Average Shear Modulus Research Articles

Quantitative evaluation of atrial radio frequency ablation using intracardiac shear-wave elastography.

Radio frequency catheter ablation (RFCA) is a well-established clinical procedure for the treatment of atrial fibrillation (AF) but suffers from a low single-procedure success rate. Recurrence of AF is most likely attributable to discontinuous or nontransmural ablation lesions. Yet, despite this urgent clinical need, there is no clinically available imaging modality that can reliably map the lesion transmural extent in real time. In this study, the authors demonstrated the feasibility of shear-wave elastography (SWE) to map quantitatively the stiffness of RFCA-induced thermal lesions in cardiac tissues in vitro and in vivo using an intracardiac transducer array. SWE was first validated in ex vivo porcine ventricular samples (N = 5). Both B-mode imaging and SWE were performed on normal cardiac tissue before and after RFCA. Areas of the lesions were determined by tissue color change with gross pathology and compared against the SWE stiffness maps. SWE was then performed in vivo in three sheep (N = 3). First, the stiffness of normal atrial tissues was assessed quantitatively as well as its variation during the cardiac cycle. SWE was then performed in atrial tissue after RFCA. A large increase in stiffness was observed in ablated ex vivo regions (average shear modulus across samples in normal tissue: 22 ± 5 kPa, average shear-wave speed (ct): 4.5 ± 0.4 m s(-1) and in determined ablated zones: 99 ± 17 kPa, average ct: 9.0 ± 0.5 m s(-1) for a mean shear modulus increase ratio of 4.5 ± 0.9). In vivo, a threefold increase of the shear modulus was measured in the ablated regions, and the lesion extension was clearly visible on the stiffness maps. By its quantitative and real-time capabilities, Intracardiac SWE is a promising intraoperative imaging technique for the evaluation of thermal ablation during RFCA.

Measurement of rolling shear modulus and strength of cross laminated timber fabricated with black spruce

The design and application of cross laminated timber (CLT) is strongly influenced by the rolling shear properties of cross layers. Hence, to predict the performance of CLT requires accurate information about its rolling shear properties. In this study, a wooden cross layer (WCL) specimen was made of 38mm by 89mm black spruce lumber of a grade of No. 3. The average rolling shear modulus of the WCL specimens measured by the two-plate shear test was 136MPa. The rolling shear modulus measured was then used as input to predict, using the shear analogy method, the deflection (dc) of a 3-layer CLT beam subjected to the centre-point bending load. Subsequently, the bending test was conducted to directly obtain the deflection (dm) of a 3-layer CLT beam for validation. It was found that dc could, with an adjustment factor (α), provide a good estimate of dm at different span-to-depth ratios under the centre-point bending test. Additionally, the bending test results showed that the specimen width did not have a statistically significant effect on apparent modulus of elasticity (Eapp) and apparent shear modulus (Gapp) of 3-layer CLT beam specimens.

Experimental determination of shear properties, buckling resistance and diagonal tension field of polyurethane coated nylon fabric

Experimental methods have been employed to acquire shear properties, examine buckling, and postbuckling response, and to characterize out-of-plane deformations of thin orthotropic polyurethane-coated nylon fabric designated for use in the finite element analysis of an inflatable structure. A custom-designed bi-axial pre-tension frame, a picture-fame rig, and a photogrammetry system were used to apply pre-tension, collect the angular and linear displacements, and to capture the buckling and wrinkle-forming mechanisms in the coupons during the shear test. The series of monotonic picture-frame tests provided with an average critical shear stress of 0.16 MPa that was required to buckle the coupons for a small range of the pre-tension force. While an average pre-buckling shear modulus (28.5 MPa) was obtained, only 2.25% of a relative difference between the average post-buckling apparent shear modulus (13.07 MPa) and the average shear modulus obtained from the 45° bias-extension test for the same material (13.36 MPa) was registered. The influence of the pre-tension not only on the initial buckling resistance and the transition point to the fully developed diagonal tension folds but also on a reduced resistance to the material damage during cyclic testing was investigated. A series of cyclic picture-frame tests gave the continuous load/unload response with appreciable hysteresis characteristics of the in-plane stress–strain with an average 10% of material degradation. When compared with the envelope of material resistance in the monotonic tests, during cycling loading, the coupons lost on average 13.9% more of its initial stress-carrying capability. The photogrammetry results allowed for the three-dimensional reconstruction of the coupon’s surface and the development of the deformation relationships between the effective force exerted on the coupons, the shear angle, and the geometric deformation variables for the wrinkles formed in the diagonal tension fold. The geometric deformation parameters, such as frequency of wrinkle formation, widths of the base and the tip, depths, the deformation angle, and the distances between the centerlines of the wrinkles occurring in the test coupon, were acquired with photogrametry and analyzed numerically with custom-written Matlab® code.

Biomechanical imaging of cell stiffness and prestress with subcellular resolution

Knowledge of cell mechanical properties, such as elastic modulus, is essential to understanding the mechanisms by which cells carry out many integrated functions in health and disease. Cellular stiffness is regulated by the composition, structural organization, and indigenous mechanical stress (or prestress) borne by the cytoskeleton. Current methods for measuring stiffness and cytoskeletal prestress of living cells necessitate either limited spatial resolution but with high speed, or spatial maps of the entire cell at the expense of long imaging times. We have developed a novel technique, called biomechanical imaging, for generating maps of both cellular stiffness and prestress that requires less than 30 s of interrogation time, but which provides subcellular spatial resolution. The technique is based on the ability to measure tractions applied to the cell while simultaneously observing cell deformation, combined with capability to solve an elastic inverse problem to find cell stiffness and prestress distributions. We demonstrated the application of this technique by carrying out detailed mapping of the shear modulus and cytoskeletal prestress distributions of 3T3 fibroblasts, making no assumptions regarding those distributions or the correlation between them. We also showed that on the whole cell level, the average shear modulus is closely associated with the average prestress, which is consistent with the data from the literature. Data collection is a straightforward procedure that lends itself to other biochemical/biomechanical interventions. Biomechanical imaging thus offers a new tool that can be used in studies of cell biomechanics and mechanobiology where fast imaging of cell properties and prestress is desired at subcellular resolution.

Elastic properties of diamond and zincblende covalent crystals

In this study, the authors have improved the existing model, in the literature, that relates the average shear modulus with the bond length and Phillips’ ionicity. The authors have derived new models for the average Young’s modulus, shear modulus and Young’s modulus on (111) plane for cubic crystals. The calculations yield results that are found to be in good accord with the available experimental and theoretical data of both elastic moduli and elastic constants. These models also shed some light on the accurate predictions of elastic constants of ternary semiconductor alloys.

Effects of pressure on the elasticity and stability of zircon (ZrSiO 4): First-principle investigations

We investigate the effects of pressure on the elasticity of zircon using the Local Density Approximation (LDA) within the density functional theory. Our LDA calculations predict the elastic constants ( C ij ) with positive pressure derivatives, except C 66 whose pressure derivatives are nearly zero, showing small positive to negative departures with increasing pressure. We calculated Young’s moduli, E 1 and E 3 along the crystallographic axes a and c, respectively. At low pressures (<4 GPa) E 1 < E 3, but the relation reverses at pressures >4 GPa, implying a directional change of axial stiffness of zircon crystals. Our LDA calculated Hill’s average bulk ( B) and shear ( G) moduli show contrasting variations with pressure. B is more sensitive to pressure with positive derivatives varying from 2.25 to 5.63, as compared to much lower pressure derivatives (0.4) of G, which drops to negative values (−0.404) at pressures >7 GPa, and then take up positive values (1.3). The zircon to reidite phase transition, involving “bond switching mechanisms” [1] increases the magnitudes of both B and G, but shows relatively weak effects on their pressure derivatives. This study shows the effects of pressure on the degrees of shear and directional bulk modulus anisotropy of zircon. We also calculated its Debye temperature (708 K) from the elastic wave velocities, which fairly agrees to the available experimental data. Our study predicts that increasing pressure widens the electronic band gap of zircon, implying its greater insulation property at high pressures.

Pressure dependent elastic properties of diluted magnetic semiconductors: Hg 1− xMn xS ( x=0.02 and 0.07)

A theoretical study of the elastic properties in diluted magnetic semiconductors Hg 1− x Mn x S ( x=0.02 and 0.07) using an effective interionic interaction potential (EIoIP) in which long-range Coulomb interactions, charge transfer mechanism (three body interaction) and the Hafemeister and Flygare type short-range overlap repulsion extending up to the second neighbor ions and the van der Waals (vdW) interaction is considered. Particular attention is devoted to evaluate Poisson's ratio ν, the ratio R S/ B of S (Voigt averaged shear modulus ) over B (bulk modulus), elastic anisotropy parameter, elastic wave velocity, average wave velocity and thermodynamic property as Debye temperature is calculated. By analyzing Poisson's ratio ν and the ratio R S/ B we conclude that Hg 1− x Mn x S is brittle in zinc blende (B3). To our knowledge this is the first quantitative theoretical prediction of the pressure dependence of ductile (brittle) nature of Hg 1− x Mn x S compounds and still awaits experimental confirmations.

On the use of hollow tube geometries for resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) can nondestructively obtain the elastic constants of compact specimens, however many materials have hollow cross-sections and frequency analysis of such geometries is required before inclusion in the RUS methodology. Resonant mode shapes of tubes with length equal to diameter and varying ratios of tube inner to outer diameter (Λ) as well as Poisson's ratio (ν) were identified by eigenvalue analysis using a commercial finite element code. Longitudinal and shear RUS experiments were conducted on tubes with Λ varying between 0 and 0.95 and compared to the numerical results. Simulations predict that the fundamental mode transitions from pure torsion to symmetric or antisymmetric ring bending at Λ = 0.3. The frequency of the first torsion mode is invariant to Λ and unequivocal identification of this mode is obscured by overlap of bending harmonics as Λ approaches 0.95. In the context of rapid calculation of isotropic elastic constants, shear moduli were calculated from the first torsional mode and Poisson's ratio was inferred from the Demarest maps of the mode structure's dependence upon Poisson's ratio. An average shear modulus of 27.5 + 1.5 ∕ -0.6 GPa, about 5% larger than literature values for 6061 aluminum, and ν of 0.33 were inferred. Errors are attributed to tube aspect ratios slightly greater than 1 and weak material anisotropy. Existing analytical solutions for ring bending modes derived from shell approximations and for infinitely long tubes under plane strain assumptions do not adequately describe the fundamental modes for short tubes. The shear modulus can be calculated for all Λ using the existing analytical solution.

Elasticity of tephroite (-Mn2SiO4) and a comparison of the elastic properties of silicate olivines

The elastic constants of pure tephroite (α-Mn 2 SiO 4 ) have been determined by Brillouin spectroscopy. From measurements, the average aggregate bulk and shear moduli at ambient conditions are 129.8 ± 0.5 and 53.1 ± 0.4 GPa, respectively, which also confirm the reality of the unexpected high elastic moduli in tephroite. An analysis based on the present data and those in literature has revealed the relative orders: fayalite > tephroite ≥ forsterite for bulk modulus and forsterite >> tephroite > fayalite for shear modulus. It also indicates that the propagation velocity of a sound wave inside forsterite will be considerably changed by dissolving a small amount of Mn 2+ and/or Fe 2+ (for shear wave) and Ni 2+ cations (for compressional wave). The causes for the significant difference between forsterite and the 3d silicate olivines and the unexpected elastic behavior in tephroite have been explored by considering the nature of both electron orbitals and MO 6 octahedra.

Pressure dependent mechanical and thermodynamical properties of Hg0.91Mn0.09Te semiconductor

The mechanical, thermodynamical and elastic properties of Hg0.91Mn0.09Te compound are calculated by formulating an effective interionic interaction potential. This potential consists of the long-range Coulomb, three body force parameter, the Hafemeister and Flygare type short-range overlap repulsion extended upto the second neighbor ions and the van der Waals (vdW) interaction. The estimated values of phase transition pressure have revealed reasonably good agreement with the available experimental data on the phase transition pressure Pt = 11.5 GPa and the vast volume discontinuity in pressure-volume (PV) phase diagram indicate the structural phase transition from zincblende (B3) to rock salt (B1) structure. Later on, the Poisson’s ratio ν, the ratio RS/B of S (Voigt averaged shear modulus) over B (bulk modulus), elastic anisotropy parameter, elastic wave velocity, average wave velocity and Debye temperature as functions of pressure is calculated. From Poisson’s ratio and the ratio RS/B it is inferred that Hg0.91Mn0.09Te is brittle in nature in both B3 phase and B1 phase. To our knowledge this is the first quantitative theoretical prediction of the pressure dependence of ductile (brittle) nature of Hg0.91Mn0.09Te compounds and still awaits experimental confirmations.

Optimizing load transfer in multiwall nanotubes through interwall coupling: Theory and simulation

An analytical model is developed to determine the length scales over which load is transferred from outer to inner walls of multiwall carbon nanotubes (MWCNTs) as a function of the amount of bonding between walls. The model predicts that the characteristic length for load transfer scales as ℓ∼tE/μ¯, where t is the CNT wall spacing, E is the effective wall Young’s modulus, and μ¯ is the average interwall shear modulus due to interwall coupling. Molecular dynamics simulations for MWCNTs with up to six walls, and with interwall coupling achieved by interwall sp3 bonding at various densities, provide data against which the model is tested. For interwall bonding having a uniform axial distribution, the analytic and simulation models agree well, showing that continuum mechanics concepts apply down to the atomic scale in this problem. The simulation models show, however, that load transfer is sensitive to natural statistical fluctuations in the spatial distribution of the interwall bonding between pairs of walls, and such fluctuations generally increase the net load transfer length needed to fully load an MWCNT. Optimal load transfer is achieved when bonding is uniformly distributed axially, and all interwall regions have the same shear stiffness, implying a linear decrease in the number of interwall bonds with distance from the outer wall. Optimal load transfer into an n-wall MWCNT is shown to occur over a length of ∼1.5nℓ. The model can be used to design MWCNTs for structural materials, and to interpret load transfer characteristics deduced from experiments on individual MWCNTs.

Pressure and doping dependent elastic and thermodynamical properties of Ga 1− xIn xP mixed valent compounds

Using a phenomenological lattice model incorporating the long-range Coulomb and charge transfer caused by the deformation of the electron shells of the overlapping ions and the Hafemeister and Flygare type short-range overlap repulsion extended upto the second neighbor ions and the van der Waals (vdW) interaction, we present a comprehensive study to understand the effects of pressure on the elastic behavior as ductility (brittleness) and thermodynamical properties of Ga 1− x In x P. Estimated phase-transition pressure and the vast volume discontinuity in pressure–volume phase diagram confirm the structural phase transition from zinc blende ( B3) to rock salt ( B1) phase. From the elastic constants the Poisson's ratio ν, the ratio R S/ B of S (Voigt averaged shear modulus) over B (bulk modulus), elastic wave velocity, average wave velocity and thermodynamical property Debye temperature is calculated. The Poisson's ratio ν and the ratio R S/ B allows one to conclude that Ga 1− x In x P is brittle in zinc blende ( B3) and ductile nature is inferred in sodium chloride ( B1) phase. To our knowledge this is the first quantitative theoretical prediction of the doping and pressure dependent elastic properties for mixed valent Ga 1− x In x P compounds and still awaits experimental confirmations.

Pressure dependent elastic and structural ( B3– B1) properties of Ga based monopnictides

By formulating an effective interionic interaction potential that incorporates the long-range Coulomb, the covalency effects, the charge transfer caused by the deformation of the electron shells of the overlapping ions, the Hafemeister and Flygare type short-range overlap repulsion extended up to the second neighbour ions and the van der Waals (vdW) interaction, the pressure dependent elastic and thermodynamical properties of the III–V semiconductors as Ga Y ( Y = N, P, As) are studied. The estimated values of phase transition pressure of Ga Y ( Y = N, P, As) are in reasonably good agreement with the available data on the phase transition pressures ( P t = 41, 22, 17 GPa). The vast volume discontinuity in pressure–volume phase diagram identifies a structural phase transition from zinc-blende ( B3) to rock salt ( B1) structure. Later on, the Poisson's ratio ν, the ratio R S/ B of S (Voigt averaged shear modulus) over B (bulk modulus), elastic anisotropy parameter, elastic wave velocity, average wave velocity and Debye temperature as functions of pressure is calculated. From Poisson's ratio and the ratio R S/ B it is inferred that Ga Y ( Y = N, P, As) is brittle [ductile] in zinc-blende ( B3) [Sodium Chloride ( B1)] phase. To our knowledge this is the first quantitative theoretical prediction of the pressure dependence of ductile (brittle) nature of Ga Y compounds and still awaits experimental confirmations.

Pressure induced mechanical properties of boron based pnictides

The elastic and thermodynamical properties of the III–V semiconductors as BY (Y = N, P, As) are calculated in zincblende and NaCl phases by formulating an effective interionic interaction potential. This potential consists of the long-range Coulomb, the Hafemeister and Flygare type short-range overlap repulsion extended up to the second neighbour ions and the van der Waals (vdW) interaction. The variations of elastic constants with pressure follow a systematic trend identical to that observed in other compounds of ZnS type structure family and the Born relative stability criteria is valid in boron monopnictides. From the elastic constants the Poisson's ratio ν, the ratio R S / B of S (Voigt averaged shear modulus) over B (bulk modulus), elastic wave velocity, average wave velocity and thermodynamical property Debye temperature are calculated. By analyzing the Poisson's ratio ν and the ratio R S / B we conclude that at low pressures the boron monopnictides are brittle in nature in ZnS phase and ductile nature at high pressures in both ZnS and NaCl phases. To our knowledge this is the first quantitative theoretical prediction of the pressure dependence of ductile (brittle) nature of BY compounds.

Existence of Local Network Structure in Binary Amorphous Metals and its Contribution to Elastic Properties

The paper focuses on the characteristic local network structure of icosahedra observed in the relaxed amorphous metals and its contribution to their elastic properties. Using molecular dynamics method, CuxZr100-x binary amorphous models are constructed by rapidly quenching process from liquid. Voronoi polyhedron analyses expose the existence of the medium-range local network structure composed of inter-penetrating icosahedra. It is found that the globally averaged shear modulus obtained from the atomistically defined elastic moduli decreases with increasing free volume content in the condensed matter. The contribution of the densely packed icosahedral cluster with higher elastic rigidity to the global elastic modulus is discussed.

Pressure induced structural phase transition and elastic properties in BSb, AlSb, GaSb and InSb compounds

By formulating an effective interionic interaction potential that incorporates the long-range Coulomb, the covalency effects, the charge transfer caused by the deformation of the electron shells of the overlapping ions, the Hafemeister and Flygare type short-range overlap repulsion extended upto the second neighbour ions and the van der Waals (vdW) interaction, the pressure dependent elastic and thermodynamical properties of the III–V antimonide semiconductors as YSb (Y=B, Al, Ga, and In) are investigated. Estimated values of phase transition pressure of YSb antimonides are consistent with the available data on the phase transition pressures. The ratio R S / B of S (Voigt averaged shear modulus) over B (bulk modulus), elastic wave velocity, average wave velocity and Debye temperature as functions of pressure is calculated. From the ratio R S / B it is inferred that YSb (Y=Al, Ga, and In) are ductile and BSb is brittle in zinc blende (B3) phase. To our knowledge this is the first quantitative theoretical prediction of the ductile (brittle) nature of YSb antimonides and still awaits experimental confirmations.

Opening Angles and Material Properties of the Early Embryonic Chick Brain

Mechanical forces play an important role during brain development. In the early embryo, the anterior end of the neural tube enlarges and differentiates into the major brain subdivisions, including three expanding vesicles (forebrain, midbrain, and hindbrain) separated by two constrictions. Once the anterior neuropore and the spinal neurocoel occlude, the brain tube undergoes further regional growth and expansion in response to increasing cerebrospinal fluid pressure. Although this is known to be a response to mechanical loads, the mechanical properties of the developing brain remain largely unknown. In this work, we measured regional opening angles (due to residual stress) and stiffness of the embryonic chick brain during Hamburger-Hamilton stages 11-13 (approximately 42-51 h incubation). Opening angles resulting from a radial cut on transverse brain slices were about 40-110 deg (depending on region and stage) and served as an indicator of circumferential residual stress. In addition, using a custom-made microindentation device and finite-element models, we determined regional indentation stiffness and material properties. The results indicate that the modulus is relatively independent of position and stage of development with the average shear modulus being about 220 Pa for stages 11-13 chick brains. Information on the regional material properties of the early embryonic brain will help illuminate the process of early brain morphogenesis.

Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy

The energies of a set of 388 distinct grain boundaries have been calculated based on embedded-atom method interatomic potentials for Ni and Al. The boundaries considered are a complete catalog of the coincident site lattice boundaries constructible in a computational cell of a prescribed size. Correlations of the boundary energy with other boundary properties (disorientation angle, Σ value, excess boundary volume and proximity of boundary normals to 〈1 1 1〉) are examined. None of the usual geometric properties associated with grain boundary energy are useful predictors for this data set. The data set is incorporated as supplementary material to facilitate the search for more complex correlations. The energies of corresponding boundaries in Ni and Al are found to differ by approximately a scaling factor related to the Voigt average shear modulus or C 44. Crystallographically close boundaries have similar energies; hence a table of grain boundary energies could be used for interpolation.

Dependence of the macroscopic elastic properties of porous media on the parameters of a stochastic spatial pore distribution

The mechanical behavior of porous ceramic materials with a stochastic structure of their pore space is numerically studied during shear loading. The calculations are performed by the mobile cellular automaton method. A procedure is proposed for a numerical description of the internal structure of such materials using the dispersion of the pore distribution in layers that are parallel to the loading direction in a sample. The dependence of the macroscopic elastic properties of porous media on their internal structure is analyzed. Samples with spherical pores and pores extended along the loading direction exhibit a correlation between their average shear modulus and the dispersion of a pore distribution. Thus, the results obtained indicate that the shear modulus of such media is a structure-sensitive property. The proposed approach can be applied to compare the elastic properties of samples using data on their pore structure.

Linear shear properties of spruce softwood

The shear test described by Arcan was used to investigate orthotropic shear properties of clear softwood from Norway spruce. The test was chosen on the basis of a thorough literature study, although the experimental setup was somewhat modified compared to the original. A total number of 85 specimens were tested for loading and unloading in 6 different configurations. Manufacturing and mounting of specimens as well as testing worked well. Video extensometry was used to measure strain in the critical specimen section, and the determined moduli were evaluated by means of FEM calculations. The average shear moduli were found to equal G LR = 640 MPa, G LT = 580 MPa and G RT = 30 MPa, which correspond well with values reported in literature for various spruce species. No significant differences in shear moduli could be found for configurations comprising the same material plane. Moduli determined from unloading generally showed higher values than those obtained in loading, but only the rolling shear RT demonstrated a significant difference. Each of the three shear moduli was found to be significantly different from each other, with G LR about 10% higher than G LT , and approximately 20 times higher than G RT . The coefficient of variation equalled 0.24, 0.37 and 0.28, respectively. The correlation with density was in general low. It was found that the 3-parameter Weibull distribution is most appropriate for a probabilistic description of the three orthotropic shear moduli of wood.