Showing papers on "Transverse isotropy published in 2019"

Wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-spaces

Abstract: The paper analyses the wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-spaces. The two piezoelectric half-spaces (left and right) are both AlN materials, the middle piezoelectric semiconductor slab is ZnO material and is assumed to be transversely isotropic. The semiconductor effect is emphasized by considering the coupling mechanical displacement, electric potential and the carrier in the slab. The state transition differential equation is derived based on the reduction of order of the governing equations and the transfer matrix of state is obtained by solving the state transition equation. The present method can deal with not only the homogeneous slab but also the heterogeneous slab. Two cases (incident QP wave and incident QSV wave) are considered, and the energy reflection and transmission coefficients varying with the incident angle are calculated. The results show that the steady carrier density and the exterior biasing electric field have obvious influences on the reflection and transmission coefficients. This investigation provides a new thought for the adjustment and controlling of elastic wave propagation in the laminated structures.

Multiscale modeling of the elastic moduli of CNT-reinforced polymers and fitting of efficiency parameters for the use of the extended rule-of-mixtures

Abstract: In this work, a bottom-up multiscale modeling approach is developed to estimate the effective elastic moduli of Carbon NanoTube (CNT)-reinforced polymer composites. The homogenization process comprises two successive steps, including an atomistic-based computational model and a micromechanics approach at the nano- and micro-scales, respectively. Firstly, the atomistic-based finite element model defines a cylindrical Representative Volume Element (RVE) that accounts for a carbon nanotube, the immediately surrounding matrix, and the CNT/polymer interface. The carbon-carbon bonds of the CNT are modeled using Timoshenko beams, whilst three-dimensional solid elements are used for the surrounding matrix. Through the application of four loading conditions, the RVEs are homogenized into transversely isotropic equivalent fibers by equating the associated strain energies. Secondly, the equivalent fibers are employed in a micromechanics approach to estimate the macroscopic response of non-dilute composites. This is performed using both the analytical Mori-Tanaka model and a computational RVE model with a hexagonal packing geometry. A wide spectrum of single- and multi-walled carbon nanotubes are studied, as well as two different polymeric matrices. Furthermore, the so-called efficiency parameters, imperative for the application of the simplified extended rule of mixtures, are characterized by polynomial expressions for practical filler contents. Finally, detailed parametric analyses are also provided to give insight into the sensitivity of the macroscopic response of CNT-reinforced polymer composites to microstructural features such as filler volume fraction, chirality or aspect ratio.

Some characteristics of elastic waves in a piezoelectric semiconductor plate

Abstract: Devices based on piezoelectric semiconductors (PSCs) have recently received particular attention due to their wide bandgap where strain energy band engineering under both static and time-harmonic deformations is the key. In this paper, we investigate and characterize the elastic waves propagating in an anisotropic n-type PSC plate. To achieve our goals, we first introduce the new notations for the extended displacements, stresses, strains, and modulus to arrive at a mathematically elegant extended Stroh formalism. Then, the elastic wave problem is converted into a linear eigenvalue system from which the extended displacements and stresses are expressed in terms of the eigenvalues and eigenvectors. Finally, making use of the boundary conditions on the top and bottom surfaces of the plate, wave dispersion and attenuation are derived analytically. Numerical examples are presented to systematically study the effect of the surface boundary condition, steady-state carrier density, plate thickness, and biasing electric field on the wave speed and attenuation of both shear horizontal and Lamb waves in the transversely isotropic ZnO PSC plate. Some interesting characteristics of the elastic waves observed in this paper could be helpful as theoretical guidance when designing PSC-based devices.

Anisotropy vs isotropy in living cell indentation with AFM.

Abstract: The measurement of local mechanical properties of living cells by nano/micro indentation relies on the foundational assumption of locally isotropic cellular deformation As a consequence of assumed isotropy, the cell membrane and underlying cytoskeleton are expected to locally deform axisymmetrically when indented by a spherical tip Here, we directly observe the local geometry of deformation of membrane and cytoskeleton of different living adherent cells during nanoindentation with the integrated Atomic Force (AFM) and spinning disk confocal (SDC) microscope We show that the presence of the perinuclear actin cap (apical stress fibers), such as those encountered in cells subject to physiological forces, causes a strongly non-axisymmetric membrane deformation during indentation reflecting local mechanical anisotropy In contrast, axisymmetric membrane deformation reflecting mechanical isotropy was found in cells without actin cap: cancerous cells MDA-MB-231, which naturally lack the actin cap, and NIH 3T3 cells in which the actin cap is disrupted by latrunculin A Careful studies were undertaken to quantify the effect of the live cell fluorescent stains on the measured mechanical properties Using finite element computations and the numerical analysis, we explored the capability of one of the simplest anisotropic models - transverse isotropy model with three local mechanical parameters (longitudinal and transverse modulus and planar shear modulus) - to capture the observed non-axisymmetric deformation These results help identifying which cell types are likely to exhibit non-isotropic properties, how to measure and quantify cellular deformation during AFM indentation using live cell stains and SDC, and suggest modelling guidelines to recover quantitative estimates of the mechanical properties of living cells

A methodology to determine the elastic properties of anisotropic rocks from a single uniaxial compression test

Abstract: This paper introduces a new methodology to measure the elastic constants of transversely isotropic rocks from a single uniaxial compression test. We first give the mathematical proof that a uniaxial compression test provides only four independent strain equations. As a result, the exact determination of all five independent elastic constants from only one test is not possible. An approximate determination of the Young's moduli and the Poisson's ratios is however practical and efficient when adding the Saint–Venant relation as the fifth equation. Explicit formulae are then developed to calculate both secant and tangent definitions of the five elastic constants from a minimum of four strain measurements. The results of this new methodology applied on three granitic samples demonstrate a significant stress-induced nonlinear behavior, where the tangent moduli increase by a factor of three to four when the rock is loaded up to 20 MPa. The static elastic constants obtained from the uniaxial compression test are also found to be significantly smaller than the dynamic ones obtained from the ultrasonic measurements.

Efficient modeling of wave propagation in a vertical transversely isotropic attenuative medium based on fractional Laplacian

Abstract: To efficiently simulate wave propagation in a vertical transversely isotropic (VTI) attenuative medium, we have developed a viscoelastic VTI wave equation based on fractional Laplacian oper...

Modeling of transversely isotropic properties of CNT-polymer composites using meso-scale FEM approach

Abstract: The CNT based nano-composites usually behave as anisotropic materials. Elastic properties vary differently in global as well as material direction. This paper proposes an efficient computational methodology to predict effective orthotropic elastic properties of nanocomposites at diverse constituent conditions. The effective orthotropic material properties have been presented with the consideration of all possible conditions of composite matrix like elastic, elastoplastic and interfacial behavior. Mori-Tanaka (MT) homogenization scheme has been implemented with finite element method (FEM) approach to predict the effective material properties of nanocomposites. In the presented study, CNTs are aligned and uniformly distributed throughout the composite matrix. The proposed computational methodology has been validated with available literature and further extended to investigate the effect of the diverse behavior of composite matrix. From the obtained numerical results, it has been seen that the matrix and filler interface significantly affect the effective elastic strength of polymer composites.

Effect of hall current on propagation of plane wave in transversely isotropic thermoelastic medium with two temperature and fractional order heat transfer

Abstract: This research is devoted to the study of plane wave propagation in homogeneous transversely isotropic magneto-thermoelastic rotating medium with combined effect of hall current and two temperature. The research is applied to fractional order theory with three-phase lag heat transfer. It is analysed that, for 2-D assumed model, three types of coupled longitudinal waves (quasi-longitudinal, quasi-transverse and quasi-thermal) are present. The wave characteristics like phase velocity, specific loss, attenuation coefficients, energy ratios, penetration depths and amplitude ratios of transmitted and reflected waves are computed numerically and illustrated graphically. The impact of hall current parameter by taking different values is represented graphically. Some particular cases are also derived from this research.

Anisotropic elasticity for inversion-safety and element rehabilitation

Abstract: We present an analysis of anisotropic hyperelasticity, specifically transverse isotropy, that obtains closed-form expressions for the eigendecompositions of many common energies. We then use these to build fast and concise Newton implementations. We leverage our analysis in two separate applications. First, we show that existing anisotropic energies are not inversion-safe, and contain spurious stable states under large deformation. We then propose a new anisotropic strain invariant that enables the formulation of a novel, robust, and inversion-safe energy. The new energy fits completely within our analysis, so closed-form expressions are obtained for its eigensystem as well. Secondly, we use our analysis to rehabilitate badly-conditioned finite elements. Using this method, we can robustly simulate large deformations even when a mesh contains degenerate, zero-volume elements. We accomplish this by swapping the badly-behaved isotropic direction with a well-behaved anisotropic term. We validate our approach on a variety of examples.

Transversely isotropic thermoelastic thin circular plate with constant and periodically varying load and heat source

Abstract: The present research deals with the deformation in transversely isotropic thermoelastic (TIT) thin circular plate. Rotation effect is studied under thermally insulated as well as isothermal boundaries. The Laplace and Hankel transform techniques have been used to find the solution to the problem. The displacement components, conductive temperature distribution, and stress components with the radial distance are computed in the transformed domain and further calculated in the physical domain using numerical inversion techniques. The effects of rotation and two temperatures are represented graphically. Some specific cases are also figured out from the current research.

Seismic amplitude inversion for the transversely isotropic media with vertical axis of symmetry

Abstract: Transverse isotropy with a vertical axis of symmetry is a common form of anisotropy in sedimentary basins, and it has a significant influence on the seismic amplitude variation with offset. Although exact solutions and approximations of the PP‐wave reflection coefficient for the transversely isotropic media with vertical axis of symmetry have been explicitly studied, it is difficult to apply these equations to amplitude inversion, because more than three parameters need to be estimated, and such an inverse problem is highly ill‐posed. In this paper, we propose a seismic amplitude inversion method for the transversely isotropic media with a vertical axis of symmetry based on a modified approximation of the reflection coefficient. This new approximation consists of only three model parameters: attribute A, the impedance (vertical phase velocity multiplied by bulk density); attribute B, shear modulus proportional to an anellipticity parameter (Thomsen's parameter e−δ); and attribute C, the approximate horizontal P‐wave phase velocity, which can be well estimated by using a Bayesian‐framework‐based inversion method. Using numerical tests we show that the derived approximation has similar accuracy to the existing linear approximation and much higher accuracy than isotropic approximations, especially at large angles of incidence and for strong anisotropy. The new inversion method is validated by using both synthetic data and field seismic data. We show that the inverted attributes are robust for shale‐gas reservoir characterization: the shale formation can be discriminated from surrounding formations by using the crossplot of the attributes A and C, and then the gas‐bearing shale can be identified through the combination of the attributes A and B. We then propose a rock‐physics‐based method and a stepwise‐inversion‐based method to estimate the P‐wave anisotropy parameter (Thomsen's parameter e). The latter is more suitable when subsurface media are strongly heterogeneous. The stepwise inversion produces a stable and accurate Thomsen's parameter e, which is proved by using both synthetic and field data.

Anisotropic breakage mechanics: From stored energy to yielding in transversely isotropic granular rocks

Abstract: The microstructure of geological solids is affected by their deposition history, which generates complex systems of grain contacts and damage patterns able to induce mechanical anisotropy. This paper aims to disclose the connection between energy storage and the yield surface of cross-anisotropic granular rocks, with the goal to simplify the representation of their mechanical anisotropy. For this purpose, a reformulation of Continuum Breakage Mechanics (CBM) is proposed to introduce material symmetries associated with energy storage processes. It is shown that, due to the thermodynamic consistency of the selected approach, the energy release resulting from comminution is influenced by the anisotropic characteristics of the elastic energy potential. As a result, the model is able to capture naturally and without additional fitting parameters the dependence of the yielding envelope on the relative orientation between bedding planes and loading direction. The performance of the new CBM model has been tested by performing parametric analyses which elucidate the role of cross-anisotropic elastic properties on the yield surface of a granular rock. Furthermore, its accuracy has been assessed against laboratory results available for two sandstones exhibiting dependence of the yield stress on the orientation of the bedding planes. Despite the simplicity of the selected model, the results emphasize that the proposed approach captures the salient features of the deformation response of anisotropic granular rocks, thereby disclosing an intimate connection between grain-scale energy release and cataclastic yielding which greatly simplifies the mathematical description of intrinsic inelastic anisotropy.

Rayleigh wave propagation in transversely isotropic magneto-thermoelastic medium with three-phase-lag heat transfer and diffusion

Abstract: The present research deals with the propagation of Rayleigh wave in transversely isotropic magneto-thermoelastic homogeneous medium in the presence of mass diffusion and three-phase-lag heat transfer. The wave characteristics such as phase velocity, attenuation coefficients, specific loss, and penetration depths are computed numerically and depicted graphically. The normal stress, tangential stress components, temperature change, and mass concentration are computed and drawn graphically. The effects of three-phase-lag heat transfer, GN type-III, and LS theory of heat transfer are depicted on the various quantities. Some particular cases are also deduced from the present investigation.

Time-dependent analysis of axially loaded piles in transversely isotropic saturated viscoelastic soils

Abstract: The flexibility matrices of transversely isotropic saturated viscoelastic soils are obtained by the extended precise integration method. We use the finite element method (FEM) to derive the stiffness matrix of pile. The pile-soil interface is divided into elements corresponding to the pile elements based on the boundary element method (BEM). The pile-soil interaction equation is established by the coupling of FEM and BEM. The solutions for the equation are achieved by combining the compatibility condition between the pile and the soil. Numerical examples are presented to study the influences of soil and pile properties on the time-dependent behaviour of piles.