Elastic Shear Modulus Research Articles

Differences in the elastic modulus of the lumbar muscles between female athletes with and without low back pain

BackgroundLow back pain is the most prevalent musculoskeletal disorder affecting performance and sports participation among athletes and is more prevalent among female athletes. Evaluating the stiffness of the lumbar muscles is important for understanding the pathophysiology of low back pain. Therefore, this study examined the differences in stiffness of the lumbar multifidus and erector spinae muscles between female university athletes with and without low back pain. MethodsThis was a cross-sectional study. The study was conducted at a single centre, the university research laboratory. Twenty female university athletes with low back pain or a history of low back pain and 20 without low back pain participated in this study. The shear elastic moduli of the multifidus and erector spinae muscles were evaluated in the prone (to relax the muscles) and sitting with 35° of trunk flexion (to stretch the muscles) positions using shear wave ultrasound imaging equipment. FindingsThe low back pain group showed significantly greater shear elastic modulus in the multifidus in both prone and sitting positions than the non-low back pain group. There were no differences in the erector spinae muscle between the two groups at either position. InterpretationThese results provide new insights into the microscopic characteristics of low back pain pathophysiology in young female athletes. Stiffness assessment using shear wave elastography will help provide a specific treatment strategy for female athletes with low back pain or a history of low back pain.

TiNi Alloy Lattice Structures with Negative Poisson Ratio: Computer Simulation

Today, one of the problems of modern implants is their high rigidity, which can lead to bone resorption at the interface between the implant and the bone and to the gradual detachment of the implant. In addition, implant detachment can occur due to the positive Poisson's ratio of the implant along its entire length. This phenomenon is described in detail in [1]. As a possible solution to these problems, it is proposed to use lattice structures with negative Poisson's ratio from TiNi alloy. This alloy has a fairly low modulus of elasticity - about 48 GPa. The use of a porous (lattice) structure of an implant made of TiNi alloy will reduce the modulus of elasticity and bring it closer to the modulus of human cortical bone – 12-17 GPa [2], and possibly the modulus of elasticity of cancellous bone – 0.1-5 GPа [3]. In this work, a computer numerical simulation of strut based lattice structures with several variants of unit cell topology with a negative Poisson's ratio is carried out. For the obtained structures, the following characteristics were calculated - elastic modulus (Young's modulus), modulus of elasticity in shear, Poisson's ratio. The modeling process is implemented using the ANSYS 2019 R2 SpaceClaim finite element analysis package. The data obtained confirmed the promising possibility of modeling and fabricating lattice structures with a low elastic modulus and negative Poisson's ratio from a TiNi alloy. Also, on the basis of this data, conclusions about the influence of the topology and porosity of unit cells on the resulting characteristics of the lattice structure were made.

Modelling of functionally graded triply periodic minimal surface (FG-TPMS) plates

Functionally graded porous plates have been validated as remarkable lightweight structures with excellent mechanical characteristics and numerous applications. With inspiration from the high strength-to-volume ratio of triply periodic minimal surface (TPMS) structures, a new model of porous plates, which is called a functionally graded TPMS (FG-TPMS) plate, is investigated in this paper. Three TPMS architectures including Primitive (P), Gyroid (G), and wrapped package-graph (IWP) with different graded functions are presented. To predict the mechanical responses, a new fitting technique based on a two-phase piece-wise function is employed to evaluate the effective moduli of TPMS structures, including elastic modulus, shear modulus, and bulk modulus. In addition, this function corresponds to the cellular structure formulation in the context of relative density. The separated phases of the function are divided by the different deformation behaviours. Furthermore, another crucial mechanical property of porous structure, i.e, Poisson’s ratio, is also achieved by a similar fitting technique. To verify the mechanical characteristics of the FG-TPMS plate, the generalized displacement field is modelled by a seventh-order shear deformation theory (SeSDT). A NURBS-based isogeometric analysis (IGA) is then employed to capture the C1 continuity in approximations. Numerical examples regarding static, buckling, and free vibration analyses of FG-TPMS plates are illustrated to confirm the reliability and accuracy of the proposed approach. The influences of various porosity distributions, average relative densities, thickness-to-length ratios, aspect ratios, and boundary conditions on the plate responses are achieved. Consequently, these FG-TPMS structures can provide much higher stiffness than the same-weight isotropic plate. The greater stiffness-to-weight ratio of these porous plates compared to the full-weight isotropic ones should be considered the most remarkable feature. Thus, these complex porous structures have numerous practical applications because of these high ratios and their fabrication ability through additive manufacturing (AM) technology.

High temperature elastic properties of sub-stoichiometric yttrium dihydrides

Yttrium hydrides are considered as candidate materials for neutron moderation applied in microreactors (akin transportable miniaturized nuclear reactors) owing to their superior thermal stability and hydrogen retention. The evolution of elastic properties of these materials at elevated temperatures, needed for predicting the thermomechanical response and performance of the moderator during in-service reactor conditions, however, is lacking. Here, we report the Young’s and shear elastic moduli of three stoichiometries of bulk yttrium hydride (YHx, x = 1.61, 1.82, and 1.84) from room temperature to 1000 °C. In situ temperature-dependent measurements of the longitudinal and shear wave velocities were performed using a laser ultrasonic technique while heating the sample in a vacuum-pumped heating stage. The elastic moduli increased linearly with increasing hydrogen content and decreased by ∼10 % during heating from room temperature to 1000 °C in the three YHx compositions. The linear relationship between the elastic moduli and the hydrogen content in yttrium hydride was verified by atomistic calculations based on density functional theory (DFT). The absence of abrupt changes in the temperature-dependent measurements of elastic modulus of the YHx samples suggested negligible loss of hydrogen at elevated temperatures. Excellent agreement was found between the measured and calculated dependence of the elastic moduli on the stoichiometry, thereby providing a new approach for investigating the effects of fabrication-induced parameters (such as porosity) on the elastic moduli. This study demonstrates the utility of the combined approach involving DFT-based atomistic calculations and measurements of the elastic moduli for the informative development of metal hydrides and can be used as a metric for novel moderator materials investigations for emerging microreactors and beyond.

Elastic shear modulus and density profiles inversion: Lipschitz stability results

In this paper, we consider the inverse coefficients problem of recovering a shear modulus μ and density ρ of a medium from the Neumann-to-Dirichlet map. This inverse problem is motivated by the reconstruction of mechanical properties of tissues in non-destructive testing. We prove Lipschitz stability results for any dimension d ≥ 2 , provided that the parameters μ and ρ have upper and lower bounds and belong to a known finite dimensional subspace. The proofs rely on monotonicity relations between the parameters and the Neumann-to-Dirichlet operator, combined with the techniques of localized potentials.

Time-Course Changes in Dorsiflexion Range of Motion, Stretch Tolerance, and Shear Elastic Modulus for 20 Minutes of Hot Pack Application.

The application of thermal agents via hot packs is a commonly utilized method. However, the time-course changes in the range of motion (ROM), stretch sensation, shear elastic modulus, and muscle temperature during hot pack application are not well understood. This study aimed to investigate the time-course changes in these variables during a 20-minute hot pack application. Eighteen healthy young men (21.1 ± 0.2 years) participated in this study. We measured the dorsiflexion (DF) ROM, passive torque at DF ROM (an indicator of stretch tolerance), and shear elastic modulus (an indicator of muscle stiffness) of the medial gastrocnemius before and every 5 minutes during a 20-minute hot pack application. The results showed that hot pack application for ≥5 minutes significantly (p < 0.01) increased DF ROM (5 minutes: d = 0.48, 10 minutes: d = 0.59, 15 minutes: d = 0.73, 20 minutes: d = 0.88), passive torque at DF ROM (5 minutes: d = 0.71, 10 minutes: d = 0.71, 15 minutes: d = 0.82, 20 minutes: d = 0.91), and muscle temperature (5 minutes: d = 1.03, 10 minutes: d = 1.71, 15 minutes: d = 1.74, 20 minutes: d = 1.66). Additionally, the results showed that hot pack application for ≥5 minutes significantly (p < 0.05) decreased shear elastic modulus (5 minutes: d = 0.29, 10 minutes: d = 0.31, 15 minutes: d = 0.30, 20 minutes: d = 0.31). These results suggest that hot pack application for a minimum 5 minutes can increase ROM and subsequently decrease muscle stiffness.

Single Hydrogel Particle Mechanics and Dynamics Studied by Combining Capillary Micromechanics with Osmotic Compression.

Hydrogels can exhibit a remarkably complex response to external stimuli and show rich mechanical behavior. Previous studies of the mechanics of hydrogel particles have generally focused on their static, rather than dynamic, response, as traditional methods for measuring single particle response at the microscopic scale cannot readily measure time-dependent mechanics. Here, we study both the static and the time-dependent response of a single batch of polyacrylamide (PAAm) particles by combining direct contact forces, applied by using Capillary Micromechanics, a method where particles are deformed in a tapered capillary, and osmotic forces are applied by a high molecular weight dextran solution. We found higher values of the static compressive and shear elastic moduli for particles exposed to dextran, as compared to water (KDex≈63 kPa vs. Kwater≈36 kPa, and GDex≈16 kPa vs. Gwater≈7 kPa), which we accounted for, theoretically, as being the result of the increased internal polymer concentration. For the dynamic response, we observed surprising behavior, not readily explained by poroelastic theories. The particles exposed to dextran solutions deformed more slowly under applied external forces than did those suspended in water (τDex≈90 s vs. τwater≈15 s). The theoretical expectation was the opposite. However, we could account for this behaviour by considering the diffusion of dextran molecules in the surrounding solution, which we found to dominate the compression dynamics of our hydrogel particles suspended in dextran solutions.

Mechanical Responses and Damage Model of Anchored Jointed Rock Mass under Fatigue Shear Load

Cyclical impact loads will transform into low-frequency fatigue loads during propagation and will induce creep deformation of far-field rock under long-term disturbance loads. Laboratory tests of specimens under different fatigue shear loads were conducted. The mechanical responses and creep laws of the specimen were analyzed in detail. Based on the experimental results, a new constitutive model was explored. The results reveal that the stress‒strain curves of the specimen show a trend of step-path increasing under stable and fatigue load circularly. With an increase in fatigue load, the shear strength and elastic modulus of the specimens decrease gradually, while the corresponding failure strain increases gradually. The damage index composed of peak time and peak shear stress can reflect the failure of rock under fatigue loading, and the fatigue amplitude has the greatest influence on specimen deterioration. A fatigue stage in the shear creep curve occurs and is caused by the fatigue load. The fatigue creep rate increases gradually as the fatigue parameter increases. A combined nonlinear damage creep model based on the Nishihara model, elastic body, nonlinear creep body, and fatigue damage function (termed the NENF model), describing the creep responses of rock, anchor, accelerated creep, and fatigue load, respectively, was established. Compared with test data, the creep equation of the model has good accuracy in describing the whole shear creep process of specimens under fatigue loading and provides a new framework for the stability of anchoring rock masses.

Hydrogen bond symmetrization and high-spin to low-spin transition of ε-FeOOH at the pressure of Earth’s lower mantle

Abstract We focus on the ferric end-member of phase H: ε-FeOOH using density functional theory at the PBEsol+U level. At 300 K, we find that ε-FeOOH undergoes a hydrogen bond symmetrization at 37 GPa and a sharp high-spin to low-spin transition at 45 GPa. We find excellent agreement with experimental measurements of the equation of state, lattice parameters, atomic positions, vibrational frequencies, and optical properties as related to the band gap, which we find to be finite and small, decreasing with pressure. The hydrogen bond symmetrization transition is neither first-nor second-order, with no discontinuity in volume or any of the elastic moduli. Computed IR and Raman frequencies and intensities show that vibrational spectroscopy may provide the best opportunity for locating the hydrogen bond symmetrization transition experimentally. We find that ε-FeOOH is highly anisotropic in both longitudinal- and shear-wave velocities at all pressures, with the shear wave velocity varying with propagation and polarization direction by as much as 24% at zero pressure and 43% at 46 GPa. The shear and bulk elastic moduli increase by 18% across the high-spin to low-spin transition.

Manufacturing of biodegradable Flax-PLA curvatures using a unique vacuum-temperature profile

In this research, the manufacturing of completely biodegradable composites with a unique single-step sheet consolidation method was discussed. Layers of unidirectional, coarse twill, and fine twill flax; and poly lactic acid (PLA) were used as the material system to manufacture cylindrical and spherical composite half-shells. The three processing parameters were vacuum pressure, temperature and time. Thickness, mass fraction, tensile strength, shear strength, shape conformance and biodegradability of the manufactured composites were experimentally determined. The composite specimens’ cross-sections were also observed under an optical microscope, to assess, the consolidation quality of the manufactured composites, that was represented by the composite thickness, and primarily governed by the polymer viscosity, and the transverse and in-plane fibre reinforcement permeability. Biodegradable Flax-PLA composites were successfully consolidated, within 5% tolerance of the targeted mass fractions and thickness values, conforming within 8% tolerance to the shape of the mould. The highest achieved shear strength, flexural modulus, tensile strength and elastic modulus, were 22 MPa, 19.9 GPa, 179 MPa and 19.5 GPa, respectively. This research will be valuable to develop, flat and curved biodegradable composites, for one-off or small scale productions, at a relatively low capital cost.

Photocrosslinkable Polymeric Bicontinuous Microemulsions.

We present an approach to photocrosslink bicontinuous microemulsions derived from ternary blends of poly(methoxyethyl acrylate) (PM, Mn = 4200 g/mol), poly(hexyl methacrylate-co-coumarin methacrylate) (PHC, Mn = 6800 g/mol), and PM-b-PHC diblock polymer (Mn = 19,400 g/mol) in a phase-selective manner, enabling structural characterization at an unprecedented level of detail. This strategy utilizes the [2 + 2] photodimerization reaction of coumarin derivatives to covalently crosslink blends without the use of harsh reagents or disruptive thermal treatment, thus preserving the intricate network structure throughout curing. The resulting crosslinked bicontinuous microemulsions exhibited rubbery behavior at elevated temperatures, achieving an elastic shear modulus of nearly 1 MPa at 70 °C, owing to the presence of the three-dimensional co-continuous network morphology. The dimensional stabilization afforded by crosslinking further allowed the microstructure to be directly imaged by scanning electron microscopy and atomic force microscopy. Contrary to recent theoretical findings, the BμE appears in a wide temperature and compositional window, suggesting that it is a robust feature of these blends. As a proof of concept demonstrating both the utility of bicontinuous microemulsion-derived materials and versatility of this strategy toward broader applications in energy storage and transport, the uncrosslinked portion of a cured blend was extracted by washing and replaced with an ionic liquid; the resultant heterogeneous solid electrolyte exhibited a room-temperature conductivity of 2 mS/cm, approximately one-quarter that of the pure ionic liquid.

Classification of deep vein thrombosis stages using convolutional neural network of electromyogram with vibrotactile stimulation toward developing an early diagnostic tool: A preliminary study on a pig model.

Deep vein thrombosis (DVT) can lead to life-threatening disorders; however, it can only be recognized after its symptom appear. This study proposed a novel method that can detect the early stage of DVT using electromyography (EMG) signals with vibration stimuli using the convolutional neural networks (CNN) algorithm. The feasibility of the method was tested with eight legs before and after the surgical induction of DVT at nine-time points. Furthermore, perfusion pressure (PP), intracompartmental pressure (IP), and shear elastic modulus (SEM) of the tibialis anterior were also collected. In the proposed method, principal component analysis (PCA) and CNN were used to analyze the EMG data and classify it before and after the DVT stages. The cross-validation was performed in two strategies. One is for each leg and the other is the leave-one-leg-out (LOLO), test without any predicted information, for considering the practical diagnostic tool. The results showed that PCA-CNN can classify before and after DVT stages with an average accuracy of 100% (each leg) and 68.4±20.5% (LOLO). Moreover, all-time points (before induction of DVT and eight-time points after DVT) were classified with an average accuracy of 72.0±11.9% which is substantially higher accuracy than the chance levels (11% for 9-class classification). Based on the experimental results in the pig model, the proposed CNN-based method can classify the before- and after-DVT stages with high accuracy. The experimental results can provide a basis for further developing an early diagnostic tool for DVT using only EMG signals with vibration stimuli.

Effect of constitutive law on the erythrocyte membrane response to large strains.

Three constitutive laws, that is the Skalak, neo-Hookean and Yeoh laws, commonly employed for describing the erythrocyte membrane mechanics are theoretically analyzed and numerically investigated to assess their accuracy for capturing erythrocyte deformation characteristics and morphology. Particular emphasis is given to the nonlinear deformation regime, where it is known that the discrepancies between constitutive laws are most prominent. Hence, the experiments of optical tweezers and micropipette aspiration are considered here, for which relationships between the individual shear elastic moduli of the constitutive laws can also be established through analysis of the tension-deformation relationship. All constitutive laws were found to adequately predict the axial and transverse deformations of a red blood cell subjected to stretching with optical tweezers for a constant shear elastic modulus value. As opposed to Skalak law, the neo-Hookean and Yeoh laws replicated the erythrocyte membrane folding, that has been experimentally observed, with the trade-off of sustaining significant area variations. For the micropipette aspiration, the suction pressure-aspiration length relationship could be excellently predicted for a fixed shear elastic modulus value only when Yeoh law was considered. Importantly, the neo-Hookean and Yeoh laws reproduced the membrane wrinkling at suction pressures close to those experimentally measured. None of the constitutive laws suffered from membrane area compressibility in the micropipette aspiration case.

First-principles calculations to investigate structural, electronic and optical properties of Cmc21-Ge2As2X (X = S, Se, Te and Po) under pressure effect

A group of new compound material Ge2As2X(X=S,Se,Te,Po) with Cmc21 space group is theoretically studied based on density functional theory (DFT) with GGA methods. By analyzing the phonon spectra and elastic constants, it is shown that these compounds have mechanical stability and dynamic stability at 0 GPa and 10 GPa. The lattice constants at different pressures indicate that these compounds are compressible. According to the elastic constants, the elastic (bulk, shear and Young's) moduli, Poisson's ratios, Pugh's ratios and elastic anisotropy indices of the material are calculated at 0 GPa and 10 GPa respectively. The calculation results show that the bulk modulus, B, of Ge2As2Se is the largest, the shear modulus, G, and Young's modulus, E, of Ge2As2S is the largest. The value of the B, G and E are increased due to pressure, indicating that their resistance to deformation is enhanced. According to Pugh ratio, K, except Ge2As2Te, the other compounds belong to brittle materials at 0 GPa, and all compounds belong to ductile materials at 10 GPa. Under pressure, the ductility of the compounds is enhanced. At 0 GPa and 10 GPa, the compounds possess elastic anisotropy. Under pressure, the elastic anisotropy of Ge2As2S and Ge2As2Se increase, while the elastic anisotropy of Ge2As2Te and Ge2As2Po decrease. The band structures and electronic densities of states of these compounds are calculated by the HSE06 method. The band gaps of the four compounds are 0.822eV, 0.725eV, 0.461eV and 0.331eV, at 0 GPa. In contrast, at pressurized 10 GPa, the band gaps of the compounds become zero, indicating their transition from semiconductor to metal. Finally, the optical properties of these compounds are calculated, including dielectric functions, refractive indices, absorption functions, loss functions, transmissivity function, reflectivity functions, conductivity functions and resistivity function. The results show that the characteristics for Ge2As2Po are significantly different from the other three compounds.

Contractile properties are less affected at long than short muscle length after eccentric exercise.

The aim of the present study was to investigate whether the electrically evoked muscle responses are differently affected over time by the knee joint angle after an exercise-induced muscle damage (EIMD). We hypothesized that low-frequency-evoked responses would be less affected at long than short muscle length, and that mechanisms located within the muscle and tendinous tissues would be involved. Fifteen males performed 45min loaded downhill walking (DW) exercise. Maximal voluntary contraction torque (MVC), optimal angle for torque production, voluntary activation level (VAL), twitch, doublet at 10 and 100Hz (Db10 and Db100, respectively), rate of torque development (RTD), post-activation potentiation (PAP), muscle shear elastic modulus (µ) and aponeurosis stiffness were assessed before, after, and 4, 24, 48, 72 and 168h after the exercise at a knee angle of 40°, 90° and 120° (0°: full extension). MVC, VAL and Db100 were similarly decreased across joint angles after the DW and optimal angle was not affected. Twitch, Db10, Db10/Db100, PAP and RTD were less affected and muscle µ more increased at long than short muscle lengths (p < 0.05), especially during the first 24h after the DW exercise. Low-frequency-evoked responses were more preserved at long than short muscle length the first 24h after the DW exercise, suggesting that joint angle should be taken into account to assess muscular alterations after EIMD. This length-dependence could be associated to the higher sensitivity to Ca2+ and the higher increase in muscle stiffness at long than short muscle length.

Memory in aging colloidal gels with time-varying attraction.

We report a combined rheology, x-ray photon correlation spectroscopy, and modeling study of gel formation and aging in suspensions of nanocolloidal spheres with volume fractions of 0.20 and 0.43 and with a short-range attraction whose strength is tuned by changing temperature. Following a quench from high temperature, where the colloids are essentially hard spheres, to a temperature below the gel point, the suspensions form gels that undergo aging characterized by a steadily increasing elastic shear modulus and slowing, increasingly constrained microscopic dynamics. The aging proceeds at a faster rate for stronger attraction strength. When the attraction strength is suddenly lowered during aging, the gel properties evolve non-monotonically in a manner resembling the Kovacs effect in glasses, in which the modulus decreases and the microscopic dynamics become less constrained for a period before more conventional aging resumes. Eventually, the properties of the gel following the decrease in attraction strength converge to those of a gel that has undergone aging at the lower attraction strength throughout. The time scale of this convergence increases as a power law with the age at which the attraction strength is decreased and decreases exponentially with the magnitude of the change in attraction. A model for gel aging in which particles attach and detach from the gel at rates that depend on their contact number reproduces these trends and reveals that the non-monotonic behavior results from the dispersion in the rates that the populations of particles with different contact number adjust to the new attraction strength.

The Effect of Glycerol-Based Suspensions on the Characteristics of Resonators Excited by a Longitudinal Electric Field

This study examines the effect of suspensions based on pure glycerol and diamond powder with different concentrations on the characteristics of resonators with a longitudinal electric field. We used two disk resonators made of the quartz and langasite plates with round electrodes on both sides of the plate and resonant frequencies of 4.4 and 4.1 MHz, operating in shear and longitudinal acoustic modes, respectively. Each resonator was mounted on the bottom of a 30 mL liquid container. During the experiments, the container was filled with the suspension under study in such a way that the resonator was completely immersed in the suspension, and the frequency dependences of the real and imaginary parts of the electrical impedance of the resonator were measured. As a result, the shear modulus of the elasticity and shear coefficient of the viscosity of the studied suspensions were determined. The material constants of the suspensions were found by fitting the theoretical frequency dependences of the real and imaginary parts of the electrical impedance of the resonator to the experimentally measured ones, which was calculated using Mason's equivalent circuit. As a result, the dependencies of the density, shear modulus of elasticity, shear viscosity coefficient, and velocity of the shear acoustic wave on the volume concentration of the diamond particles were constructed.

Dynamic Testing of Elastic Modulus, Shear Modulus, and Poisson’s Ratio of Bamboo Scrimber

Dynamic Testing of Elastic Modulus, Shear Modulus, and Poisson’s Ratio of Bamboo Scrimber

Calculation of damage accumulation taking into account changes in material characteristics

One of the important issues in the study of composite materials are microdefects and their accumulation in the binder. Cracks that occur in the transverse directions of the layers are considered to be the most common macrodefect. During cracking, the elastic modulus and shear modulus decrease. This article discusses the issue of obtaining calculation formulas that take into account the accumulation of damage, taking into account cracks in the layers and interlayer cracks on the example of the wing joint with the center section.

Determination of the Complex-Valued Elastic Moduli of Polymers by Electrical-Impedance Spectroscopy for Ultrasound Applications

A method is presented for the determination of complex-valued compression and shear elastic moduli of polymers for ultrasound applications. The resulting values, which are scarcely reported in the literature, are found with uncertainties typically around 1% (real part) and 6% (imaginary part). The method involves a setup consisting of a cm-radius, mm-thick polymer ring glued concentrically to a disk-shaped piezoelectric transducer. The ultrasound electrical-impedance spectrum of the transducer is computed numerically and fitted to measured values as an inverse problem in a wide frequency range, typically from 500 Hz to 5 MHz, both on and off resonance. The method is validated experimentally by ultrasonic through transmission around 1.9 MHz. The method is low cost, not limited to specific geometries and crystal symmetries, and, given the developed software, easy to execute. The method has no obvious frequency limitations before severe attenuation sets in above 100 MHz.