Showing papers on "Isotropy published in 2016"

Elastic anisotropy of crystals

Abstract: An anisotropy index seeks to quantify how directionally dependent the properties of a system are. In this article, the focus is on quantifying the elastic anisotropy of crystalline materials. Previous elastic anisotropy indices are reviewed and their shortcomings discussed. A new scalar log-Euclidean anisotropy measure AL is proposed, which overcomes these deficiencies. It is based on a distance measure in a log-Euclidean space applied to fourth-rank elastic tensors. AL is an absolute measure of anisotropy where the limiting case of perfect isotropy yields zero. It is a universal measure of anisotropy applicable to all crystalline materials. Specific examples of strong anisotropy are highlighted. A supplementary material provides an anisotropy table giving the values of AL for 2,176 crystallite compounds.

Isotropic and anisotropic elasticity and yielding of 3D printed material

Abstract: 3D printing provides an innovative manufacturing method for composite materials. The mechanical property is vital for understanding the performance of 3D printed material and needs to be further studied. In this paper, the elasticity and yielding performance of acrylonitrile butadiene styrene (ABS) material created by 3D printing is investigated and the effect of printing orientation on mechanical property is quantitatively evaluated with experiments. Due to the layer by layer process procedure, 3D printed materials behave with anisotropic property. According to this characteristic, a transversely isotropic model is put forward in form of constitutive equations and is compared with isotropic model. Considering the influence of printing orientation, isotropic and anisotropic elastic and yielding model are established. The printed materials with different printing orientations are applied in uniaxial tensile tests. The material parameters, meaning the Young’s modulus, Possion’s ratio and yielding stress are determined by experiments. The results show that the printed ABS material has the Young’s modules as 2400 MPa, Poisson’s ratio as 0.37 and yielding stress as 26.84 MPa as isotropic material when the influence of printing orientation is neglected. Parameters for anisotropic model are also given and the model is recommended if the better precision concerning printing orientations is required. The obtained material parameters can be used in the mechanical simulation of 3D printed objects. The established isotropic and anisotropic models are basic findings to describe mechanical property of printed materials and can be expanded to other materials produced by 3D printing.

Tailoring the texture of IN738LC processed by selective laser melting (SLM) by specific scanning strategies

Abstract: Selective laser melting (SLM) is an emerging technology of additive manufacturing, which is used to directly produce metallic parts from thin powder layers. This study aims at correlating laser scanning strategies with the resulting textures and corresponding anisotropy of the elastic behavior of bulk materials. Tensile test specimens made of the γ’-containing Ni-base superalloy IN738LC were built with the loading direction oriented either parallel (z-specimens) or perpendicular to the build-up direction (xy-specimens). Their bulk mechanical properties were determined at room temperature and at 850 °C. Specimens were investigated in the ‘as-built’ condition and after recrystallization heat treatment. SEM-based electron backscatter diffraction (EBSD) was applied to measure their crystallographic preferred orientations (texture) and to correlate the anisotropy of Young's modulus with the texture of the material. It is shown that the applied laser scanning strategies allow to tailor the crystallographic texture locally. The possibility to switch from transverse anisotropic to transverse isotropic properties and reverse is demonstrated for triple layered tensile samples. A recrystallization heat treatment reduces the degree of crystallographic texture and thus the elastic anisotropy by abundant annealing twinning. Predictions of Young's modulus calculated from the measured textures compare well with the data from tensile tests.

Isotropic Negative Thermal Expansion Metamaterials.

Abstract: Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve two- and three-dimensional negative thermal expansion metamaterials via antichiral structures. The two-dimensional metamaterial is constructed with unit cells that combine bimaterial strips and antichiral structures, while the three-dimensional metamaterial is fabricated by a multimaterial 3D printing process. Both experimental and simulation results display isotropic negative thermal expansion property of the samples. The effective coefficient of negative thermal expansion of the proposed models is demonstrated to be dependent on the difference between the thermal expansion coefficient of the component materials, as well as on the circular node radius and the ligament length in the antichiral structures. The measured value of the linear negat...

Thermal stability of functionally graded sandwich plates using a simple shear deformation theory

Abstract: In the present work, a simple first-order shear deformation theory is developed and validated for a variety of numerical examples of the thermal buckling response of functionally graded sandwich plates with various boundary conditions. Contrary to the conventional first-order shear deformation theory, the present first-order shear deformation theory involves only four unknowns and has strong similarities with the classical plate theory in many aspects such as governing equations of motion, and stress resultant expressions. Material properties and thermal expansion coefficient of the sandwich plate faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are considered as uniform, linear and non-linear temperature rises within the thickness direction. The results reveal that the volume fraction index, loading type and functionally graded layers thickness have significant influence on the thermal buckling of functionally graded sandwich plates. Moreover, numerical results prove that the present simple first-order shear deformation theory can achieve the same accuracy of the existing conventional first-order shear deformation theory which has more number of unknowns.

A new model for spherically symmetric anisotropic compact star

Abstract: In this article we obtain a new anisotropic solution for Einstein’s field equations of embedding class one metric. The solution represents realistic objects such as Her X-1 and RXJ 1856-37. We perform a detailed investigation of both objects by solving numerically the Einstein field equations with anisotropic pressure. The physical features of the parameters depend on the anisotropic factor i.e. if the anisotropy is zero everywhere inside the star then the density and pressures will become zero and the metric turns out to be flat. We report our results and compare with the above mentioned two compact objects as regards a number of key aspects: the central density, the surface density onset and the critical scaling behaviour, the effective mass and radius ratio, the anisotropization with isotropic initial conditions, adiabatic index and red shift. Along with this we have also made a comparison between the classical limit and theoretical model treatment of the compact objects. Finally we discuss the implications of our findings for the stability condition in a relativistic compact star.

Chiral three‐dimensional isotropic lattices with negative Poisson's ratio

Abstract: Chiral three-dimensional isotropic cubic lattices with rigid cubical nodules and multiple deformable ribs are developed and analyzed via finite element analysis. The lattices exhibit geometry-dependent Poisson's ratio that can be tuned to negative values. Poisson's ratio decreases from positive to negative values as the number of cells increases. Isotropy is obtained by adjustment of aspect ratio. The lattices exhibit significant size effects. Such a phenomenon cannot occur in a classical elastic continuum but it can occur in a Cosserat solid.

Second strain gradient elasticity of nano-objects

Abstract: Mindlin's second strain gradient continuum theory for isotropic linear elastic materials is used to model two different kinds of size-dependent surface effects observed in the mechanical behaviour of nano-objects. First, the existence of an initial higher order stress represented by Mindlin's cohesion parameter, b0, makes it possible to account for the relaxation behaviour of traction-free surfaces. Second, the higher order elastic moduli, ci, coupling the strain tensor and its second gradient are shown to significantly affect the apparent elastic properties of nano-beams and nano-films under uni-axial loading. These two effects are independent from each other and allow for separated identification of the corresponding material parameters. Analytical results are provided for the size-dependent apparent shear modulus of a nano-thin strip under shear. Finite element simulations are then performed to derive the dependence of the apparent Young modulus and Poisson ratio of nano-films with respect to their thickness, and to illustrate hole free surface relaxation in a periodic nano-porous material.

Visualization of anisotropic-isotropic phase transformation dynamics in battery electrode particles

Abstract: Anisotropy, or alternatively, isotropy of phase transformations extensively exist in a number of solid-state materials, with performance depending on the three-dimensional transformation features. Fundamental insights into internal chemical phase evolution allow manipulating materials with desired functionalities, and can be developed via real-time multi-dimensional imaging methods. Here, we report a five-dimensional imaging method to track phase transformation as a function of charging time in individual lithium iron phosphate battery cathode particles during delithiation. The electrochemically driven phase transformation is initially anisotropic with a preferred boundary migration direction, but becomes isotropic as delithiation proceeds further. We also observe the expected two-phase coexistence throughout the entire charging process. We expect this five-dimensional imaging method to be broadly applicable to problems in energy, materials, environmental and life sciences.

The elastic wave motions for a photothermal medium of a dual-phase-lag model with an internal heat source and gravitational field

Abstract: In this work, the dual-phase-lag (DPL) heat transfer model is introduced to study the problem of an isotropic generalized thermoelastic medium with an internal heat source that is moving with a con...

Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel

Abstract: The present study deals with buckling analysis of simply supported conical panels based on the Donnell's shell theory. Different material properties have been considered such as isotropic, composite laminated and functionally graded (FG). The governing differential equation for buckling of laminated conical panel is derived. These equations are discrete using method of discrete singular convolution (DSC). Shannon's delta kernel is used for trial functions. To check the presented DSC method and computer program, the critical buckling loads for isotropic and composite conical panels are calculated which compare very well with earlier available results. The effect of some geometric parameters and material parameters on critical buckling of panels is also investigated. It is noticed that the present DSC methodology can predict accurately the buckling loads of conical panels.

The Electron Temperature and Anisotropy in the Solar Wind. Comparison of the Core and Halo Populations

Abstract: Estimating the temperature of solar wind particles and their anisotropies is particularly important for understanding the origin of their deviations from thermal equilibrium and the effects this has. In the absence of energetic events, the velocity distribution of electrons reveals a dual structure with a thermal (Maxwellian) core and a suprathermal (kappa) halo. This article presents a detailed observational analysis of these two components, providing estimations of their temperatures and temperature anisotropies, and decoding any potential interdependence that their properties may indicate. The dataset used in this study includes more than 120 000 of the distributions measured by three missions in the ecliptic within an extended range of heliocentric distances from 0.3 to over 4 AU. The core temperature is found to decrease with the radial distance, while the halo temperature slightly increases, clarifying an apparent contradiction in previous observational analyses and providing valuable clues about the temperature of the kappa-distributed populations. For low values of the power-index kappa, these two components manifest a clear tendency to deviate from isotropy in the same direction, which seems to confirm the existence of mechanisms with similar effects on both components, e.g., the solar wind expansion, or the particle heating by the fluctuations. However, the existence of plasma states with anticorrelated anisotropies of the core and halo populations and the increase in their number for high values of the power-index kappa suggest a dynamic interplay of these components, mediated, most probably, by the anisotropy-driven instabilities.

Yielding the yield-stress analysis: a study focused on the effects of elasticity on the settling of a single spherical particle in simple yield-stress fluids

Abstract: The sedimentation of a single particle in materials that exhibit simultaneously elastic, viscous and plastic behavior is examined in an effort to explain phenomena that contradict the nature of purely yield-stress materials. Such phenomena include the loss of the fore-and-aft symmetry with respect to an isolated settling particle under creeping flow conditions and the appearance of the “negative wake” behind it. Despite the fact that similar observations have been reported in studies involving viscoelastic fluids, researchers conjectured that thixotropy is responsible for these phenomena, as the aging of yield-stress materials is another common feature. By means of transient calculations, we study the effect of elasticity on both the fluidized and the solid phase. The latter is considered to behave as an ideal Hookean solid. The material properties of the model are determined under the isotropic kinematic hardening framework via Large Amplitude Oscillatory Shear (LAOS) measurements. In this way, we are able to predict accurately the unusual phenomena observed in experiments with simple yield-stress materials, irrespective of the appearance of slip on the particle surface. Viscoelasticity favors the formation of intense shear and extensional stresses downstream of the particle, significantly changing the entrapment mechanism in comparison to that observed in viscoplastic fluids. Therefore, the critical conditions under which the entrapment of the particle occurs deviate from the well-known criterion established theoretically by Beris et al. (1985) and verified experimentally by Tabuteau et al. (2007) for similar materials under conditions that elastic effects are negligible. Our predictions are in quantitative agreement with published experimental results by Holenberg et al. (2012) on the loss of the fore–aft symmetry and the formation of the negative wake in Carbopol with well-characterized rheology. Additionally, we propose simple expressions for the Stokes drag coefficient, as a function of the gravity number, Yg (related to the Bingham number), for different levels of elasticity and for its critical value, under which entrapment of particles occurs. These criteria are in agreement with the results found in the recent work by Ahonguio et al. (2014). Finally, we propose a method to quantify experimentally the elastic effects in viscoplastic particulate systems.

Experimental Investigations of Fracture Process in Concrete by Means of X-ray Micro-computed Tomography

Abstract: The paper describes investigation results on fracture in notched concrete beams under quasi-static three-point bending by the X-ray micro-computed tomography. The two-dimensional (2D) and three-dimensional image procedures were used. Attention was paid to width, length, height and shape of cracks along beam depth. In addition, the displacements on the surface of concrete beams during the deformation process were measured with the 2D digital image correlation technique in order to detect strain localisation before a discrete crack occurred. The 2D fracture patterns in beams were numerically simulated with the finite-element method using an isotropic damage constitutive model enhanced by a characteristic length of micro-structure. Concrete was modelled as a random heterogeneous four-phase material composed of aggregate, cement matrix, interfacial transitional zones and air voids. The advantages of the X-ray micro-computed tomography were outlined.

Three-dimensional chiral microstructures fabricated by structured optical vortices in isotropic material

Abstract: Optical vortices, as a kind of structured beam with helical phase wavefronts and doughnut shape intensity distribution, have been used for fabricating chiral structures in metal and spiral patterns in anisotropic polarization-dependent azobenzene polymer. However, in isotropic polymer, the fabricated microstructures are typically confined to non-chiral cylindrical geometry due to two-dimensional doughnut intensity profile of optical vortices. Here we develop a powerful strategy for realizing chiral microstructures in isotropic material by coaxial interference of a vortex beam and a plane wave, which produces three-dimensional (3D) spiral optical fields. This coaxial interference beams are creatively produced by designing the contrivable holograms consisting of azimuthal phase and equiphase loaded on liquid-crystal spatial light modulator. Then, in isotropic polymer, 3D chiral microstructures are achieved under illumination of the coaxial interference femtosecond laser beams with their chirality controlled by the topological charge. Our further investigation reveals that the spiral lobes and chirality are caused by the interfering patterns and helical phase wavefronts, respectively. This technique is simple, stable, and easy-operation, and offers broad applications in optical tweezers, optical communications and fast metamaterial fabrication.

Planar auxeticity from elliptic inclusions

Abstract: Composites with elliptic inclusions of long semi-axis a and short semi-axis b are studied by the Finite Element method. The centres of ellipses form a square lattice of the unit lattice constant. The neighbouring ellipses are perpendicular to each other and their axes are parallel to the lattice axes. The influence of geometry and material characteristics on the effective mechanical properties of these anisotropic composites is investigated for deformations applied along lattice axes. It is found that for anisotropic inclusions of low Young's modulus, when a + b → 1 the effective Poisson's ratio tends to −1, while the effective Young's modulus takes very low values. In this case the structure performs the rotating rigid body mechanism. In the limit of large values of Young's modulus of inclusions, both effective Poisson's ratio and effective Young's modulus saturate to values which do not depend on Poisson's ratio of inclusions but depend on geometry of the composite and the matrix Poisson's ratio. For highly anisotropic inclusions of very large Young's modulus, the effective Poisson's ratio of the composite can be negative for nonauxetic both matrix and inclusions. This is a very simple example of an auxetic structure being not only entirely continuous, but with very high Young's modulus. A severe qualitative change in the composite behaviour is observed as a/b reaches the limit of 1, i.e. inclusions are isotropic. The observed changes in both Poisson's ratio and Young's modulus are complex functions of parameters defining the composite. The latter allows one to tailor a material of practically arbitrary elastic parameters.

An efficient shear deformation theory for wave propagation of functionally graded material plates

Abstract: An efficient shear deformation theory is developed for wave propagation analysis of an infinite functionally graded plate in the presence of thermal environments. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The thermal effects and temperature-dependent material properties are both taken into account. The temperature field is assumed to be a uniform distribution over the plate surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton\'s principle and the physical neutral surface concept. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions and temperature on wave propagation of functionally graded plate are discussed in detail. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded plate. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.

An improved Moving Kriging-based meshfree method for static, dynamic and buckling analyses of functionally graded isotropic and sandwich plates

Abstract: A meshfree method with a modified distribution function of Moving Kriging (MK) interpolation is investigated. This method is then combined with a high order shear deformation theory (HSDT) for static, dynamic and buckling analyses of functionally graded material (FGM) isotropic and sandwich plates. A meshfree method uses the normalized form of MK interpolation under a new quartic polynomial correlation to build the basis shape functions in high order approximations. The Galerkin weak form is used to separate the system equations which is numerically solved by meshfree method. A rotation-free technique extracted from isogeometric analysis is introduced to eliminate the degrees of freedom of slopes. Then, the method retains a highly computational effect with a lower number of degrees of freedom. In addition, the requirement of shear correction factors is ignored and the traction free is at the top and bottom surfaces of FGM plates. Various thickness ratios, boundary conditions and material properties are studied to validate the numerical analyses of the rectangular and circular plates. The numerical results show that the present theory is more stable and well accurate prediction as compared to three-dimensional (3D) elasticity solution and other meshfree methods in the literature.

Geometry and mechanics of thin growing bilayers.

Abstract: We investigate how thin sheets of arbitrary shapes morph under the isotropic in-plane expansion of their top surface, which may represent several stimuli such as nonuniform heating, local swelling and differential growth. Inspired by geometry, an analytical model is presented that rationalizes how the shape of the disk influences morphing, from the initial spherical bending to the final isometric limit. We introduce a new measure of slenderness that describes a sheet in terms of both thickness and plate shape. We find that the mean curvature of the isometric state is three fourths the natural curvature, which we verify by numerics and experiments. We finally investigate the emergence of a preferred direction of bending in the isometric state, guided by numerical analyses. The scalability of our model suggests that it is suitable to describe the morphing of sheets spanning several orders of magnitude.