Effect Of Transverse Isotropy Research Articles

The effect of transverse isotropy on the creep behavior of bedded salt under confining pressures

The effect of transverse isotropy on the creep behavior of bedded salt under confining pressures

Mixed mode axisymmetric cracks in transversely isotropic infinite solid cylinders

• New analytical dislocation solution in a transversely isotropic cylinder is developed. • Material anisotropy has an efficient effect on stress intensity factors. • Interaction of cracks implies that need for mixed-mode analysis is essential. • Loading type and crack length have also a crucial effect on stress intensity factors. The present study examined mixed mode cracking in a transversely isotropic infinite cylinder. The solutions to axisymmetric Volterra climb and glide dislocations in an infinite circular cylinder of the transversely isotropic material are first obtained. The solutions are represented in terms of the biharmonic stress function. Next, the problem of a transversely isotropic infinite cylinder with a set of concentric axisymmetric penny-shaped, annular, and circumferential cracks is formulated using the distributed dislocation technique. Two types of loadings are considered: (i) the lateral cylinder is loaded by two self-equilibrating distributed shear stresses; (ii) the curved surface of the cylinder is under the action of a distributed normal stress. The resulting integral equations are solved by using a numerical scheme to compute the dislocation density on the borders of the cracks. The dislocation densities are employed to determine stress intensity factors for axisymmetric interacting cracks. Finally, a good amount of examples are solved to depict the effect of crack type and location on the stress intensity factors at crack tips and interaction between cracks. Numerical solutions for practical materials are presented and the effect of transverse isotropy on stress intensity factors is discussed.

Wave propagation in an incompressible transversely isotropic thermoelastic solid

In the present paper, the equations of motion and heat conduction equation of an incompressible transversely isotropic thermoelastic solid are formulated in view of Lord and Shulman theory on generalized thermoelastcity. The equations of motion and heat conduction equation reduce to two coupled equations in temperature and a scalar function depending on displacement. Plane harmonic solution of these coupled equations shows the existence of two homogeneous plane waves. These coupled equations are also solved for surface wave solutions which satisfy the required radiation conditions in the half-space. The surface wave solutions satisfy the appropriate boundary conditions at traction-free thermally insulated or isothermal surface of half-space and a secular equation of Rayleigh wave speed is obtained for thermally insulated case and isothermal case. For thermally insulated case, the numerical values of non-dimensional speed of Rayleigh wave are computed by using Iteration method. The wave speeds of plane waves and Rayleigh wave are illustrated graphically to observe the effects of transverse isotropy, material constants, frequency, angle of propagation and thermal relaxation in time.

Tuning Molecular Adhesion via Material Anisotropy

AbstractCell adhesion with extracellular matrix depends on the collective behaviors of a large number of receptor‐ligand bonds at the compliant cell‐matrix interface. While most biological tissues and structures, including cells and extracellular matrices, exhibit strongly anisotropic material properties, existing studies on molecular adhesion via receptor‐ligand bonds have been largely limited to isotropic materials. Here the effects of transverse isotropy, a common form of material anisotropy in biological systems, in modulating the adhesion behavior of a cluster of receptor‐ligand bonds are investigated. The results provide a theoretical basis to understand cell adhesion on anisotropic extracellular matrices and to explore the possibility of controlling cell adhesion via anisotropy design in material properties. The combined analysis and simulations show that the orientation of material anisotropy strongly affects the apparent softness felt by the adhesive bonds, thereby altering their ensemble lifetime by several orders of magnitude. An implication of this study is that distinct cellular behaviors can be achieved through remodeling of material anisotropy in either extracellular matrix or cytoskeleton. Comparison between different loading conditions, together with the effects of material anisotropy, yields a rich array of out‐of‐equilibrium behaviors in the molecular interaction between reactant‐bearing soft surfaces, with important implications on the mechanosensitivity of cells.

FE-studies on Shear Localization in an Anistropic Micro-polar Hypoplastic Granular Material

The effect of transverse isotropy on shear localization in cohesionless granular materials is numerically investigated upon monotonous plane strain deformation paths using a hypoplastic constitutive model enhanced by micro-polar terms. In this model, a so-called density function is reformulated and made anisotropic. Dense sand specimens under constant lateral pressure are numerically tested for uniform and stochastic distributions of the initial void ratio and for two different mean grain diameters.

Wave propagation along a cylindrical borehole in an anisotropic poroelastic solid

SUMMARY This paper deals with the propagation of elastic waves along a cylindrical borehole embedded in an anisotropic fluid-saturated porous solid of infinite extent. Biot’s theory is used to derive the Christoffel equation for the propagation of cylindrical waves in an anisotropic fluid-saturated porous material. The saturated fluid is viscous. Waves of axial symmetry are considered here. The frequency equations of surface waves corresponding to the empty and liquid-filled borehole are obtained. The effects of transverse isotropy on the phase velocity of surface waves are studied. The phase velocity of surface waves increases with anisotropy. Surface modes in empty and liquid-filled boreholes in an isotropic poroelastic solid and Rayleigh waves propagating on the free surface of a transversely isotropic fluid-saturated porous solid are obtained as particular cases. The presence or absence of fluid in the borehole affects the phase velocity considerably. The phase velocity increases when the empty borehole is filled with liquid.

Rayleigh-wave dispersion function for a transversely isotropic layered spherical earth using the Thomson-Haskell matrix method

We consider the two coupled differential equations of the two radial functions appearing in the displacement components of spheroidal oscillations for a transversely isotropic (TI) medium in spherical coordinates. Elements of the layer matrix have been explicitly written—perhaps for the first time—to extend the use of the Thomson-Haskell matrix method to the derivation of the dispersion function of Rayleigh waves in a transversely isotropic spherical layered earth. Furthermore, an earth-flattening transformation (EFT) is found and effectively used for spheroidal oscillations. The exponential function solutions obtained for each layer give the dispersion function for TI spherical media the same form as that on a flat earth. This has been achieved by assuming that the five elastic parameters involved vary as rp and that the density varies as rp−2, where p is an arbitrary constant and r is the radial distance. A numerical illustration with p= − 2 shows that, in spite of the inhomogeneity assumed within layers, the results for spherical harmonic degree n, versus time period T, obtained here for the Primary Reference Earth Model (PREM), agree well with those obtained earlier by other authors using numerical integration or variational methods. The results for isotropic media derived here are also in agreement with previous results. The effect of transverse isotropy on phase velocity for the first two modes of Rayleigh waves in the period range 20 to 240 s is calculated and discussed for continental and oceanic models.

Effects of transverse isotropy on modes and mode coupling in shallow water

Most marine sediments exhibit transverse isotropy (TI) that can have a significant effect on the signal properties of strongly bottom interacting sound. Locally, transverse isotropy has the greatest effect on the fundamental and near fundamental modal overtones. The local shallow water TI modes have reduced amplitude in the sediment relative to the corresponding shallow water modes for an isotropic bottom. Even a small departure from isotropy (2.4%) can have a significant (15%) effect on the phase velocity of bottom interacting modes. Calculations of mode–mode coupling coefficients for a range-dependent medium indicate that mode coupling is more strongly confined to modal nearest neighbors for a TI medium characterized predominantly by shear wave anisotropy, when compared to the corresponding isotropic medium. As the frequency increases, the strongest coupling occurs between higher overtones and also becomes more strongly peaked around nearest neighbors. The coupled mode theory of Maupin [Geophys. J. 93, 173–185 (1988)] is employed to model the coupling. This theory can treat smooth gradients and sloping layer boundaries for all five of the bottom elastic moduli in a TI medium, the densities, and the range dependence of the water column itself. This coupled mode formulation also properly accounts for the continuity of stress and displacement boundary conditions in an exact way at irregular interfaces.

Normal-mode splitting due to inner-core anisotropy

SUMMARY There is a collection of core-sensitive normal modes that is split much more than predicted from the Earth's rotation, ellipticity, and lateral heterogeneity. Pk'lk'P traveltime observations suggest that the Earth's inner core exhibits cylindrical anisotropy about a nearly corotational axis. We investigate the effect of transverse isotropy, which is the simplest type of anisotropy that exhibits cylindrical symmetry, on the free oscillations of the Earth. We demonstrate that transverse isotropy with a symmetry axis parallel to the rotation axis produces splitting of the form h,,, = w(u' + c'm' + dm')), where m denotes the azimuthal order of a specific singlet within a given multiplet with degenerate eigenfrequency w; the scalars a', c', and rl represent the effects of transverse isotropy on a particular normal mode. The effect of a tilt in the anisotropic symmetry axis relative to the axis of rotation can be easily incorporated and leads to non-zonal splitting

Synthetic seismograms for a long spread of seismometer stations

The assumption that the earth is made up of planeparallel, homogeneous, elastic layers, which can exhibit transverse isotropy and moderate constant‐Q attenuation, leads to an effective method of modeling the response from a point source into a long spread of seismometer stations. Most of the computations are carried out in the complex frequency and complex horizontal wavenumber domains. Minimum sampling criteria are based on an algorithm that suppresses time and distance aliasing at the expense of the large dynamic range available on the digital computer. Other artifacts can be identified and are removed by additional wavenumber filtering. Computational effort is almost independent of the number of detectors and their nature. The structure and symmetry properties of the propagator matrices describing the response are the same for isotropic and transversely isotropic layers. Synthetic seismic panels for a regional model of a west Texas well site exhibit strong, shot‐generated surface waves. A very simple model, based on a south Texas well site, shows the effects of transverse isotropy and the reverberatory nature of converted signals generated by a surface P‐wave.

Effects of transverse isotropy on P-wave AVO for gas sands : Kim, K Y; Wrolstad, K H; Aminzadeh, F GeophysicsV58, N6, June 1993, P883–888

Effects of transverse isotropy on P-wave AVO for gas sands : Kim, K Y; Wrolstad, K H; Aminzadeh, F GeophysicsV58, N6, June 1993, P883–888

Azimuthal variations in scattering amplitudes induced by transverse isotropy

The study of amplitude variations of reflected and transmitted seismic waves due to anistropy has received considerable attention in recent years, but most investigations have concentrated on the effect of transverse isotropy with the symmetry axis either vertical or horizontal. The published results on the whole tend to exclude mode conversions. Amplitudes of all reflected and transmitted wave modes are addressed for [Formula: see text]-waves incident on boundaries between isotropic and transversely isotropic media, the symmetry axis of which is oriented at 45 degrees to the interface. The results cover the full range of incidence angles and all “acquisition azimuth” in the plane of the interface. When the anistropy axis is not normal to the interface, the scattering coefficients are shown to be highly dependent on the azimuth. The pattern of azimuthal variation is especially complicated in the case of mode conversion, and scattering coefficient profiles that are 180 degrees apart are not the same. This has the implication that source‐receiver interchangeability does not hold and could have serious consequences to amplitude studies in split‐spread surveys. Both the [Formula: see text] and [Formula: see text] reflections show strong azimuthal variations, dependent on both the dip and the strike of the anisotropy axis. It may be possible to recover shown that the scattered amplitude patterns are dominantly controlled by the value of the elastic modulus [Formula: see text].

Ductile penny-shaped crack in a transversely isotropic cylinder

The problem of a penny-shaped crack contained in a transversely isotropic cylinder of elastic perfectly-plastic material is considered for the case when the crack is extended by an axial load. The problem is reduced to solving numerically a Fredholm integral equation of the second kind for the width of the plastic zone. Graphical results are presented showing the effect of transverse isotropy upon the width of the plastic zone and these are compared with the results for isotropic materials.

An Axisymmetric Contact Problem of a Transversely Isotropic Layer Indented by an Annular Rigid Punch

A solution is given for the frictionless identation of a transversely isotropic layer by an annular rigid punch, where the elastic layer is resting on a rigid foundation. The problem is reduced to an infinite system of simultaneous equations using the method of expressing the normal stress under the punch as appropriate series. The effects of transverse isotropy and identational load on the stress field are studied. The results are compared with numerical solutions for the corresponding isotropic problem.

Transient thermal stresses in a transversely isotropic finite circular cylinder inserted into a rigid heated circular ring.

Transient thermal stresses are investigated in a transversely isotropic finite circular cylinder inserted into a rigid heated circular ring. The temperature and thermal stress fields are analyzed by means of the Laplace transform and the transversely isotropic potential functions method, respectively. The radial, hoop and axial thermal stresses have singularities at the end of the contacted rigid ring on the cylindrical surface. For that, factors are defined to evaluate the singularities of these stresses. Numerical calculations of these factors were carried out for transversely isotropic graphite. The effects of transverse isotropy, Biot numbers and the length of the circular cylinder on the factors are examined.

An axisymmetric contact problem of a transversely isotropic layer indented by an annular rigid punch.

A solution is given for the frictionless indentation of a transversely isotropic layer by an annular rigid punch, where the elastic layer is resting on a rigid foundation. The problem is reduced to an infinite system of simultaneous equations using the method of expressing the normal stress under the punch as appropriate series. The effect of transverse isotropy and indentational load on the stress field are studied. Results are compared with numerical solutions for the corresponding isotropic problem.

Transient thermoelastic crack problems in transverse isotropy.

The present paper if concerned with two transient thermal stress problems in a transversely isotropic infinite solid containing a crack with heat exchange on the crack surface. One is the problem of a penny-shaped crack, and the other is the problem of an external circular crack. It is very difficult to obtain the analytical solution for the temperature field, so only the finite difference method with respect to the time variable is introduced. Thermal stresses are analyzed by means of the transversely isotropic potential functions method. Numerical calculations were carried out for a graphite which belongs under transverse isotropy. The effects of transverse isotropy on the stress intensity factor are shown in the figures.

Plastic deformation in a thick transversely isotropic layer containing a penny-shaped crack

The width of a thin plastic annular zone formed during the deformation of a pennyshaped crack in a transversely isotropic layer of an ideal elasto-plastic material is determined. Considered are the cases where the penny-shaped crack is extended by normal stresses and by torsional stresses. The faces of the layer are shear free and deformation of the plastic zone around the penny-shaped crack occurs according to the Dugdale hypothesis. For each case, the solution of the problem is reduced to a Fredholm integral equation of the second kind. Iterative solutions are obtained for small values of the parameters and numerical results for the width of the plastic zone are determined. Graphical results showing the effect of transverse isotropy upon the width of the plastic zone are also presented.

THREE‐TERM TAYLOR SERIES FOR t2 ‐ x2‐CURVES OF P‐ AND S‐WAVES OVER LAYERED TRANSVERSELY ISOTROPIC GROUND*

AbstractThe arrival‐time curve of a reflection from a horizontal interface, beneath a homogeneous isotropic layer, is a hyperbola in the x ‐ t‐domain.If the subsurface is one‐dimensionally inhomogeneous (horizontally layered), or if some or all of the layers are transversely isotropic with vertical axis of symmetry, the statement is no longer strictly true, though the arrival‐time curves are still hyperbola‐like. In the case of transverse isotropy, however, classical interpretation of these curves fails. Interval velocities calculated from t2 ‐ x2‐curves do not always approximate vertical velocities and therefore cannot be used to calculate depths of reflectors.To study the relationship between velocities calculated from t2 ‐ x2‐curves and the true velocities of a transversely isotropic layer, we approximate t2 ‐ x2‐curves over a vertically inhomogeneous transversely isotropic medium by a three‐term Taylor series and calculate expressions for these terms as a function of the elastic parameters. It is shown that both inhomogeneity and transverse isotropy affect slope and curvature of t2 ‐ x2‐curves. For P‐waves the effect of transverse isotropy is that the t2 ‐ x2‐curves are convex upwards; for SV‐waves the curves are convex downwards. For SH‐waves transverse isotropy has no effect on curvature.

A transversely isotropic composite with a penny-shaped crack

We consider the problem of determining the stress intensity factor and the crack energy in a transversely isotropic composite medium, containing a penny-shaped crack. We assume that the crack surface is perpendicular to the bond face and the crack is opened by constant internal pressure. By use of integral transform, we reduce the problem to solving a Fredholm integral equation of the second kind. Numerical results are given for the combination of some practical materials such as magnesium and cadmium. The effect of transverse isotropy upon the stress intensity factor, the crack energy and the deformation on the crack surface is discussed.