Anisotropic Elastic Properties Research Articles

Mechanics of ultrasound elastography

Ultrasound elastography enables in vivo measurement of the mechanical properties of living soft tissues in a non-destructive and non-invasive manner and has attracted considerable interest for clinical use in recent years. Continuum mechanics plays an essential role in understanding and improving ultrasound-based elastography methods and is the main focus of this review. In particular, the mechanics theories involved in both static and dynamic elastography methods are surveyed. They may help understand the challenges in and opportunities for the practical applications of various ultrasound elastography methods to characterize the linear elastic, viscoelastic, anisotropic elastic and hyperelastic properties of both bulk and thin-walled soft materials, especially the in vivo characterization of biological soft tissues.

Theoretical prediction of new C–Si alloys in -20 structure**Project supported by the National Natural Science Foundation of China (Grant No. 61474089) and the Open Fund of Key Laboratory of Complex Electromagnetic Environment Science and Technology, China Academy of Engineering Physics (Grant No. 2015-0214.XY.K).

We study structural, mechanical, and electronic properties of C20, Si20 and their alloys (C16Si4, C12Si8, C8Si12, and C4 in structure by using density functional theory (DFT) based on first-principles calculations. The obtained elastic constants and the phonon spectra reveal mechanical and dynamic stability. The calculated formation enthalpy shows that the C–Si alloys might exist at a specified high temperature scale. The ratio of B/G and Poisson’s ratio indicate that these C–Si alloys in -20 structure are all brittle. The elastic anisotropic properties derived by bulk modulus and shear modulus show slight anisotropy. In addition, the band structures and density of states are also depicted, which reveal that C20, C16Si4, and Si20 are indirect band gap semiconductors, while C8Si12 and C4Si16 are semi-metallic alloys. Notably, a direct band gap semiconductor (C12Si8) is obtained by doping two indirect band gap semiconductors (C20 and Si20).

Molecular Dynamics Modeling of the Effect of Axial and Transverse Compression on the Residual Tensile Properties of Ballistic Fiber

Ballistic impact induces multiaxial loading on Kevlar® and polyethylene fibers used in protective armor systems. The influence of multiaxial loading on fiber failure is not well understood. Experiments show reduction in the tensile strength of these fibers after axial and transverse compression. In this paper, we use molecular dynamics (MD) simulations to explain and develop a fundamental understanding of this experimental observation since the property reduction mechanism evolves from the atomistic level. An all-atom MD method is used where bonded and non-bonded atomic interactions are described through a state-of-the-art reactive force field. Monotonic tension simulations in three principal directions of the models are conducted to determine the anisotropic elastic and strength properties. Then the models are subjected to multi-axial loads—axial compression, followed by axial tension and transverse compression, followed by axial tension. MD simulation results indicate that pre-compression distorts the crystal structure, inducing preloading of the covalent bonds and resulting in lower tensile properties.

Electronic structure and mechanical properties of layered compound YB2C2: A promising precursor for making two dimensional (2D) B2C2 nets

Layered compounds play pivotal roles as precursors for producing 2D materials through mechanical exfoliation (micro-mechanical cleavage) or chemical approaches. Therefore, searching for layered compounds with sharp anisotropic chemical bonding and properties becomes emergent. In this work, the stability, electronic structure, elastic properties, and lattice dynamics of YB2C2 were investigated. Strong anisotropy in elastic properties is revealed, i.e., high Young's modulus in a-b plane but low Young's modulus in c direction. The maximum to minimum Young's modulus ratio is 2.41 and 2.45 for YB2C2 with P42/mmc and P4/mbm symmetry, respectively. The most likely systems for shear sliding or micro-delaminating are (001)[100] and (001)[010]. The anisotropic elastic properties are underpinned by the anisotropic chemical bonding, i.e., strong bonding within the B2C2 nets and weak bonding between Y atom layers and B2C2 nets. YB2C2 is electrically conductive and the contributions to the electrical conductivity are from delocalized Y 4deg as well as B 2pz and C 2pz electrons. The layered crystal structure, sharp anisotropic mechanical properties, and metallic conductivity endorse YB2C2 promising as a precursor for new 2D B2C2 nets.

Elastic anisotropy of Tambo gneiss from Promontogno, Switzerland: a comparison of crystal orientation and microstructure-based modeling and experimental measurements

Author(s): Vasin, RN; Kern, H; Lokajicek, T; Svitek, T; Lehmann, E; Mannes, DC; Chaouche, M; Wenk, HR | Abstract: Felsic and mafic gneisses constitute large proportions of the upper and lower continental crust. Gneisses often display high anisotropy of elastic properties associated with preferred orientations of sheet silicates. Here we study the elastic anisotropy of a sample of Tambo gneiss from Promontogno in the Central Alps. We apply optical microscopy, time-of-flight neutron diffraction, neutron and X-ray tomography to quantify mineral composition and microstructures and use them to construct self-consistent models of elastic properties. They are compared to results of ultrasonic measurements on a cube sample in a multi-anvil apparatus and on a spherical sample in an apparatus that can measure velocities in multiple directions. Both methods provide similar results. It is shown that models of microstructure-derived elastic properties provide a good match with ultrasonic experiment results at pressures above 100 MPa. At a pressure of 0.1 MPa the correspondence between the model and the experiment is worse. This may be caused by an oversimplification of the model with respect to microfractures or uncertainties in the experimental determination of S-wave velocities and elastic tensor inversion. The study provides a basis to determine anisotropic elastic properties of rocks either by ultrasonic experiments or quantitative models based on microstructures. This information can then be used for interpretation of seismic data of the crust.

Pressure effects on electronic, anisotropic elastic and thermal properties of Ti3AC2(A[dbnd]Si, Ge and Sn) by ab initio calculations

The structural, electronic bonding characteristics, mechanical and thermal properties of Ti3AC2 (ASi, Ge and Sn) compounds under pressure from 0GPa to 60GPa are investigated by first-principles calculations. Whether under pressure or not, each compound reflects anisotropic elastic properties and their calculated bulk, shear and Young’s moduli are consistent with those determined theoretically and experimentally records. The quasi-harmonic Debye model is introduced in this work to investigate thermal properties of all compounds. Thermal expansion coefficient α of each compound under pressure is firstly discussed in the present paper. It is obviously that α decreases with the pressure increase and Ti3SnC2 shows the highest thermal expansion under pressure. The Debye temperature, CV and Grüneisen parameters are both obtained and the agreement between our calculations and other references are pretty good.

INFLUENCE OF SPATIAL INTERACTIONS OF INCLUSIONS ON THE EFFECTIVE ELASTIC TENSOR OF CRACKED POROUS MEDIUM

The determination of effective stiffness tensor of microinhomogeneous and, in general, macroscopically homogeneous composite medium is related to so-called problem of many-body interaction. Solution to the problem can be found only as an approximation. In this paper we consider a solution to such a problem for porous-cracked medium that is a terrigenous rock having anisotropic elastic properties. The elastic anisotropy is a result of many factors including anisotropic properties of clay minerals and preferential orientation of non-isometric heterogeneities. Different Effective Medium Theories for calculating effective stiffness tensor of cracked porous medium use so called Effective Field Hypothesis (H1, H2 and H3). For example, T-matrix method, Mori-Tanaka method, General Singular Approximation method, and Effective Field Methods use the Effective Field Hypothesis. Thus, different methods produce similar results. When constructing models of rock’s effective properties the rock is treated a composite “made by nature”. In this case of importance is a proper approximation of the real medium by a parametric model medium that reflects specific features of rock’s microstructure. The microstructure is a result of rock evolution. Therefore, the model of the medium and the model parameters play very important roles in the modelling. To prove this statement, two models of a cracked- porous medium’s properties were created using two different methods: the T-matrix method and General Singular Approximation Method. The methods were applied for two different parametric models of one and the same rock. The models were build based on visual analysis of rock’s thin sections. Each of the constructed models has different number of parameters. The parameters are also different. However, a common feature of the two models is that for rocks of this type it is necessary to take into account a rigidity of contact between mineral grains and organic material. Besides, a connectivity of different heterogeneities should be also parametrized. For each model a set of parameters was found and a porosity interval where the models produce similar results in terms of elastic wave velocities is determined.

Analytic Modelling for Wellbore Stability Analysis

1D geomechanical model based on cross-dipole wideband acoustic logging for unconventional reservoir is calculated. TIV anisotropic zones were highlighted and corresponding anisotropic elastic properties were confirmed by core samples tests. Final minimal stress profile was calibrated on the data set including log and laboratory studies, drilling and hydrofracturing. Calibrated model was used to optimize frac design for multiple hydrofracing in the horizontal wells.

Modeling anisotropic static elastic properties of soft mudrocks with different clay fractions

We have quantified the effects of clay fraction and fabric on the static elastic properties of soft mudrocks with emphasis on microlevel mechanisms. Soft mudrocks are treated as a mixture of nonclay minerals and clay-water composites. We have devised a simplified approach to estimate the fabric orientation distribution of soft mudrocks based on measured parameters such as clay fraction and porosity. A single parameter (fabric angle) that characterizes the fabric orientation distribution of soft mudrocks is related to the void ratio of clay-water composites. The static transversely isotropic (TI) elastic properties of soft mudrocks are modeled using an anisotropic differential effective medium approach. The effect of variation in fabric orientation distribution on the TI elastic parameters of clay-water composites is studied by applying the Voigt approximation. With an increase of clay fraction, soft mudrocks have decreasing trends in the deformation moduli because some nonclay minerals are replaced by clay-water composites. However, the deformation moduli of clay-water composites could increase when there is more anisotropy in the fabric due to an increase in the clay fraction. Thus, the correlations between anisotropic elastic moduli and volume fraction of clay-water composites will display some fluctuations. Such nonlinear relationships are validated against published experimental data on Colorado shale samples from the Western Canadian Sedimentary Basin.

An ab initio prediction study of the electronic structure and elastic properties of V3GeC2

The electronic structure and elastic properties of the ternary layered carbide V3GeC2 were investigated by the first-principle plane-wave pseudopotential total energy calculation method based on density functional theory. It is found that the computed P63/mmc lattice constants and internal coordinates are a = 2.9636?, c = 17.2256? and zV2 = 0.1325, zC = 0.5712, respectively. The predictable cohesive energy of V3GeC2 reflects that it could be a stable Mn+1AXn phase like Ti3GeC2 and V2GeC, while the band structure shows that the V3GeC2 has anisotropic electrical conductivity, with a high density of states at the Fermi energy. The V3GeC2 exhibits potential anisotropic elastic properties, as well as self-lubricating and ductile behaviour, related to the V-Ge bonds being relatively weaker than the V-C bonds.

Modeling the Dynamic Behavior of the Upper Structure of the Railway Track

The present work is devoted to modeling the behavior of railway track under dynamic load of wheel pair in view of elastic, viscoelastic and elastic-plastic properties of the area of interaction between two solids and elastic anisotropic properties of the subgrade, which differ in three main areas: along the rails along the sleepers and vertically downwards. The wave equation railway tracks suggest that the deformation and the permanent way and the mound itself is the field of interaction of bodies takes place in view of the spread of a finite speed of the wave surfaces. The solution methods used methods of asymptotic expansions in the time and space coordinate, the method of matching the expansions obtained for short times in the contact zone and outside it.

AFM Identification of Beetle Exocuticle: Bouligand Structure and Nanofiber Anisotropic Elastic Properties

One of the common architectures in natural materials is the helicoidal (Bouligand) structure, where fiber layers twist around a helical screw. Despite the many studies that have shown the existence of Bouligand structures, methods for nanoscale structural characterization and identification of fiber mechanical properties remain to be developed. In this study, we used the exocuticle of Cotinis mutabilis (a beetle in the Cetoniinae) as a model material to develop a new experimental‐theoretical methodology that combines atomic force microscopy‐based nanoindentation and anisotropic contact mechanics analysis. Using such methodology, we studied both the helicoidal structure and the mechanical properties of its constituent fibers. The twist angle between the layers was found to be in the range of 12°–18° with a pitch size of 220 nm for the helicoidal pattern. In addition, the constituent fiber diameter was measured to be approximately 20 nm, which is consistent with the fiber diameters found in helicoids of other arthropod species. The longitudinal, transverse, and shear modulus of the nanofiber were determined to be 710 MPa, 70 MPa, and 90 MPa, respectively. The established experimental‐theoretical methodology promises to be a useful tool for nanoscale characterization of helicoidal and other structures found in biological materials.

A simple basis for determination of the modulus and hydraulic conductivity of human ocular surface using nano-indentation

This manuscript attempts to provide a relatively simply model for the contact loading of fluid containing tissues and materials. It shows that the response of such materials provides a basis for determining the effective modulus and effective hydraulic conductivity (permeability) in much the same manner that hardness and modulus do for the indentation of elastic-plastic materials. Eye tissue with its anisotropic elastic and permeability properties is used to illustrate the approach.

Investigation of structural, electronic and anisotropic elastic properties of Ru-doped WB2 compound by increased valence electron concentration

First principles density functional theory (DFT) calculations have been used to investigate the structural, anisotropic elastic and electronic properties of ruthenium doped tungsten-diboride ternary compounds (W1−xRuxB2) for an increasing molar fraction of Ru atom from 0.1 to 0.9 by 0.1. Among the nine different compositions, W0.3Ru0.7B2 has been found as the most stable one due to the formation energy and band filling theory calculations. Moreover, the band structures and partial density of states (PDOS) have been computed for each x composition. After obtaining the elastic constants for all x compositions, the secondary results such as Bulk modulus, Young’s modulus, Poisson’s ratio, Shear modulus, and Vickers Hardness of polycrystalline aggregates have been derived and the relevant mechanical properties have been discussed. In addition, the elastic anisotropy has been visualized in detail by plotting the directional dependence of compressibility, Poisson ratio, Young’s and Shear moduli.

A new multiscale micromechanical model of vertebral trabecular bones.

A new three-dimensional (3D) multiscale micromechanical model has been suggested as adept at predicting the overall linear anisotropic mechanical properties of a vertebral trabecular bone (VTB) highly porous microstructure. A nested 3D modeling analysis framework spanning the multiscale nature of the VTB is presented herein. This hierarchical analysis framework employs the following micromechanical methods: the 3D parametric high-fidelity generalized method of cells (HFGMC) as well as the 3D sublaminate model. At the nanoscale level, the 3D HFGMC method is applied to obtain the effective elastic properties of a representative unit cell (RUC) representing the mineral collagen fibrils composite. Next at the submicron scale level, the 3D sublaminate model is used to generate the effective elastic properties of a repeated stack of multilayered lamellae demonstrating the nature of the trabeculae (bone-wall). Thirdly, at the micron scale level, the 3D HFGMC method is used again on a RUC of the highly porous VTB microstructure. The VTB-RUC geometries are taken from microcomputed tomography scans of VTB samples harvested from different vertebrae of human cadavers [Formula: see text]. The predicted anisotropic overall elastic properties for native VTBs are, then, examined as a function of age and sex. The predicted results of the VTBs longitudinal Young's modulus are compared to reported values found in the literature. The proposed 3D nested modeling analysis framework provides a good agreement with reported values of Young's modulus of single trabeculae as well as for VTB-RUC in the literature.

Structural, anisotropic and thermodynamic properties of Imm2-BCN

Structural, anisotropic, and thermodynamic properties of Imm2-BCN were studied based on density function theory with the ultrasoft psedopotential scheme in the frame of the generalized gradient approximation (GGA). The elastic constants were confirmed that the predicted Imm2-BCN is mechanically stable. The anisotropy of elastic properties were also studied systematically. The anisotropy studies of Young’s modulus, shear modulus, linear compressibility, and Poisson’s ratio show that the Imm2-BCN exhibits a large anisotropy. Through the quasi-harmonic Debye model, the relations between the equilibrium volume V, thermal expansion α, the heat capacity C V and C P, the Gruneisen parameter γ, and the Debye temperature Θ D with pressure P and temperature T were also studied systematically.

Elasticity of ferropericlase and seismic heterogeneity in the Earth's lower mantle

AbstractDeciphering the origin of seismic heterogeneity has been one of the major challenges in understanding the geochemistry and geodynamics of the deep mantle. Fully anisotropic elastic properties of constituent minerals at relevant pressure‐temperature conditions of the lower mantle can be used to calculate seismic heterogeneity parameters in order to better understand chemically and thermally induced seismic heterogeneities. In this study, the single‐crystal elastic properties of ferropericlase (Mg0.94Fe0.06)O were measured using Brillouin spectroscopy and X‐ray diffraction at conditions up to 50 GPa and 900 K. The velocity‐density results were modeled using third‐order finite‐strain theory and thermoelastic equations along a representative geotherm to investigate high pressure‐temperature and compositional effects on the seismic heterogeneity parameters. Our results demonstrate that from 660 to 2000 km, compressional wave anisotropy of ferropericlase increased from 4% to 9.7%, while shear wave anisotropy increased from 9% to as high as 22.5%. The thermally induced lateral heterogeneity ratio (RS/P = ∂lnVS/∂lnVP) of ferropericlase was calculated to be 1.48 at ambient pressure but decreased to 1.43 at 40 GPa along a representative geotherm. The RS/P of a simplified pyrolite model consisting of 80% bridgmanite and 20% ferropericlase was approximately 1.5, consistent with seismic models at depths from 670 to 1500 km, but showed an increased mismatch at lower mantle depths below ~1500 km. This discrepancy below mid‐lower mantle could be due to either a contribution from chemically induced heterogeneity or the effects of the Fe spin transition in the deeper parts of the Earth's lower mantle.

Application of laser-ultrasonics to texture measurements in metal processing

The paper describes in principle how information about textures can be obtained through the application of laser-ultrasonics (LUS) which can be carried out at elevated temperatures, for example in connection with hot rolling. The benefits from getting a measure of texture in this way are explained together with the proposed methodology which is based on the elastic anisotropic properties of the textured material. Measurements are made using only a single laser pulse and in real-time.Two approaches are presented to modelling the propagation of elastic waves, ray tracing and finite difference modelling. These give consistent results but the latter provides a more complete prediction of the ultrasonic spectrum that can be quantitatively related to measured signals through a cross-correlation procedure.Some experimental results are presented for room temperature measurements on a sheet of interstitial-free steel. Agreement between experimental data and modelling results is good and allows estimation of the 4th order coefficients of the orientation distribution function.

Elastically mediated interactions between grain boundaries and precipitates in two-phase coherent solids

We investigate analytically and numerically the interaction between grain boundaries and second phase precipitates in two-phase coherent solids in the presence of misfit strain. Our numerical study uses amplitude equations that describe the interaction of composition and stress [R. Spatschek and A. Karma, Phys. Rev. B {\bf 81}, 214201 (2010)] and free-energies corresponding to two-dimensional hexagonal and three-dimensional BCC crystal structures that exhibit isotropic and anisotropic elastic properties, respectively. We consider two experimentally motivated geometries where (i) a lamellar precipitate nucleates along a planar grain boundary that is centered inside the precipitate, and (ii) a circular precipitate nucleates inside a grain at a finite distance to an initially planar grain boundary. For the first geometry, we find that the grain boundary becomes morphologically unstable due to the combination of long-range elastic interaction between the grain boundary and compositional domain boundaries, and shear-coupled grain boundary motion. We characterize this instability analytically by extending the linear stability analysis carried out recently [P.-A. Geslin, Y.-C. Xu, and A. Karma, Phys. Rev. Lett. {\bf 114}, 105501 (2015)] to the more general case of elastic anisotropy. The analysis predicts that elastic anisotropy hinders but does not suppress the instability. Simulations also reveal that, in a well-developed non-linear regime, this instability can lead to the break-up of low-angle grain boundaries when the misfit strain exceeds a threshold that depends on the grain boundary misorientation. For the second geometry, simulations show that the elastic interaction between an initially planar grain boundary and an adjacent circular precipitate causes the precipitate to migrate to and anchor at the grain boundary.

Simulation of self-piercing rivetting processes in fibre reinforced polymers: Material modelling and parameter identification

This paper addresses the numerical simulation of self-piercing rivetting processes to join fibre reinforced polymers and sheet metals. Special emphasis is placed on the modelling of the deformation and failure behaviour of the composite material. Different from the simulation of rivetting processes in metals, which requires the modelling of large plastic deformations, the mechanical response of composites is typically governed by intra- and interlaminar damage phenomena. Depending on the polymeric matrix, viscoelastic effects can interfere particularly with the long-term behaviour of the joint. We propose a systematic approach to the modelling of composite laminates, discuss limitations of the used model, and present details of parameter identification.Homogenisation techniques are applied to predict the mechanical behaviour of the composite in terms of effective anisotropic elastic and viscoelastic material properties. In combination with a continuum damage approach this model represents the deformation and failure behaviour of individual laminae. Cohesive zones enable the modelling of delamination processes. The parameters of the latter models are identified from experiments. The defined material model for the composite is eventually utilised in the simulation of an exemplary self-piercing rivetting process.