Showing papers on "Isotropy published in 2017"

Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness

Abstract: A wide variety of high-performance applications require materials for which shape control is maintained under substantial stress, and that have minimal density. Bio-inspired hexagonal and square honeycomb structures and lattice materials based on repeating unit cells composed of webs or trusses, when made from materials of high elastic stiffness and low density, represent some of the lightest, stiffest and strongest materials available today. Recent advances in 3D printing and automated assembly have enabled such complicated material geometries to be fabricated at low (and declining) cost. These mechanical metamaterials have properties that are a function of their mesoscale geometry as well as their constituents, leading to combinations of properties that are unobtainable in solid materials; however, a material geometry that achieves the theoretical upper bounds for isotropic elasticity and strain energy storage (the Hashin-Shtrikman upper bounds) has yet to be identified. Here we evaluate the manner in which strain energy distributes under load in a representative selection of material geometries, to identify the morphological features associated with high elastic performance. Using finite-element models, supported by analytical methods, and a heuristic optimization scheme, we identify a material geometry that achieves the Hashin-Shtrikman upper bounds on isotropic elastic stiffness. Previous work has focused on truss networks and anisotropic honeycombs, neither of which can achieve this theoretical limit. We find that stiff but well distributed networks of plates are required to transfer loads efficiently between neighbouring members. The resulting low-density mechanical metamaterials have many advantageous properties: their mesoscale geometry can facilitate large crushing strains with high energy absorption, optical bandgaps and mechanically tunable acoustic bandgaps, high thermal insulation, buoyancy, and fluid storage and transport. Our relatively simple design can be manufactured using origami-like sheet folding and bonding methods.

Light-Steered Isotropic Semiconductor Micromotors

Abstract: Intelligent photoresponsive isotropic semiconductor micromotors are developed by taking advantage of the limited penetration depth of light to induce asymmetrical surface chemical reactions. Independent of the Brownian motion of themselves, the as-proposed isotropic micromotors are able to continuously move with both motion direction and speed just controlled by light, as well as precisely manipulate particles for nanoengineering.

Phase field modeling of fracture in anisotropic brittle solids

Abstract: A phase field model of fracture that accounts for anisotropic material behavior at small and large deformations is outlined within this work. Most existing fracture phase field models assume crack evolution within isotropic solids, which is not a meaningful assumption for many natural as well as engineered materials that exhibit orientation-dependent behavior. The incorporation of anisotropy into fracture phase field models is for example necessary to properly describe the typical sawtooth crack patterns in strongly anisotropic materials. In the present contribution, anisotropy is incorporated in fracture phase field models in several ways: (i) Within a pure geometrical approach, the crack surface density function is adopted by a rigorous application of the theory of tensor invariants leading to the definition of structural tensors of second and fourth order. In this work we employ structural tensors to describe transverse isotropy, orthotropy and cubic anisotropy. Latter makes the incorporation of second gradients of the crack phase field necessary, which is treated within the finite element context by a nonconforming Morley triangle. Practically, such a geometric approach manifests itself in the definition of anisotropic effective fracture length scales. (ii) By use of structural tensors, energetic and stress-like failure criteria are modified to account for inherent anisotropies. These failure criteria influence the crack driving force, which enters the crack phase field evolution equation and allows to set up a modular structure. We demonstrate the performance of the proposed anisotropic fracture phase field model by means of representative numerical examples at small and large deformations.

An Experimental Method to Determine the Elastic Properties of Transversely Isotropic Rocks by a Single Triaxial Test

Abstract: A novel method is proposed for determining the deformation anisotropy of rocks by a single triaxial test using a single specimen sampled from an arbitrary direction. Transversely isotropic elasticity is assumed for the purpose of application of the test method to sedimentary and metamorphic rocks, and the non-axial symmetric stress–strain relationships of anisotropic rocks are determined by triaxial testing by means of a simple improvement to the cap in the triaxial testing apparatus. Both the elastic parameters and the directions of the transversely isotropic elasticity can be obtained by measuring the shear deformations that occur under triaxial stress conditions. An overview of the method for determining transversely isotropic elasticity is presented in this paper, along with the results of a sensitivity analysis performed assuming simulated strains with random measurement errors. The results show that the directions of anisotropy can be determined precisely using the directions of the principal strains measured during isotropic compression and that the elastic parameters can be determined uniquely from the stress–strain relationships observed during both the isotropic and axial compression processes.

How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity.

Abstract: The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales.

Effect of thermal loading due to laser pulse on thermoelastic porous medium under G-N theory

Abstract: The aim of this paper is to study the wave propagation of generalized thermoelastic medium with voids under the effect of thermal loading due to laser pulse with energy dissipation. The material is a homogeneous isotropic elastic half-space and heated by a non-Gaussian laser beam with the pulse duration of 0.2 ps. A normal mode method is proposed to analyse the problem and obtain numerical solutions for the displacement components, stresses, temperature distribution and the change in the volume fraction field. The results of the physical quantities have been illustrated graphically by comparison between both types II and III of Green-Naghdi theory for two values of time, as well as with and without void parameters.

A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method

Abstract: The main aim of the present paper is to solve numerically the free vibration problem of sandwich shell structures with variable thickness and made of Functionally Graded Materials (FGMs). Several Higher-order Shear Deformation Theories (HSDTs), defined by a unified formulation, are employed in the study. The FGM structures are characterized by variable mechanical properties due to the through-the-thickness variation of the volume fraction distribution of the two constituents and the arbitrary thickness profile. A four-parameter power law expression is introduced to describe the FGMs, whereas general relations are used to define the thickness variation, which can affect both the principal coordinates of the shell reference domain. A local scheme of the Generalized Differential Quadrature (GDQ) method is employed as numerical tool. The natural frequencies are obtained varying the exponent of the volume fraction distributions using higher-order theories based on a unified formulation. The structural models considered are two-dimensional and require less degrees of freedom when compared to the corresponding three-dimensional finite element (FE) models, which require a huge number of elements to describe the same geometries accurately. A comparison of the present results with the FE solutions is carried out for the isotropic cases only, whereas the numerical results available in the literature are used to prove the validity as well as accuracy of the current approach in dealing with FGM structures characterized by a variable thickness profile.

A new and simple HSDT for thermal stability analysis of FG sandwich plates

Abstract: The novelty of this work is the use of a new displacement field that includes undetermined integral terms for analyzing thermal buckling response of functionally graded (FG) sandwich plates. The proposed kinematic uses only four variables, which is even less than the first shear deformation theory (FSDT) and the conventional higher shear deformation theories (HSDTs). The theory considers a trigonometric variation of transverse shear stress and verifies the traction free boundary conditions without employing the shear correction factors. Material properties of the sandwich plate faces are considered to be graded in the thickness direction according to a simple power-law variation 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 assumed as uniform, linear and non-linear temperature rises within the thickness direction. An energy based variational principle is employed to derive the governing equations as an eigenvalue problem. The validation of the present work is checked by comparing the obtained results the available ones in the literature. The influences of aspect and thickness ratios, material index, loading type, and sandwich plate type on the critical buckling are all discussed.

The sequential addition and migration method to generate representative volume elements for the homogenization of short fiber reinforced plastics

Abstract: We present an algorithm for generating volume elements of short fiber reinforced plastic microstructures for prescribed fourth order fiber orientation tensor, fiber aspect ratio and solid volume fraction. The algorithm inserts fibers randomly into an existing microstructure, and removes the resulting overlap systematically based on a gradient descent method. In contrast to existing methods, large fiber aspect ratios (up to 150) and large volume fractions (60 vol% for isotropic orientation and aspect ratio of 33) can be reached. We study the effective linear elastic properties of the resulting microstructures, depending on fiber orientation, volume fraction as well as aspect ratio, and examine the size of a corresponding representative volume element.

Micropolar elasticity theory: a survey of linear isotropic equations, representative notations, and experimental investigations

Abstract: This paper is devoted to a review of the linear isotropic theory of micropolar elasticity and its development with a focus on the notation used to represent the micropolar elastic moduli and the ex...

A study on photothermal waves in an unbounded semiconductor medium with cylindrical cavity

Abstract: The theory of coupled plasma, thermal, and elastic waves was used to investigate the wave propagation on semiconductor material with cylindrical cavity during photo-thermoelastic process. An unbounded material, elastic semiconductor containing a cylindrical cavity with isotropic and homogeneous thermal and elastic properties has been considered. The inner surface of cavity is constrained, and the carrier density is photogenerated by an exponentially decaying pulse boundary heat flux. The eigenvalue approach, together with Laplace transform techniques, was used to obtain the analytical solutions. Numerical computations have been done for a silicon-like semiconductor material, and the results are presented graphically to estimate the effect of the coupling between the plasma, thermal, and elastic waves. The graphical results indicate that the thermal activation coupling parameter is an important phenomenon and has a great effect on the distribution of field quantities.

Buckling of FG-CNT-reinforced composite plates subjected to parabolic loading

Abstract: It is known that the distribution of stresses in a rectangular plate is the same as the applied stresses on the boundaries when the loading is uniform or linearly varying. For other types of compressive loads, for instance parabolic compressive loading, the distribution of stresses in the plate is different from the applied loads at the boundaries of the plate. For such conditions, to obtain the buckling loads of the plate, an accurate prebuckling analysis should be performed. The present research aims to obtain the buckling loads and buckling pattern of composite plates reinforced with carbon nanotubes with uniform or functionally graded distribution across the plate thickness. The properties of the composite media are obtained based on a modified rule of mixtures approach with the introduction of efficiency parameters. First-order shear deformation plate theory is used to approximate the plate kinematics. The plate is subjected to uniaxial compressive loads which vary as parabolic functions across the width of the plate. At first, using the Ritz method and Airy stress function formulation, the distribution of stress resultants in the plate domain is obtained as a two-dimensional elasticity formulation. Afterwards, by means of the Chebyshev polynomials as the basic functions of the Ritz solution method, an eigenvalue problem is established to obtain the buckling load and buckling shape of the plate. Comparison studies are provided to assure the accuracy of the presented formulation for isotropic homogeneous and cross-ply laminated plates. Afterwards, parametric studies are performed for composite plates reinforced with carbon nanotubes.

A unified mechanical and retention model for saturated and unsaturated soil behaviour

Abstract: The coupled mechanical and water retention elasto-plastic constitutive model of Wheeler, Sharma and Buisson (the Glasgow coupled model, GCM) predicts unique unsaturated isotropic normal compression and unsaturated critical state planar surfaces for specific volume and degree of saturation when soil states are at the intersection of mechanical (M) and wetting retention (WR) yield surfaces. Experimental results from tests performed by Sivakumar on unsaturated samples of compacted speswhite kaolin confirm the existence and form of these unique surfaces. The GCM provides consistent representation of transitions between saturated and unsaturated conditions, including the influence of retention hysteresis and the effect of plastic volumetric strains on retention behaviour, and it gives unique expressions to predict saturation and de-saturation conditions (air-exclusion and air-entry points, respectively). Mechanical behaviour is modelled consistently across these transitions, including appropriate variation of mechanical yield stress under both saturated and unsaturated conditions. The expressions defining the unsaturated isotropic normal compression planar surfaces for specific volume and degree of saturation are central to the development of a relatively straightforward methodology for determining values of all GCM parameters (soil constants and initial state) from a limited number of laboratory tests. This methodology is demonstrated by application to the experimental data of Sivakumar. Comparison of model simulations with experimental results for the full set of Sivakumar’s isotropic loading stages demonstrates that the model is able to predict accurately the variation of both specific volume and degree of saturation during isotropic stress paths under saturated and unsaturated conditions.

Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The θ-group collaboration

Abstract: Turbulent Richtmyer–Meshkov instability (RMI) is investigated through a series of high resolution three-dimensional simulations of two initial conditions with eight independent codes. The simulations are initialised with a narrowband perturbation such that instability growth is due to non-linear coupling/backscatter from the energetic modes, thus generating the lowest expected growth rate from a pure RMI. By independently assessing the results from each algorithm and computing ensemble averages of multiple algorithms, the results allow a quantification of key flow properties as well as the uncertainty due to differing numerical approaches. A new analytical model predicting the initial layer growth for a multimode narrowband perturbation is presented, along with two models for the linear and non-linear regimes combined. Overall, the growth rate exponent is determined as θ=0.292±0.009, in good agreement with prior studies; however, the exponent is decaying slowly in time. Also, θ is shown to be relatively insensitive to the choice of mixing layer width measurements. The asymptotic integral molecular mixing measures Θ=0.792±0.014, Ξ=0.800±0.014, and Ψ=0.782±0.013 are lower than some experimental measurements but within the range of prior numerical studies. The flow field is shown to be persistently anisotropic for all algorithms, at the latest time having between 49% and 66% higher kinetic energy in the shock parallel direction compared to perpendicular and does not show any return to isotropy. The plane averaged volume fraction profiles at different time instants collapse reasonably well when scaled by the integral width, implying that the layer can be described by a single length scale and thus a single θ. Quantitative data given for both ensemble averages and individual algorithms provide useful benchmark results for future research.

Free vibration of joined conical-conical shells

Abstract: Free vibration analysis of a joined shell system composed of two conical shells is analysed in this research It is assumed that the system of joined shell is made from a linearly elastic isotropic homogeneous material Both shells are unified in thickness To capture the through-the-thickness shear deformations and rotary inertias, first order theory of shells is accompanied with the Donnell type of kinematic assumptions to establish the general motion equations and the associated boundary and continuity conditions with the aid of Hamilton's principle The resulted system of equations are discreted using the semi-analytical generalised differential quadrature (GDQ) method Considering various types of boundary conditions for the shell ends and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies as well as the associated mode shapes After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells, some parametric studies are carried out for the system of combined moderately thick conical-conical

Geometric Limitation and Tensile Properties of Wire and Arc Additive Manufacturing 5A06 Aluminum Alloy Parts

Abstract: Wire and arc additive manufacture (WAAM), as an emerging and promising technology of metal additive manufacturing, it lacks of experimental works to clarify the feature of geometrical configuration, microstructure and tensile properties, which can be used for further evaluating whether the as-deposited part can be used directly, and providing design reference for structure optimization. Taking 5A06 aluminum alloy additive manufacturing for example, in this paper, the geometric limitation and tensile property criteria are characterized using experimental method. The minimum angle and curvature radius that can be made by WAAM are 20° and 10 mm when the layer width is 7.2 mm. It shows isotropy when loading in build direction and perpendicular one. When loading in the direction of parallel and perpendicular to texture orientation, the tensile properties are anisotropic. The difference between them is 22 MPa.

Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two-temperature

Abstract: In this work, a novel generalized model of photothermal theory with two-temperature thermoelasticity theory based on memory-dependent derivative (MDD) theory is performed. A one-dimensional problem for an elastic semiconductor material with isotropic and homogeneous properties has been considered. The problem is solved with a new model (MDD) under the influence of a mechanical force with a photothermal excitation. The Laplace transform technique is used to remove the time-dependent terms in the governing equations. Moreover, the general solutions of some physical fields are obtained. The surface taken into consideration is free of traction and subjected to a time-dependent thermal shock. The numerical Laplace inversion is used to obtain the numerical results of the physical quantities of the problem. Finally, the obtained results are presented and discussed graphically.

Reynolds number scaling of velocity increments in isotropic turbulence.

Abstract: Using the largest database of isotropic turbulence available to date, generated by the direct numerical simulation (DNS) of the Navier-Stokes equations on an 8192^{3} periodic box, we show that the longitudinal and transverse velocity increments scale identically in the inertial range. By examining the DNS data at several Reynolds numbers, we infer that the contradictory results of the past on the inertial-range universality are artifacts of low Reynolds number and residual anisotropy. We further show that both longitudinal and transverse velocity increments scale on locally averaged dissipation rate, just as postulated by Kolmogorov's refined similarity hypothesis, and that, in isotropic turbulence, a single independent scaling adequately describes fluid turbulence in the inertial range.

Anisotropy of elasticity and fabric of granular soils

Abstract: Anisotropy of elasticity is a very important feature of granular soils. In this paper, numerical experiments using discrete element method were performed to emulate drained triaxial tests and simple shear tests at different stress levels. From these numerical experiments the macroscopic elasticity parameters were determined. The results show that at isotropic stress states the stiffness of the numerical specimen increases, while the Poisson’s ratio decreases with increasing confining pressure. The small strain shear modulus of the numerical specimen agrees well with the laboratory experimental results on a specimen with similar conditions. At anisotropic stress states, there is a threshold stress ratio ( $${ SR}_{\mathrm{th}}$$ ), which characterizes the degrees of stiffness change and fabric change during the shearing. When the stress ratio (SR) is less than $${ SR}_{\mathrm{th}}$$ , the microscopic contact number does not change and its distribution remains nearly isotropic, while the distribution of contact forces change and become anisotropic to resist the applied anisotropic stress. Therefore the stiffness anisotropy of the specimen mainly results from the anisotropy of contact forces. When SR is larger than $${ SR}_{\mathrm{th}}$$ , however, the contact number decreases significantly in the minor principal stress direction resulting in the fabric anisotropy, along with the adjustments of contact forces. The stiffness anisotropy of the specimen results from both the fabric anisotropy and the contact force anisotropy. It also indicates that the stress normalized stiffness may be used as an index of the degree of fabric anisotropy. Moreover, the Poisson’s ratio of the specimen increases continuously with increasing stress ratio and its anisotropy can be approximately related to the stiffness anisotropy.

Generalized magneto-thermoelastic half-space with diffusion under initial stress using three-phase-lag model

Abstract: The present paper is aimed at studying the effect of initial stress and the magnetic field on thermoelastic interactions in an isotropic, thermally and electrically conducting half-space whose surface is subjected to mechanical and thermal loads. The formulation is applied under the thermoelasticity theory with three-phase-lag, proposed by Choudhuri (2007). The normal mode analysis is used to obtain the expressions for the variables considered. Numerical and computations are performed for a specific material and the results obtained are represented graphically. Comparisons are made with the results predicted by different theories Lord–Shulman theory (L–S), the theory of thermoelasticity type III (G-N III) and the three-phase-lag model (3PHL) in the absence and presence of the initial stress and magnetic field.

Isotropic and anisotropic total variation regularization in electrical impedance tomography

Abstract: This paper focuses on studying the effects of isotropic and anisotropic total variation (TV) regularization in electrical impedance tomography (EIT). A characteristic difference between these two widely used TV regularization methods is that the isotropic TV is rotationally invariant and the anisotropic TV is not. The rotational variance of the anisotropic TV is known to cause geometric distortions by favoring edge orientations that are aligned with co-ordinate axes. In many applications, such as transmission tomography problems, these distortions often play only a minor role in the overall accuracy of reconstructed images, because the measurement data is sensitive to the shapes of the edges in the imaged domain. In EIT and other diffusive image modalities, however, the data is severely less sensitive to the fine details of edges, and it is an open question how large impact the selection of the TV regularization variant has on the reconstructed images. In this work, this effect is investigated based on a set of experiments. The results demonstrate that the choice between isotropic and anisotropic TV regularization indeed has a significant impact on the properties of EIT reconstructions; especially, the tendency of the anisotropic TV to favor edges aligned with co-ordinate axes is shown to yield large geometric distortions in EIT reconstructions.

Torsional vibration of nano-cone based on nonlocal strain gradient elasticity theory

Abstract: This paper investigates free torsional vibration behavior of a nonlinear nano-cone, based on the nonlocal strain gradient elasticity theory. The nano-cone is made of homogeneous and isotropic materials. Moreover, the cross-sectional area of the nano-cone varies in the longitudinal direction by a nonlinear function. Governing equation and boundary conditions are derived using Hamilton’s principle. These equations are solved by employing the generalized differential quadrature method (GDQM). The effects of some parameters, such as cross-sectional area change and small-scale parameter, are investigated. Results show that the cross-sectional area change has a significant effect on the torsional vibration behavior of the nano-cone. These results are also compared with the results reported in the literature, which shows consistency.

Anisotropic Self-Assembly from Isotropic Colloidal Building Blocks.

Abstract: Spherical colloidal particles generally self-assemble into hexagonal lattices in two dimensions. However, more complex, non-hexagonal phases have been predicted theoretically for isotropic particles with a soft repulsive shoulder but have not been experimentally realized. We study the phase behavior of microspheres in the presence of poly(N-isopropylacrylamide) (PNiPAm) microgels at the air/water interface. We observe a complex phase diagram, including phases with chain and square arrangements, which exclusively form in the presence of the microgels. Our experimental data suggests that the microgels form a corona around the microspheres and induce a soft repulsive shoulder that governs the self-assembly in this system. The observed structures are fully reproduced by both minimum energy calculations and finite temperature Monte Carlo simulations of hard core-soft shoulder particles with experimentally realistic interaction parameters. Our results demonstrate how complex, anisotropic assembly patterns can be realized from entirely isotropic building blocks by control of the interaction potential.

Spectra and statistics in compressible isotropic turbulence

Abstract: Spectra and statistics in compressible isotropic turbulence are studied. In weakly compressible turbulence, the pseudosound mode dominates over the acoustic mode at relatively small scales, and the spectrum of pseudosound velocity exhibits a power-law scaling with the exponent -3.

A hierarchy of simplified constitutive models within isotropic strain gradient elasticity

Abstract: Simplified isotropic models of strain gradient elasticity are presented, based on the mutual relationship between the inherent (dual) gradient directions (i.e. the gradient direction of any strain gradient source and the lever arm direction of the promoted double stress). A class of gradient-symmetric materials featured by gradient directions obeying a reciprocity relation and by 4 independent h.o. (higher order) coefficients is envisioned, along with the sub-classes of hemi-collinear materials (3 h.o. coefficients, gradient directions in part coincident), collinear materials (2 h.o. coefficients, equal gradient directions) and micro-affine materials (1 h.o. coefficient, behavioral affinity at micro- and macro-scale, coincident with the Aifantis model). All models comply with the energy positive definiteness conditions. The boundary-value problem for the wide class of gradient-symmetric materials is governed by a set of Poisson–Helmholtz type differential equations almost unaffected by the number of independent h.o. coefficients; instead the boundary conditions carry in, in general, problem-dependent computational difficulties increasing with the number of these coefficients. As an application, gradient-symmetric beam models are discussed. A parallel hierarchy of simplified isotropic models with couple stresses is also presented, in which the novel concept of rotational volumetric strain gradient is exploited. A graphical overview on isotropic strain gradient elasticity models is reported. An Appendix is devoted to the concepts of extensional and rotational volumetric strain gradients and to the related pressure-like stresses.