generate insights on the role of both spatial coupling and integration of the signals to generate large scale changes in cellular dynamics. We also investigate the role of geometric anisotropy through non-circular shapes during spreading. The overarching aim of this work has been to specify what minimal physical mechanisms are required to recapitulate cellular spreading and FA evolution and their mechanical response to the underlying substrate.

Thermal transport properties of penta-graphene with grain boundaries

Penta-graphene (PG), composed of carbon pentagons, has attracted considerable attention because of its unique atomic configuration and novel properties. Here, for the first time, we study the effect of grain boundaries (GBs) on the thermal transport properties of PG by using non-equilibrium molecular dynamics simulations. Compared with pristine PG, the thermal conductivity of grains in polycrystalline penta-graphenes (PPGs) decreases by about 20%. The boundary conductance of PPGs with different GBs is in a small range of 0.43 × 1010 to 0.57 × 1010 W/mK, which differs from the situation of polycrystalline graphene where the boundary conductance decreases dramatically with the increase of grain orientation angles. The critical size of the grains is found to be about 25 nm, below which the contribution from GBs to the thermal conductivity is comparable to that from the grains. This critical size is much smaller than that of polycrystalline graphene (100 nm). A detailed analysis of the phonon group velocity and vibrational density of states reveals that the geometric anisotropy and the phonon scattering induced by the GBs in PPG are the main reasons for the reduction of thermal conductivity. Our study sheds lights on tuning thermal conductivity via GB engineering in 2D materials.

Influence geometric anisotropy in management zones delineation

The proper handling soil allows the reduction of contaminants, maximize agricultural productivity, and is directly related the knowledge spatial variability of soil attributes. This spatial variability can express isotropic and anisotropic form. The latter being neglected in research related to management zones delineation. In this context, the present study aimed to evaluate the effect of the geometric anisotropy correction on the management zone delineation. The methodology was applied under database of soybean productivity and apparent electrical conductivity (CEa) of a rural property in Ponta Pora – MS. By means of this georeferenced database, maps was interpolated with ordinary kriging. For each combination, attribute (productivity and CEa) and number of classes, were produced two maps management zones, one without and one with anisotropy correction, the same were compared through the kappa index, with significance tested by the Z-test. The management zones number was also evaluated by Fuzziness Performance Index (FPI) and the Modified Partition Entropy (MPE). The area subdivision in two management zones, without and with anisotropy correction, presented higher Kappa index, with values of 0.89 and 0.91 respectively, but not presented significant differences with each other.

Modification of crustal seismic anisotropy by geological structures (“structural geometric anisotropy”)

Modification of crustal seismic anisotropy by geological structures (“structural geometric anisotropy”)

Optical beam propagation in soft anisotropic biological tissues

We introduce a geometrical anisotropy parameter in the power spectrum of soft biological tissue and study its effects on the statistics of light beams propagating in it, in addition to the effects of other parameters, such as the refractive index variance, the slope of the power spectrum, and the inner/outer scales of the tissue. In particular, we discuss the behavior of widely known Gaussian Schell-model beams, and the theory can be readily adapted to other beams. Our results based on the extended Huygens-Fresnel integral indicate that the spectral density of the beam starts acquiring an elliptical profile at distances on the order of millimeters from the plane of incidence. We also find that, since the inner scale of a typical bio-tissue is smaller than the wavelength of light, the beams become incoherent at submicron distances and, hence, the effects of the source degree of coherence of the beam are not practically detectable. Our results may be applicable to light propagation in inherently anisotropic biological tissues, such as the ones containing fibers, or isotropic tissues under mechanical stresses.

On the avascular ellipsoidal tumour growth model within a nutritive environment

The present work is part of a series of studies conducted by the authors on analytical models of avascular tumour growth that exhibit both geometrical anisotropy and physical inhomogeneity. In particular, we consider a tumour structure formed in distinct ellipsoidal regions occupied by cell populations at a certain stage of their biological cycle. The cancer cells receive nutrient by diffusion from an inhomogeneous supply and they are subject to also an inhomogeneous pressure field imposed by the tumour microenvironment. It is proved that the lack of symmetry is strongly connected to a special condition that should hold between the data imposed by the tumour’s surrounding medium, in order for the ellipsoidal growth to be realizable, a feature already present in other non-symmetrical yet more degenerate models. The nutrient and the inhibitor concentration, as well as the pressure field, are provided in analytical fashion via closed-form series solutions in terms of ellipsoidal eigenfunctions, while their behaviour is demonstrated by indicative plots. The evolution equation of all the tumour’s ellipsoidal interfaces is postulated in ellipsoidal terms and a numerical implementation is provided in view of its solution. From the mathematical point of view, the ellipsoidal system is the most general coordinate system that the Laplace operator, which dominates the mathematical models of avascular growth, enjoys spectral decomposition. Therefore, we consider the ellipsoidal model presented in this work, as the most general analytic model describing the avascular growth in inhomogeneous environment. Additionally, due to the intrinsic degrees of freedom inherited to the model by the ellipsoidal geometry, the ellipsoidal model presented can be adapted to a very populous class of avascular tumours, varying in figure and in orientation.

Undrained behavior of binary granular mixtures with different fines contents

Binary granular mixtures are comprehensively explored from both macro- and microscopic perspectives. In this study, the undrained behavior of binary granular mixtures constituted by fine and coarse particles is investigated using the discrete element method (DEM) under different fines contents (FCs). The peak deviatoric stress ratio has a linear relation with the effective void ratio. The increase in the FC to a certain value (approximately 10% in this work) can change the material response from strain hardening to limited “liquefaction”. The enhanced strain hardening behaviors were observed when the FC exceeds 15%. The location of the critical state line (CSL) depends on the fines content. Voronoi tessellation was adopted to explore the mesoscale structures of binary mixtures. The local isotropy, local anisotropy, and sphericity of the Voronoi cells are clearly related to the FC. The radial distribution functions (RDFs) also exhibit clear correlations with the FC. The abundance and mechanical contributions of different types of contacts, e.g., coarse-coarse, coarse-fine, and fine-fine contacts, are analyzed. For these binary systems, the proportions of the sliding contacts with respect to the FCs are contact-type dependent. The coaxiality between the loading direction and fabric orientation of the different contact types depends on the relative proportions of the contact types. The evolutions of the global anisotropies are also explored, and the contact-based anisotropy parameters extracted at peak states under various FCs are compared to the global anisotropy parameters. The stress-force-fabric relationship is evaluated in various subnetworks of the mixtures and discussed in terms of the strong-weak partition and nonsliding-sliding partition networks. The dominant role of geometrical anisotropy derived from the strong subnetwork is emphasized, and the linear relationship between the global stress ratio and the geometrical anisotropy within strong-nonsliding subnetwork is evidently observed under various conditions of fines content.

Geometric anisotropy modeling and shear behavior evaluation of graded crushed rocks

To reveal the meso-mechanical mechanism of shear behaviors in the graded crushed rocks (GCRs), which are heterogeneous in geometry and widely used in the flexible pavement, a numerical technique was proposed to simulate the geometric anisotropy of the GCRs using randomly generated models. Then, studies on meso-mechanical responses during the loading were performed through the biaxial shear test and California bearing ratio (CBR) test. The results showed that the changes of both friction and anisotropy had a similar trend with the particle size enlarging in the dense assembly, which maintain stable when the size is less than 3.0 mm. In addition, the breaking sieve (BS) between coarse and fine aggregates was six times of the base diameter (0.8 mm). The predicted shear properties in macrostructure were in good agreement with those laboratory measurements. For the shear behaviors, the fractures and force chains were mainly distributed in the area of action that was limited by force size and side boundary.

Density functional theory calculations for magnetic properties of Co3W systems

Cheaper permanent magnetic nanostructures with magnetic properties equivalent to those of noble-metal or rare-earth nanomagnets have been experimentally developed for their potential applications in ultrahigh storage densities in magnetic memory. To date, their intrinsic magnetic properties are not well understood under the micro-level of local atomic arrangements and electronic structures. In this work, we performed theoretical investigations on the Co3W bulk, the clean surface, nanoclusters, and the Co|Co3W bilayers and superlattices for their geometrical structures, magnetic moments, and magnetic anisotropy energies (MAEs). We found that the Co3W nanostructures we constructed are stable and have the local minima in the energetic landscape, whose stabilities increase with increasing proportion of W and cluster size. The Co and W atoms in clusters are antiferromagnetically coupled, and their local magnetic moments decrease with increasing proportion of W. The breakdown of the Hund's third rule in W atoms observed in experiment can be interpreted as the competition between the intra-atomic spin-orbit coupling in W atoms and interatomic Co-W hybridizations. The highest MAE of about a few tens of meV is obtained in small cluster sizes, whereas it is an order of magnitude reduction in large cluster sizes. The magnetic systems of Co3W clean surface, Co|Co3W bilayer and superlattice can present large MAEs, and their easy-axes of magnetization are perpendicular to the (001) surface. Our calculated MAEs are of the same order of magnitude as that of the experimental measurements, and the electronic origin is revealed through the second-order perturbation method.

Prediction of tensile deformation behavior of Al-Li alloy 2060-T8 by computational homogenization-based crystal plasticity finite element method

In current study, a computational homogenization-based crystal plasticity (CP) modelling was presented to determine the deformation behavior of a novel third-generation AL-Li alloy 2060-T8 at room temperature, strain rate of 0.01 s−1and various loading directions. The computational homogenization strategy used a representative volume element (RVE) which describes the real microstructure of AA2060-T8 sheet to consider the in-grains deformation behavior. Besides, a periodically boundary condition was modified to consider both deformation induced anisotropy and the geometrical anisotropy. The initial microstructures and micro-textures of the AA2060-T8 sheet were determined by EBSD measurements, as well as used to build up the RVE model. The material parameters used in CP modelling was determined from the stress-strain curve obtained from the tensile test at strain rate of 0.001 s−1 and loading direction of 30° with reference to rolling direction. The results obtained from computational homogenisation strategy keep a remarkable agreement with the results determined from experimentation. In conclusion, the computational homogenization based CPFEM is able to predict the deformation behavior and capture the anisotropic response of AA2060-T8 sheet at various deformation conditions.

Multifunctional ferrofluid-infused surfaces with reconfigurable multiscale topography.

Developing adaptive materials with geometries that change in response to external stimuli provides fundamental insights into the links between the physical forces involved and the resultant morphologies and creates a foundation for technologically relevant dynamic systems1,2. In particular, reconfigurable surface topography as a means to control interfacial properties3 has recently been explored using responsive gels4, shape-memory polymers5, liquid crystals6-8 and hybrid composites9-14, including magnetically active slippery surfaces12-14. However, these designs exhibit a limited range of topographical changes and thus a restricted scope of function. Here we introduce a hierarchical magneto-responsive composite surface, made by infiltrating a ferrofluid into a microstructured matrix (termed ferrofluid-containing liquid-infused porous surfaces, or FLIPS). We demonstrate various topographical reconfigurations at multiple length scales and a broad range of associated emergent behaviours. An applied magnetic-field gradient induces the movement of magnetic nanoparticles suspended in the ferrofluid, which leads to microscale flow of the ferrofluid first above and then within the microstructured surface. This redistribution changes the initially smooth surface of the ferrofluid (which is immobilized by the porous matrix through capillary forces) into various multiscale hierarchical topographies shaped by the size, arrangement and orientation of the confining microstructures in the magnetic field. We analyse the spatial and temporal dynamics of these reconfigurations theoretically and experimentally as a function of the balance between capillary and magnetic pressures15-19 and of the geometric anisotropy of the FLIPS system. Several interesting functions at three different length scales are demonstrated: self-assembly of colloidal particles at the micrometre scale; regulated flow of liquid droplets at the millimetre scale; and switchable adhesion and friction, liquid pumping and removal of biofilms at the centimetre scale. We envision that FLIPS could be used as part of integrated control systems for the manipulation and transport of matter, thermal management, microfluidics and fouling-release materials.

An experimental evidence of the failure of Cauchy elasticity for the overall modeling of a non-centro-symmetric lattice under static loading

Materials with coarse inner architecture being easily made with modern additive or folding processes, the question of their overall behavior rises. Do they behave like classical elastic continua, or do they exhibit additional higher-order effects ? Further, if present are those effects stable with respect to imperfections (geometry, constitutive material, ...) ? In this view, the current work is an experimental investigation for the need, in static, of a higher-order overall description. It comes from noticing that such behaviors are up to now nearly exclusively studied from a theoretical and numerical point of view. In the present study a non-centro-symmetric sample has been manufactured, based on an industrial honeycomb geometry used for aeronautic/aerospace composite materials. The geometrical anisotropy of the elementary cell and the scale separation ratio have been chosen in order to detect non-classical couplings. Samples are obtained by Fused Deposition Modeling (FDM), one of the most widespread 3D printing techniques. Simple experiments based on load controlled tests with full-field kinematic measurement have been performed. A distributed load control reveals that the overall behavior of the architectured material cannot be described within the realm of Cauchy elasticity.

Effect of the particle size ratio on the structural properties of granular mixtures with discrete particle size distribution

In this study, the discrete element method was used to examine the structural properties and geometric anisotropy of polydisperse granular packings with discrete uniform particle size distributions. Confined uniaxial compression was applied to granular mixtures with different particle size fractions. The particle size fraction (class) was defined as the fraction of the sample composed of particles with a certain size. The threshold value of number of particle size fractions (i.e., the value above which structural properties of assemblies remain constant) was determined. The effect of heterogeneity in particle size on the critical value of number of particle size fractions was investigated for packings with different ratios between diameters of the largest and smallest grains. The threshold number of particle size classes decreased from five to three as the diameter ratio between the largest and smallest grains increased. Regardless of the diameter ratio, the critical number of particle size fractions (above which the packing density and coordination number of the granular mixtures remained constant) was determined to be five. The study has also shown an increase in packing density of binary mixtures with particle size ratio increasing up to 2.5, which was followed by decrease in density of mixtures with larger particle size ratios, which has not so far been reported in the literature.

RELATIONSHIP BETWEEN SAMPLE DESIGN AND GEOMETRIC ANISOTROPY IN THE PREPARATION OF THEMATIC MAPS OF CHEMICAL SOIL ATTRIBUTES

Spatial variability depends on the sampling configuration and characteristics associated with the georeferenced phenomenon, such as geometric anisotropy. This study aimed to determine the influence of the sampling configuration on parameter estimation in an anisotropic geostatistical model and the spatial estimation of a georeferenced variable at non-sampled locations. The simulation results are used as a reference to select anisotropic models to describe the spatial dependence structure in chemical soil properties. The choice of the sampling configuration influenced the spatial estimation of the georeferenced variable and the quality of the estimation of the geostatistical anisotropic model. The incorporation of geometric anisotropy in the spatial estimation of simulated data sets and soil chemical properties produced a difference in the spatial estimation and improved the level of detail of subregions in thematic maps.