Elastic Wave Speed Research Articles

Acute alcohol consumption modulates corneal biomechanical properties as revealed by optical coherence elastography

Acute alcohol ingestion has been found to impact visual functions, including eye movement, but its effects on corneal biomechanical properties remain unclear. This study aimed to investigate the influence of acute alcohol consumption on corneal biomechanical properties using optical coherence elastography (OCE). An air-coupled ultrasound transducer induced elastic waves in mice corneas in vivo, and a high-resolution phase-sensitive optical coherence tomography (OCT) system tracked the mechanical waves to quantify the elastic wave speed. In vivo measurements were performed on three groups of age- and gender-matched mice: control, placebo (administered saline), and alcohol (administered ethanol) groups. Longitudinal measurements were conducted over a one-hour period to assess acute temporal changes in wave speeds, which are associated with inherent biomechanical properties of the cornea. The results showed a significant decrease in wave speed for the alcohol group after 10 min of ingestion in comparison to pre-ingestion values (p = 0.0096), whereas the temporal wave speed changes for the placebo group were statistically insignificant (p = 0.076). In contrast, the control group showed no significant changes in elastic wave speed and corneal thickness. Furthermore, a significant difference was observed between the wave speeds of the placebo and alcohol groups at each measurement time point between 10 and 50 min (p < 0.05), though both groups exhibited a similar trend in corneal thickness change. The findings of this study have important implications for clinical assessments and research in corneal disorders, highlighting the potential of OCE as a valuable tool for evaluating such changes.

The influence of hydrocarbons on the physical properties of sea bottom sediments of the Black Sea of different stages of diagenesis under conditions of high pressures and temperatures and the degree of saturation

The influence of hydrocarbons on the physical properties of sea bottom sediments of the Black Sea of different stages of diagenesis under conditions of high pressures and temperatures and the degree of saturation

Elastic wave speeds, Debye temperature and microhardness of YX3 (X = In, Sn, Tl and Pb) intermetallic compounds

In the present work, we reviewed and report on the theoretical prediction of the longitudinal, transverse and average elastic wave veloci-ties, and the Debye temperature for some nonmagnetic YX3 (X = In, Sn, Tl, and Pb) intermetallic compounds with stable cubic AuCu3-type structure. The lattice parameters and the elastic constants used here are taken from the work of Abraham et al [1] using the general-ized gradient approximation (PBE-GGA). Our results are analyzed and compared with the available theoretical and experimental data, and in general a good agreement is found. The deviation between our value (224.4 K) of the Debye temperature θD for YSn3 material and the experimental one (210 K) is around 6.62%, while the deviation between our result (1401 m/s) of the transverse elastic wave velocity for YTl3 intermetallic material and the calculated one (1470 m/s) is about 4.93%. In addition the Young’s Modulus and Poisson’s Ratio of YX3 intermetallic compounds for the crystallographic planes (100), (110) and (111) are predicted.

Direct, model-free acoustic evaluation of stresses and strains in loaded nonlinear soft solids

We show analytically and experimentally that the states of stress and strain existing in a mechanically loaded elastic material can be accessed directly from elastic wave speed measurements, without having to determine, or even know, its material linear and nonlinear elastic parameters. These techniques are expected to have important applications in the health monitoring of loaded structures. Examples include stressed hydrogels, muscles, and thin membranes, such as a stretched rubber sheet, a piece of cling film (∼10 μm thick), and the animal skin of a bodhrán, a traditional Irish drum.

Accurate Finite Element Simulations of Dynamic Behaviour: Constitutive Models and Analysis with Deep Learning.

Owing to the challenge of capturing the dynamic behaviour of metal experimentally, high-precision numerical simulations have become essential for analysing dynamic characteristics. In this study, calculation accuracy was improved by analysing the impact of constitutive models using the finite element (FE) model, and the deep learning (DL) model was employed for result analysis. The results showed that FE simulations with these models effectively capture the elastic-plastic response, and the ZA model exhibits the highest accuracy, with a 26.0% accuracy improvement compared with other models at 502 m/s for Hugoniot elastic limit (HEL) stress. The different constitutive models offer diverse descriptions of stress during the elastic-plastic response because of temperature effects. Concurrently, the parameters related to the yield strength at quasi-static influence the propagation speed of elastic waves. Calculation show that the yield strength at quasi-static of 6061 Al adheres to y = ax + b for HEL stress. The R-squared (R2) and mean absolute error (MAE) values of the DL model for HEL stress predictions are 0.998 and 0.0062, respectively. This research provides a reference for selecting constitutive models for simulation under the same conditions.

Optical coherence elastography measures the biomechanical properties of the ex vivo porcine cornea after LASIK.

The biomechanical impact of refractive surgery has long been an area of investigation. Changes to the cornea structure cause alterations to its mechanical integrity, but few studies have examined its specific mechanical impact. To quantify how the biomechanical properties of the cornea are altered by laser assisted in situ keratomileusis (LASIK) using optical coherence elastography (OCE) in ex vivo porcine corneas. Three OCE techniques, wave-based air-coupled ultrasound (ACUS) OCE, heartbeat (Hb) OCE, and compression OCE were used to measure the mechanical properties of paired porcine corneas, where one eye of the pair was left untreated, and the fellow eye underwent LASIK. Changes in stiffness as a function of intraocular pressure (IOP) before and after LASIK were measured using each technique. ACUS-OCE showed that corneal stiffness changed as a function of IOP for both the untreated and the treated groups. The elastic wave speed after LASIK was lower than before LASIK. Hb-OCE and compression OCE showed regional changes in corneal strain after LASIK, where the absolute strain difference between the cornea anterior and posterior increased after LASIK. The results of this study suggest that LASIK may soften the cornea and that these changes are largely localized to the region where the surgery was performed.

Advanced absorbing boundaries for elastodynamic finite element analysis: The added degree of freedom method

Absorbing boundaries are essential in engineering simulations, especially for elastodynamic problems, to ensure accuracy, reliability and numerical stability. In this paper, the added degree of freedom method (ADM) is developed as a novel approach to address absorbing boundary challenges in finite element analysis. In ADM, additional degrees of freedom (DOFs) are introduced within the absorbing domain to attenuate outgoing elastic waves. For the proposed ADM to implement the absorbing boundary, the stiffness and mass properties of both the added DOFs and conventional DOFs within the absorbing domain are adjusted. This adjustment aims to reduce the propagation speed of elastic waves within the medium, and to prolong the duration of interaction between elastic waves and the surrounding medium. Consequently, the vibrations of nodes can be effectively attenuated by applying damping forces to the added DOFs. The numerical results show that the ADM has the ability to absorb one-dimensional and two-dimensional elastic waves across a broad range of frequencies. Therefore, the proposed ADM offers an innovative solution for modeling absorbing boundaries in various scientific and engineering applications, addressing the challenges of simulating wave propagation within finite computational domains.

Acoustic black hole designs for circular beams under axial loading

Acoustic Black Hole (ABH), as a non-reflecting wave effect, has been realised in beams and plates by locally changing their thickness. Geometrical ABH designs stem from their transverse-load bearing properties, assuming isotropic material properties associated with engineering materials (e.g., steels). The underlying physics is to manipulate stiffness locally for a transversely-loaded structure, leading to a change in the elastic wave speed. However, the same ABH would have limitations for axial loading, i.e., slender beams for which longitudinal waves dominate. Here, we present a wave propagation approach using wavefront tracking to identify a potential ABH for axially-loaded circular beams. We study wave propagation in three exponential designs of finite length, monitoring the wave-travel time. Indicative of an effective ABH in finite length sections, the wave-travel time increases compared to the case of a beam without ABH. By employing the wave front tracking method for the design of an ABH with axial loading, it is possible to verify the effectiveness of ABHs. Also, various material models, e.g., orthotropic materials such as wood, and different loading conditions can be considered, which opens a new avenue in applications of ABH phenomena beyond conventional vibro-acoustic control problems.

Beyond the Stokes approximation: shallow visco-elastic ice-sheet models

Abstract The hypothesis that ice-sheet evolution is only controlled by the long-term non-Newtonian viscous behavior of ice has been challenged by observations indicating that effects like brittle failure, stick-slip sliding, tides and wave action may affect ice-sheet evolution on sub-daily timescales. Over these timescales, the quasi-static-creep approximation is no longer appropriate and elastic effects become important. Simulating elastic effects in ice-sheet models over relevant timescales, however, remains challenging. Here, we show that by including a visco-elastic rheology and reintroducing the oft neglected acceleration term back into the ice-sheet stress balance, we can create a visco-elastic system where the velocity is locally determined and information propagates at the elastic wave speed. Crucially, the elastic wave speed can be treated like an adjustable parameter and set to any value to reproduce a range of phenomena, provided the wave speed is large compared to the viscous velocity. We illustrate the system using three examples. The first two examples demonstrate that the system converges to the steady-state viscous and elastic limits. The third example examines ice-shelf rifting and iceberg calving. This final example hints at the utility of the visco-elastic formulation in treating both long-term evolution and short-term environmental effects.

S Hmax orientation in the Alpine region from observations of stress-induced anisotropy of nonlinear elasticity

SUMMARY The orientation of SHmax is commonly estimated from in situ borehole breakouts and earthquake focal mechanisms. Borehole measurements are expensive, and therefore sparse, and earthquake measurements can only be made in regions with many well-characterized earthquakes. Here, we derive the stress-field orientation using stress-induced anisotropy in nonlinear elasticity. In this method, we measure the strain derivative of velocity as a function of azimuth. We use a natural pump-probe (NPP) approach which consists of measuring elastic wave speed using empirical Green’s functions (probe) at different points of the earth tidal strain cycle (pump). The approach is validated using a larger data set in the Northern Alpine Foreland region where the orientation of maximum horizontal compressive stress is known from borehole breakouts and drilling-induced fractures. The technique resolves NNW-SSW to N-S directed SHmax which is in good agreement with conventional methods and the recent crustal stress model. We confirm that the NPP method can be applied to dense large-scale seismic arrays. The technique is then applied to the Southern Alps to understand the contemporary stress pattern associated with the ongoing deformation due to counterclockwise rotation of the Adriatic plate with respect to the European plate. Our results explain why the two major faults in Northeastern Italy, the Giudicarie Fault and the Periadriatic Line (Pustertal–Gailtal Fault) are currently inactive, while the currently acting stress field allows faults in Slovenia to deform actively. We have demonstrated that the pump-probe method has the potential to fill in the measurement gap left by conventional approaches, both in terms of regional coverage and in depth.

Poster Session: Optical coherence elastography for In situ measurement of stiffness increase in posterior sclera after crosslinking.

During eye growth, scleral development critically determine eye size and thus the refractive status of the eye. Scleral remodeling in myopia includes scleral thinning, loss of scleral tissue, and weakening of the mechanical properties. Therefore, an intervention aiming at stiffening scleral tissues (crosslinking, SCXL) may provide a way to prevent or treat myopia. The development of SCXL requires tools to evaluate the effects of crosslinking on the mechanical properties of tissues, particularly in sclera where the mechanical properties are more spatially heterogeneous than in the cornea, anisotropic, and varying locally from the anterior to posterior regions. Here, we apply the high-frequency OCE technique to measure the heterogeneous mechanical properties of posterior scleral tissues and, evaluate the changes in shear moduli after SCXL. As a model system, we use ex vivo in porcine eyes and riboflavin-assisted UV crosslinking. From measured elastic wave speeds (6-16kHz), the average out-of-plane shear modulus was 0.71±0.12MPa (n=20) for normal scleras. After treatment, the shear modulus increased to 1.50±0.39MPa. This 2-fold change was consistent with the increase of static Young's modulus from 5.5±.1 to 9.3±1.9MPa after crosslinking, using conventional uniaxial extensometry. OCE revealed regional stiffness differences across the temporal, nasal, and deeper posterior sclera, demonstrating its potential as a noninvasive tool to test the effect of scleral crosslinking.

Poster Session: Time resolved modulation of neuronal activity associated with attention to low-level visual features.

During eye growth, scleral development critically determine eye size and thus the refractive status of the eye. Scleral remodeling in myopia includes scleral thinning, loss of scleral tissue, and weakening of the mechanical properties. Therefore, an intervention aiming at stiffening scleral tissues (crosslinking, SCXL) may provide a way to prevent or treat myopia. The development of SCXL requires tools to evaluate the effects of crosslinking on the mechanical properties of tissues, particularly in sclera where the mechanical properties are more spatially heterogeneous than in the cornea, anisotropic, and varying locally from the anterior to posterior regions. Here, we apply the high-frequency OCE technique to measure the heterogeneous mechanical properties of posterior scleral tissues and, evaluate the changes in shear moduli after SCXL. As a model system, we use ex vivo in porcine eyes and riboflavin-assisted UV crosslinking. From measured elastic wave speeds (6-16kHz), the average out-of-plane shear modulus was 0.71±0.12MPa (n=20) for normal scleras. After treatment, the shear modulus increased to 1.50±0.39MPa. This 2-fold change was consistent with the increase of static Young's modulus from 5.5±.1 to 9.3±1.9MPa after crosslinking, using conventional uniaxial extensometry. OCE revealed regional stiffness differences across the temporal, nasal, and deeper posterior sclera, demonstrating its potential as a noninvasive tool to test the effect of scleral crosslinking.

Large displacements and rotations of a local linear elastic rod

AbstractThe Local Linear Timoshenko (LLT) model for the planar motion of a rod that undergoes flexure, shear and extension, was recently derived in Van Rensburg et al. (2021). In this paper we present an algorithm developed for this model. The algorithm is based on the mixed finite element method, and projections into finite dimensional subspaces are used for dealing with nonlinear forces and moments. The algorithm is used for an investigation into elastic waves propagated in the LLT rod. Interesting properties of the LLT rod include the increased propagation speed of elastic waves when compared to the linear Timoshenko beam, and the appearance of buckled states or equilibrium solutions for compressed LLT beams. It is also shown that the LLT rod is applicable to large displacements and rotations for a wide range of slender elastic objects; from beams to highly slender flexible rods.

Non-destructive detection of disintegrant levels in compressed oral solid dosage forms

Quality issues related to compressed oral solid dosage (OSD) forms, such as tablets, arise during the design, development, and production stages, despite established processes and robust production tools. One of the primary quality concerns is the disintegration properties and drug release profile of immediate-release OSD products, which depend on their micro-texture and micro-viscoelastic properties at the grain level. These properties are influenced by the composition of the formulation, particularly the disintegrant level in the tablet matrix and the porosity of the matrix. In this study, a novel, rapid, non-destructive ultrasonic characterization technique was proposed to correlate the sensitivity of propagating elastic wave speeds, physical/mechanical properties, and the dispersion profile of the OSD material with the disintegrant level (% w/w) in the formulation and the compression force applied during tableting. The proposed characterization framework involves transmitting pressure (longitudinal) and shear (transverse) waves through the OSDs to calculate the speed of sound, which in turn provides information on the apparent Young's and shear moduli. In addition, the attenuation profile of the propagating wave is obtained through dispersion analysis. To investigate the impact of disintegrants and compression force on ultrasonic wave propagation in OSDs, we incorporated seven levels of a frequently used disintegrant. In each formulation, OSDs are compacted in five compaction forces. The sensitivity of wave speeds, physical/mechanical properties, and attenuation profile was observed with each disintegrant and compression force level. The utilization of ultrasonic techniques may present a viable solution for rapid, non-destructive, non-invasive, and cost-effective testing methods required in continuous manufacturing (CM) and real-time release testing (RTRT), and its practical utility in pharmaceutical manufacturing is also discussed.

Effects of CO 2 phase state on the seismological properties of porous materials: implications for seismic monitoring of volcanic hazards and sequestered carbon

Abstract Time-lapse seismic monitoring is a key component in the geological sequestration of greenhouse gases. Currently, a lack of understanding of the influence of injected CO 2 on rocks’ geophysical signatures is reported. Using a novel ultrasonic experimental system, we measured the variations in the longitudinal (P) and transverse (S) elastic wave speeds of a CO 2 -saturated porous medium at different pressure and temperature conditions around the CO 2 critical point. The results show that both P- and S-wave speeds, corrected to seismic frequencies, decreased by more than 4.5% across the CO 2 gas to liquid and gas to supercritical states, primarily as a consequence of CO 2 density increase. This study provides a-20 firm basis for the use of seismological methods in monitoring sequestered CO 2 ; although the abruptness, and hence remote seismic detectability, depends on which phase boundary is crossed. Further, these measurements also allow us to compare observations to frequency-dependent wave propagation theory. The observed wave speeds mostly align with those calculated at 1 MHz using the Biot theory for both CO 2 and H 2 O saturated states. However, the observed and calculated wave speeds diverge above the phase transition in some of the tests, possibly due to the kinetics of the phase transition within a porous medium. As such, aside from the direct utility in providing information on the expected seismic responses, the CO 2 provides a highly tunable fluid that can be advantageous for experimental studies.

Analysis of In Vivo Skin Anisotropy Using Elastic Wave Measurements and Bayesian Modelling

In vivo skin exhibits viscoelastic, hyper-elastic and non-linear characteristics. It is under a constant state of non-equibiaxial tension in its natural configuration and is reinforced with oriented collagen fibers, which gives rise to anisotropic behaviour. Understanding the complex mechanical behaviour of skin has relevance across many sectors including pharmaceuticals, cosmetics and surgery. However, there is a dearth of quality data characterizing the anisotropy of human skin in vivo. The data available in the literature is usually confined to limited population groups and/or limited angular resolution. Here, we used the speed of elastic waves travelling through the skin to obtain measurements from 78 volunteers ranging in age from 3 to 93 years old. Using a Bayesian framework allowed us to analyse the effect that age, gender and level of skin tension have on the skin anisotropy and stiffness. First, we propose a new measurement of anisotropy based on the eccentricity of angular data and conclude that it is a more robust measurement when compared to the classic “anisotropic ratio”. Our analysis then concluded that in vivo skin anisotropy increases logarithmically with age, while the skin stiffness increases linearly along the direction of Langer Lines. We also concluded that the gender does not significantly affect the level of skin anisotropy, but it does affect the overall stiffness, with males having stiffer skin on average. Finally, we found that the level of skin tension significantly affects both the anisotropy and stiffness measurements employed here. This indicates that elastic wave measurements may have promising applications in the determination of in vivo skin tension. In contrast to earlier studies, these results represent a comprehensive assessment of the variation of skin anisotropy with age and gender using a sizeable dataset and robust modern statistical analysis. This data has implications for the planning of surgical procedures and questions the adoption of universal cosmetic surgery practices for very young or elderly patients.

Simultaneous Assessment of the Whole Eye Biomechanics Using Ultrasonic Elastography.

Current elastography techniques in the field of ophthalmology usually target one specific tissue, such as the cornea or the sclera. However, the eye is an inter-related organ, and some ocular diseases can alter the biomechanical properties of multiple anatomical structures. Hence, there is a need to develop an imaging tool that can non-invasively, quantitatively, and accurately characterize dynamic changes among these biomechanical properties. A high resolution ultrasound elastography system was developed to achieve this goal. The efficacy and accuracy of the system was first validated on tissue-mimicking phantoms while mechanical testing measurements served as the gold standard. Next, an in vivo elevated intraocular pressure (IOP) model was established in rabbits to further test our system. In particular, elastography measurements were obtained at 5 IOP levels, ranging from 10 mmHg to 30 mmHg in 5 mmHg increments. Spatial-temporal maps of the multiple ocular tissues (cornea, lens, iris, optic nerve head, and peripapillary sclera) were obtained. The spatial-temporal maps were acquired simultaneously for the ocular tissues at the 5 different IOP levels. The statistical analysis of the elastic wave speed was presented for ocular tissues. Finally, the mapping for the elastic wave speed of each ocular component was acquired at each IOP level. Our elastography system can concurrently assess the biomechanical properties of multiple ocular structures and detect changes in biomechanical properties associated with changes in IOP. This system provides a novel tool to measure and quantify the biomechanical properties of the whole eye.

Mechanical Properties and Synergistic Interfacial Interactions of ZnO Nanorod-Reinforced Polyamide–Imide Composites

Metal oxide nanoparticle -reinforced polymers have received considerable attention due to their favorable mechanical properties compared to neat materials. However, the effect of nanoscale reinforcements of the interface on the composites' mechanical properties has not been investigated in-depth to reach their optimal performance in structural applications. Aiming at revealing the effect of synergistic interfacial interactions on the mechanical properties of polymer composites, using a nanoscale reinforcement, herein, a series of zinc oxide nanorod-reinforced polyamide-imide (PAI)/ZnO) composites were fabricated and their mechanical properties and viscoelastic responses were investigated. The composite prepared by reinforcing them with 5 wt % ZnO nanorods resulted in improved elastic modulus, stiffness, and hardness values by 32%, 14% and 35%, respectively, compared to neat polymer thin films. The viscoelastic dynamics of the composites revealed that there was an 11% increase in elastic wave speed in the composite, containing 5 wt % ZnO nanorods, indicating better response to high impacts. Delayed viscoelastic response decreased by 67% spatially and 51% temporally, with a corresponding decrease in the creep rate, for the 5 wt % ZnO nanorod- containing composite, evidencing its potential applicability in high strength lightweight structures. The improved mechanical properties with respect to the filler concentration evidence strong particle-polymer interfacial interactions, creating "chain-bound" clusters, providing clear reinforcement and polymer chain mobility retardation. However, hypervelocity impact testing revealed that all the composites' films were vulnerable to hypervelocity impact, but the spallation region of the composite films reinforced with 2.5 wt % and 5 wt % ZnO nanorods exhibited a cellular-like matrix with shock-induced voids compared to a rather hardened spallation region with cracks in the neat film.

Mesh objectivity in dynamic fracture analyses with rate dependent continuum damage models

This paper is aimed at investigating the mesh objectivity in dynamic fracture analyses employing strain rate dependent damage evolution as the localization limiter. Specifically, the goal is investigating and understanding the limits of applicability across various loading rates. For this purpose, dynamic fracture of a brittle material is simulated using a rate dependent scalar damage model. Dynamic fracture scenarios under a wide range of loading rates are considered, which yield various fracturing patterns ranging from localized to branched/diffused. The rate dependent damage model is seen to yield mesh objective predictions only at higher loading rates, which correspond to branched/diffused fractures. Results are not mesh objective at lower loading rates, which correspond to localized fractures. The regularization effect, at higher rates, is due to an intrinsic length-scale induced by the rate dependent damage law, and is related to the strain rate sensitivity parameter. For these cases, the predicted fracture patterns consist of thickened damage bands, spanning multiple element widths, and are wider than the intrinsic length-scale induced by the model. Thus, this feature can be viewed as a physical manifestation of the intrinsic length-scale. Wave propagation and dispersion in a one-dimensional version of the present damage model is analyzed further to explain the results. It is demonstrated that the group and phase velocity are finite and approach the elastic wave speed at higher loading rates, helping retain mesh objectivity. However they approach infinity at lower loading rates, causing the regularizing effect to vanish. Thus, the rate dependent damage model does not yield mesh objective results across all loading rates, and must be employed with caution.

Design, development, and calibration of split Hopkinson pressure bar system for Dynamic material characterization of concrete

Split Hopkinson pressure bar (SHPB) system is significantly used for dynamic material characterization in the range of strain rates 102–104 s-1; however, there is no standard design methodology or readily available technique for the development of this apparatus. The objective of this study is to present a detailed design, development and calibration of SHPB apparatus for dynamic material characterization of concrete in compression. The calibration of the loading and bar components has been presented with the help of experimental results and validated following an analytical approach for one-dimensional stress wave propagation. The experimental pulse duration, 124.5 microsecond, and elastic wave speed, 4820 m/s, was measured with 2% deviation from the analytical results. Under three different impact velocities, a minimum 1.09% and maximum 4.14% decrement was observed in the incident wave as compared to analytical formulation. The recorded strain signals were captured in the transmission bar with a decrement of 1, 3, and 3.3% in peak strain when compared to the incident bar, at 4.5, 4.9, and 5.7 m/s impact velocities. The incident and transmission bars had almost identical wave characteristics demonstrating that the bar system has been perfectly and precisely aligned, and almost complete wave transfer is seen to have occurred. Experiments performed on M35 concrete specimens using the developed SHPB setup have been presented and discussed. The results demonstrated that the developed SHPB setup is capable to provide accurate results for the dynamic material characterization of concrete at high strain rate loading.