Showing papers on "Transverse isotropy published in 2014"

A recipe for practical full-waveform inversion in anisotropic media: An analytical parameter resolution study

Abstract: In multiparameter full-waveform inversion (FWI) and specifically one describing the anisotropic behavior of the medium, it is essential that we have an understanding of the parameter resolution possibilities and limits. Because the imaging kernel is at the heart of the inversion engine (the model update), we drew our development and choice of parameters from what we have experienced in imaging seismic data in anisotropic media. In representing the most common (first-order influence and gravity induced) acoustic anisotropy, specifically, a transversely isotropic medium with a vertical symmetry direction (VTI), with the P-wave normal moveout velocity, anisotropy parameters δ, and η, we obtained a perturbation radiation pattern that has limited trade-off between the parameters. Because δ is weakly resolvable from the kinematics of P-wave propagation, we can use it to play the role that density plays in improving the data fit for an imperfect physical model that ignores the elastic nature of the earth...

Numerical Modelling of the Anisotropic Mechanical Behaviour of Opalinus Clay at the Laboratory-Scale Using FEM/DEM

Abstract: The Opalinus Clay (OPA) is an argillaceous rock formation selected to host a deep geologic repository for high-level nuclear waste in Switzerland. It has been shown that the excavation damaged zone (EDZ) in this formation is heavily affected by the anisotropic mechanical response of the material related to the presence of bedding planes. In this context, the purpose of this study is twofold: (i) to illustrate the new developments that have been introduced into the combined finite-discrete element method (FEM/DEM) to model layered materials and (ii) to demonstrate the effectiveness of this new modelling approach in simulating the short-term mechanical response of OPA at the laboratory-scale. A transversely isotropic elastic constitutive law is implemented to account for the anisotropic elastic modulus, while a procedure to incorporate a distribution of preferentially oriented defects is devised to capture the anisotropic strength. Laboratory results of indirect tensile tests and uniaxial compression tests are used to calibrate the numerical model. Emergent strength and deformation properties, together with the simulated damage mechanisms, are shown to be in strong agreement with experimental observations. Subsequently, the calibrated model is validated by investigating the effect of confinement and the influence of the loading angle with respect to the specimen anisotropy. Simulated fracture patterns are discussed in the context of the theory of brittle rock failure and analyzed with reference to the EDZ formation mechanisms observed at the Mont Terri Underground Research Laboratory.

Mechanical and Elastic Properties of Transversely Isotropic Slate

Abstract: Planes of weakness like schistosity and foliation affect the strength and deformational behaviors of rocks. In this paper, an attempt has been made to study the elastic and strength behavior of slate rocks obtained from foundation of Sardasht dam site in Iran. Wet and dry specimens with different orientation of foliation were evaluated under uniaxial, triaxial, and Brazilian tests. According to the results obtained, slate mechanically pronounced U-shaped anisotropy in uniaxial and triaxial compression tests. In addition, the degree of anisotropy for the slates tested in current study was relatively high, showing the effect of foliation plane on strength and elastic parameters. It was concluded that stiffness of the samples decrease as the angle of anisotropy reaches 30–40°. This change was more pronounced for wet comparing to dry samples. However, the tensile strength obtained during Brazilian tests indicated that there is no apparent relationship between angle of anisotropy and tensile strength. However, increasing the water saturation decreased the tensile strength of the samples. The calculated elastic moduli referring to different anisotropy angles could be valuable for the design of various engineering structures in planar textured rock masses.

The Hertz-Type and Adhesive Contact Problems for Depth-Sensing Indentation

Abstract: Connections between the Hertz-type contact problems and depth-sensing indentation of materials are studied. Formulations of Hertz-type contact problems with various boundary conditions within the contact area are discussed in detail. The problems under investigations can be subdivided into two large groups: self-similar problems for anisotropic materials with various rheological properties and adhesive contact problems for arbitrary bodies of revolution or for power-law shaped blunt indenters. Specific features of indentation problems are described and the common methods for extracting elastic and adhesive properties of materials are briefly reviewed. The basic formulae are extended to the case of nonslipping boundary conditions between a probe and the material. The main formulae of the JKR theory of adhesion are extended to any material with rotational symmetry of the elastic properties. These materials include not only isotropic or transversely isotropic elastic solids but also homogeneously prestressed isotropic or transversely isotropic nonlinear elastic materials. The BG method introduced for extracting adhesive and elastic properties of isotropic elastic materials from depth-sensing diagrams of spherical indenters, is described and extended to linear or linearized materials with rotational symmetry of the elastic properties.

Pump-probe measurements of the thermal conductivity tensor for materials lacking in-plane symmetry.

Abstract: We previously demonstrated an extension of time-domain thermoreflectance (TDTR) which utilizes offset pump and probe laser locations to measure in-plane thermal transport properties of multilayers. However, the technique was limited to systems of transversely isotropic materials studied using axisymmetric laser intensities. Here, we extend the mathematics so that data reduction can be performed on non-transversely isotropic systems. An analytic solution of the diffusion equation for an N-layer system is given, where each layer has a homogenous but otherwise arbitrary thermal conductivity tensor and the illuminating spots have arbitrary intensity profiles. As a demonstration, we use both TDTR and time-resolved magneto-optic Kerr effect measurements to obtain thermal conductivity tensor elements of α-SiO2. We show that the out-of-phase beam offset sweep has full-width half-maxima that contains nearly independent sensitivity to the in-plane thermal conductivity corresponding to the scanning direction. Also, we demonstrate a Nb-V alloy as a low thermal conductivity TDTR transducer layer that helps improve the accuracy of in-plane measurements.

Mechanical characterization of CFRP composites by ultrasonic immersion tests: Experimental and numerical approaches

Abstract: We study an innovative experimental approach for the characterization of the elastic response of anisotropic composite materials by ultrasonic immersion tests. In particular, the class of anisotropy and the elastic moduli can be determined starting from measurements of the velocities of ultrasonic waves propagating in suitable directions. To this aim, we have designed and developed a goniometric ultrasonic test bench and a software for the management of the test and the processing of the acquired data. By employing this experimental device, we determine in a non-destructive way the five elastic moduli of a transversely isotropic unidirectional CFRP composite. The experimental analyses are supported by numerical simulations, which are useful for a deeper insight of the propagation phenomena and for enhancing the experimental strategies to be adopted.

A modified failure criterion for transversely isotropic rocks

Abstract: A modified failure criterion is proposed to determine the strength of transversely isotropic rocks. Mechanical properties of some metamorphic and sedimentary rocks including gneiss, slate, marble, schist, shale, sandstone and limestone, which show transversely isotropic behavior, were taken into consideration. Afterward, introduced triaxial rock strength criterion was modified for transversely isotropic rocks. Through modification process an index was obtained that can be considered as a strength reduction parameter due to rock strength anisotropy. Comparison of the parameter with previous anisotropy indexes in literature showed reasonable results for the studied rock samples. The modified criterion was compared to modified Hoek-Brown and Ramamurthy criteria for different transversely isotropic rocks. It can be concluded that the modified failure criterion proposed in this study can be used for predicting the strength of transversely isotropic rocks.

Vibration Analysis of a Rigid Circular Disk Embedded in a Transversely Isotropic Solid

Abstract: The analytical treatment of normal, rocking, and torsional forced time-harmonic vibrations of a rigid circular disk in a transversely isotropic full-space is revisited. A complete discussion on frequently used contact assumptions of adhesive and smooth models is given, and the effects of different contact models on the results of each vibration mode are discussed. With the aid of appropriate dynamic Green’s functions, the in-plane mode of vibration of the disk is treated analytically for the first time, and the results are expressed in terms of the solution of a Fredholm integral equation. For all four vibration modes, the relations for the contact stress, the resultant force acting on the disk, and the dimensionless compliance factor are given. The available closed-form results in the literature corresponding to the static loading are exactly recovered as the limiting cases of the current study. Furthermore, the results are verified with the special case of an isotropic full-space. By virtue of t...

Extended precise integration method for consolidation of transversely isotropic poroelastic layered media

Abstract: A new numerical method for calculating the consolidation behavior of the stratified, transversely isotropic and poroelastic material is presented by combining the extended precise integration algorithm with the integral transformation techniques. Starting with the governing partial differential equations of a saturated medium with transversely isotropic skeleton and compressible fluid constituents, an ordinary differential matrix equation is deduced with the aid of a Laplace-Hankel transform. An extended precise integration method for internal loading situations is proposed to solve the ordinary differential matrix equation in the transformed domain, and the actual solution is recovered by a numerical inverse transformation. Numerical examples are also provided to prove the feasibility of this method.

Vertical Dynamic Response of Pile Embedded in Layered Transversely Isotropic Soil

Abstract: The dynamic response of pile embedded in layered transversely isotropic soil and subjected to arbitrary vertical harmonic force is investigated. Based on the viscoelastic constitutive relations for a transversely isotropic medium, the dynamic governing equation of the transversely isotropic soil is obtained in cylindrical coordinates. By introducing the fictitious soil pile model and the distributed Voigt model, the governing equations of soil-pile system are also derived. Firstly, the vertical response of the soil layer is solved by using the Laplace transform technique and the separation of variables technique. Secondly, the analytical solution of velocity response in the frequency domain and its corresponding semianalytical solution of velocity response in the time domain are derived by means of inverse Fourier transform and convolution theorem. Finally, based on the obtained solutions, a parametric study has been conducted to investigate the influence of the soil anisotropy on the vertical dynamic response of pile. It can be seen that the influence of the shear modulus of soil in the vertical plane on the dynamic response of pile is more notable than the influence of the shear modulus of soil in the horizontal plane on the dynamic response of pile.

Constraining melt geometries beneath the Afar Depression, Ethiopia from teleseismic receiver functions: The anisotropic H-κ stacking technique

Abstract: Understanding the nature of the crust has long been a goal for seismologists when imaging the Earth. This is particularly true in volcanic regions where imaging melt storage and migration can have important implications for the size and nature of an eruption. Receiver functions and the H-κ stacking (Hκ) technique are often used to constrain crustal thickness (H) and the ratio of P to S wave velocities (κ). In this paper, I show that it is essential to consider anisotropy when performing Hκ. I show that in a medium with horizontally transverse isotropy a strong variation in κ with back azimuth is present, which characterizes the anisotropic medium. In a vertically transverse isotropic medium, no variation in κ with back azimuth is observed, but κ is increased across all back azimuths. Thus, estimates of κ are more difficult to relate to composition than previously thought. I extend these models to melt-induced anisotropy and show that similar patterns are observed, but with more significant variations and increases in κ. Based on these observations, I develop a new anisotropic H-κ stacking technique which inverts Hκ data for melt fraction, aspect ratio, and orientation of melt inclusions. I apply this to data for the Afar Depression and show that melt is stored in interconnected stacked sills in the lower crust, which likely supply the recent volcanic eruptions and dike intrusions. This new technique can be applied to any anisotropic medium where it can provide constraints on the average crustal anisotropy.

Resonant ultrasound spectroscopy for viscoelastic characterization of anisotropic attenuative solid materials

Abstract: Resonant ultrasound spectroscopy (RUS) is an accurate measurement method in which the full stiffness tensor of a material is assessed from the free resonant frequencies of a small sample, and the viscoelastic damping is measured from the resonant peaks width. High viscoelastic damping causes the resonant peaks to overlap and therefore complicate the measurement of the resonant frequencies and the inverse identification of material properties. For that reason, RUS has been known to be fully applicable only to low damping materials. The purpose of this work is to adapt RUS for the characterization of highly attenuating viscoelastic materials. Spectrum measurement using shear transducers combined with dedicated signal processing is employed to retrieve the resonant frequencies despite overlapping. A probabilistic (Bayesian) formulation of the inverse problem, tackling the problem of correctly pairing the measured and predicted frequencies, is proposed. Applications to polymethylmethacrylate (isotropic) and glass/epoxy transversely isotropic samples are presented. The full set of viscoelastic properties is obtained with good repeatability. Particularly, elastic moduli of the isotropic samples are obtained within 1%.

Small strain stiffness anisotropy of natural sedimentary clays: review and a model

Abstract: Very small strain stiffness anisotropy of sedimentary clays is investigated. First, a general formulation of transversely isotropic elastic model is summarised, followed by a description of its complete parameter identification using transversal and longitudinal wave velocity measurements. Then, an extensive experimental database from the literature is reviewed. A number of general trends in the anisotropy evolution is identified, based on which a model is developed describing the dependency of the ratio of in-plane and transversal very small strain shear moduli on the stress state and overconsolidation ratio. Subsequently, an empirical relation between the ratios of shear moduli and Young moduli is quantified. The most problematic tends to be the evaluation of Poisson ratios and evolution of stiffness anisotropy under general stress conditions. These issues remain to be investigated experimentally in future work.

Numerical experiments of fracture-induced velocity and attenuation anisotropy

Abstract: SUMMARY FracturesarecommonintheEarth’scrustduetodifferentfactors,forinstance,tectonicstresses and natural or artificial hydraulic fracturing caused by a pressurized fluid. A dense set of fractures behaves as an effective long-wavelength anisotropic medium, leading to azimuthally varying velocity and attenuation of seismic waves. Effective in this case means that the predominant wavelength is much longer than the fracture spacing. Here, fractures are represented by surface discontinuities in the displacement u and particle velocity v as [κ ·u + η ·v], where the brackets denote the discontinuity across the surface, κ is a fracture stiffness and η is a fracture viscosity. We consider an isotropic background medium, where a set of fractures are embedded. There exists an analytical solution—with five stiffness components—for equispaced plane fractures and an homogeneous background medium. The theory predicts that the equivalent medium is transversely isotropic and viscoelastic. We then perform harmonic numerical experiments to compute the stiffness components as a function of frequency, by using a Galerkin finite-element procedure, and obtain the complex velocities of the medium as a function of frequency and propagation direction, which provide the phase velocities, energy velocities (wavefronts) and quality factors. The algorithm is tested with the analytical solution and then used to obtain the stiffness components for general heterogeneous cases, where fractal variations of the fracture compliances and background stiffnesses are considered.

Instability of a magnetoelastic layer resting on a non-magnetic substrate

Abstract: Magnetorheological elastomers (MREs) are ferromagnetic particle impregnated rubbers whose mechanical properties are altered by the application of external magnetic fields. Due to their coupled magneto-mechanical response, MREs are finding an increasing number of engineering applications. One such application is in haptics, where the goal is to actively control surface roughness. One way to achieve this is by exploiting the unstable regime of MRE substrate/layer assemblies subjected to transverse magnetic fields. In this work, we study the response of such an assembly subjected to a transverse magnetic field and in-plane stress. The layer is made up of a transversely isotropic MRE material, whose energy density has been obtained experimentally, while the substrate is a non-magnetic isotropic pure polymer/gel. An analytical solution to this problem based on a general, finite strain, 2D continuum modeling for both the MRE layer and the substrate, shows that for adequately soft substrates there is a finite-wavelength buckling mode under a transverse magnetic field. Moreover, the critical magnetic field can be substantially reduced in the presence of a compressive stress of the assembly, thus opening the possibility for haptic applications operating under low magnetic fields.

A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates

Abstract: In the present study, a sinusoidal shear and normal deformation theory taking into account effects of transverse shear as well as transverse normal is used to develop the analytical solution for the bidirectional bending analysis of isotropic, transversely isotropic, laminated composite and sandwich rectangular plates. The theory accounts for adequate distribution of the transverse shear strains through the plate thickness and traction free boundary conditions on the plate boundary surface, thus a shear correction factor is not required. The displacement field uses sinusoidal function in terms of thickness coordinate to include the effect of transverse shear and the cosine function in terms of thickness coordinate is used in transverse displacement to include the effect of transverse normal. The kinematics of the present theory is much richer than those of the other higher order shear deformation theories, because if the trigonometric term is expanded in power series, the kinematics of higher order theories are implicitly taken into account to good deal of extent. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The Navier solution for simply supported laminated composite plates has been developed. Results obtained for displacements and stresses of simply supported rectangular plates are compared with those of other refined theories and exact elasticity solution wherever applicable.

Pore fluid viscosity effects on P‐ and S‐wave anisotropy in synthetic silica‐cemented sandstone with aligned fractures

Abstract: Ultrasonic (500 kHz) P- and S-wave velocity and attenuation anisotropy were measured in the laboratory on synthetic, octagonal-shaped, silica-cemented sandstone samples with aligned penny-shaped voids as a function of pore fluid viscosity. One control (blank) sample was manufactured without fractures, another sample with a known fracture density inline image (measured from X-ray CT images). Velocity and attenuation were measured in four directions relative to the bedding fabric (introduced during packing of successive layers of sand grains during sample construction) and the coincident penny-shaped voids (fractures). Both samples were measured when saturated with air, water (viscosity 1 cP) and glycerin (100 cP) to reveal poro-visco-elastic effects on velocity and attenuation, and their anisotropy. The blank sample was used to estimate the background anisotropy of the host rock in the fractured sample; the bedding fabric was found to show transverse isotropy with shear wave splitting (SWS) of 1.45 ± 1.18% (i.e. for S-wave propagation along the bedding planes). In the fractured rock, maximum velocity and minimum attenuation of P-waves was seen at 90° to the fracture normal. After correction for the background anisotropy, the fractured sample velocity anisotropy was expressed in terms of Thomsen's weak anisotropy parameters ?, ? & ?. A theory of frequency-dependent seismic anisotropy in porous, fractured, media was able to predict the observed effect of viscosity and bulk modulus on ? and ? in water- and glycerin-saturated samples, and the higher ? and ? values in air-saturated samples. Theoretical predictions of fluid independent ? are also in agreement with the laboratory observations. We also observed the predicted polarisation cross-over in shear-wave splitting for wave propagation at 45° to the fracture normal as fluid viscosity and bulk modulus increases.

On the Buckling of Isotropic, Transversely Isotropic and Laminated Composite Rectangular Plates

Abstract: This paper presents the uniaxial and biaxial buckling analysis of rectangular plates based on new trigonometric shear and normal deformation theory. The theory accounts for the cosine distribution of the transverse shear strain through the plate thickness and on the free boundary conditions on the plate surfaces without using the shear correction factor. Governing equations and boundary conditions of the theory are derived by the principle of virtual work. The Navier type solutions for the buckling analysis of simply supported isotropic, transversely isotropic, orthotropic and symmetric cross-ply laminated composite rectangular plates subjected to uniaxial and biaxial compressions are presented. The effects of variations in the degree of orthotropy of the individual layers, side-to-thickness ratio and aspect ratio of the plate are examined on the buckling characteristics of composite plates. The present results are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT) and exact three-dimensional (3D) elasticity theory wherever applicable. Good agreement is achieved of the present results with those of higher order shear deformation theory (HSDT) and elasticity theory.

Full-Field Measurements for Determining Orthotropic Elastic Parameters of Woven Glass-Epoxy Composites Using Off-Axis Tensile Specimens

Abstract: Using theoretical formulations to describe the general response of an orthogonally woven glass-epoxy composite subjected to off-axis tension loading, a simple experimental methodology incorporating stereovision and 3D digital image correlation (3D-DIC) into several optimization procedures is described that provides a direct approach for quantitatively determining all of the elastic properties. During each off-axis tensile loading experiment, axial strains are determined using both mechanical extensometry and 3D-DIC, with the 3D-DIC measurements also used to extract both the in-plane transverse normal strain and the shear strain fields. The effectiveness of various optimization procedures are then evaluated and compared by performing a series of off-axis tensile loading experiments to determine the material engineering constants, including E1, E2, G12, and v12 for the nominally transversely isotropic material. Results indicate excellent agreement between the extensometer measurements and the average axial strain obtained by 3D-DIC. Furthermore, direct comparison of the proposed optimization methods indicates that each method is robust and effective, especially when employing 3D-DIC to extract additional information to complete the elastic property characterization procedure.