Axial Load Measurement of Bolts with Different Clamping Lengths Based on High-Frequency Ultrasonic ZnO Film Sensor.

The ultrasonic testing method has been widely used for measuring the axial load of bolts. However, systematic calibrations are prerequisite if specific bolts have different clamping length configurations, which leads to low efficiency and measurement errors. The focus of this work was to measure the axial load of bolts with different clamping lengths by proposing a method of clamping length correction based on piezoelectric films in order to avoid the complicated calibration steps. Firstly, the relationship between longitudinal wave time-of-flight (TOF) and axial load under different clamping lengths was studied to correct the difference between the effective stress length and the actual clamping length. Secondly, the high-frequency ZnO piezoelectric film sensor was fabricated on the bolts to improve the accuracy of longitudinal wave TOF measurement. The results showed that the center frequency of the fabricated ultrasonic sensor reached 25 MHz, which could realize the high precision measurement of TOF. The proposed correction model proved to be effective for decreasing the measurement error below 2.7% in this experiment. In conclusion, the proposed method simplified the calibration procedure for different application configurations of the same bolt and realized the efficient measurement of bolt axial load.

Supershear surface waves reveal prestress and anisotropy of soft materials.

Surface waves play important roles in many fundamental and applied areas from seismic detection to material characterizations. Supershear surface waves with propagation speeds greater than bulk shear waves have recently been reported, but their properties are not well understood. Here we describe theoretical and experimental results on supershear surface waves in rubbery materials. We find that supershear surface waves can be supported in viscoelastic materials with no restriction on the shear quality factor. Interestingly, the effect of prestress on the speed of the supershear surface wave is opposite to that of the Rayleigh surface wave. Furthermore, anisotropy of material affects the supershear wave much more strongly than the Rayleigh surface wave. We offer heuristic interpretation as well as theoretical verification of our experimental observations. Our work points to the potential applications of supershear waves for characterizing the bulk mechanical properties of soft solid from the free surface.

Muscle compression improves reliability of ultrasound echo intensity.

INTRODUCTION: Muscle echo intensity has been shown to correlate with disease status in muscle disorders, including Duchenne muscular dystrophy (DMD). We report the effect of sonographer-applied load on measurements of muscle echo intensity. METHODS: Quadriceps ultrasound scans were performed on 22 healthy boys and 16 boys with DMD between the ages of 2.2 and 15.3 years. Transducer contact force was increased linearly from 1.5 to 10 N, and echo intensity was measured throughout. RESULTS: Echo intensity increased linearly with strain at a rate of 42 (95% confidence interval [CI]: 21-63) and 74 (95% CI: 49-98) in the healthy and DMD populations, respectively. Echo intensity reliability was moderate at low strain (intraclass correlation coefficient [ICC] = 0.82) and was improved at high strain (ICC = 0.92). DISCUSSION: Sonographer-applied load introduces error in measurements of echo intensity, but it can be minimized by measuring echo intensity at near-maximal levels of compression. Muscle Nerve 57: 423-429, 2018.

PCA Based Stress Monitoring of Cylindrical Specimens Using PZTs and Guided Waves.

Since mechanical stress in structures affects issues such as strength, expected operational life and dimensional stability, a continuous stress monitoring scheme is necessary for a complete integrity assessment. Consequently, this paper proposes a stress monitoring scheme for cylindrical specimens, which are widely used in structures such as pipelines, wind turbines or bridges. The approach consists of tracking guided wave variations due to load changes, by comparing wave statistical patterns via Principal Component Analysis (PCA). Each load scenario is projected to the PCA space by means of a baseline model and represented using the Q-statistical indices. Experimental validation of the proposed methodology is conducted on two specimens: (i) a 12.7 mm ( 1 / 2 " ) diameter, 0.4 m length, AISI 1020 steel rod, and (ii) a 25.4 mm ( 1 " ) diameter, 6m length, schedule 40, A-106, hollow cylinder. Specimen 1 was subjected to axial loads, meanwhile specimen 2 to flexion. In both cases, simultaneous longitudinal and flexural guided waves were generated via piezoelectric devices (PZTs) in a pitch-catch configuration. Experimental results show the feasibility of the approach and its potential use as in-situ continuous stress monitoring application.

Unravelling anisotropic nonlinear shear elasticity in muscles: Towards a non-invasive assessment of stress in living organisms.

Acoustoelasticity theory describes propagation of shear waves in uniaxially stressed medium and allows the retrieval of nonlinear elastic coefficients of tissues. In transverse isotropic medium such as muscles the theory leads to 9 different configurations of propagating shear waves (stress axis vs. fibers axis vs. shear wave polarization axis vs. shear wave propagation axis). In this work we propose to use 4 configurations to quantify these nonlinear parameters ex vivo and in vivo. Ex vivo experiments combining ultrasound shear wave elastography and mechanical testing were conducted on iliopsoas pig muscles to quantify three third-order nonlinear coefficients A, H and K that are possibly linked to the architectural structure of muscles. In vivo experiments were performed with human volunteers on biceps brachii during a stretching exercise on an ergometer. A combination of the third order nonlinear elastic parameters was assessed. The knowledge of this nonlinear elastic parameters paves the way to quantify in vivo the local forces produced by muscle during exercise, contraction or movements.

Feasibility and repeatability for in vivo measurements of stiffness gradients in the canine gastrocnemius tendon using an acoustoelastic strain gauge.

B-mode ultrasound is an established imaging modality for evaluating canine tendon injury. However, full extent of tendon injury often remains difficult to estimate, as small changes in sonographic appearance are associated with large changes in biomechanical strength. The acoustoelastic strain gauge (ASG) is an ultrasound-based tissue evaluation technique that relates the change in echo intensity observed during relaxation or stretching of tendons to the tissue's mechanical properties. This technique deduces stiffness gradient (the rate of change of normalized stiffness as a function of tissue strain) by analyzing the ultrasound dynamic images captured from gradually deforming tissue. ASG has been proven to accurately model strain and stiffness within tendons in vitro. To determine the feasibility and repeatability for in vivo ASG measurements of canine tendon function, stiffness gradients for the gastrocnemius tendons of 10 clinically normal dogs were recorded by two nonindependent observers at three sites (musculotendinous junction, mid tendon, and insertion). Average stiffness gradient indices (0.0132, 0.0141, 0.0136) and dispersion values (0.0053, 0.0054, 0.0057) for each site, respectively, were consistent with published mechanical properties for normal canine tendon. Mean differences of the average stiffness gradient index and dispersion value between observers and between limbs for each site were less than 16%. Using interclass coefficients (ICC), intra-observer (ICC 0.79-0.98) and interobserver (ICC 0.77-0.95) reproducibility was good to excellent. Right and left limb values were symmetric (ICC 0.74-0.92). Findings from this study indicated that ASG is a feasible and repeatable technique for measuring stiffness gradients in canine tendons.

Decoupling Uniaxial Tensile Prestress and Waveguide Effects From Estimates of the Complex Shear Modulus in a Cylindrical Structure Using Transverse-Polarized Dynamic Elastography.

Dynamic elastography, whether based on magnetic resonance, ultrasound, or optical modalities, attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties altered by disease and injury, by noninvasively measuring mechanical wave motion in the tissue. Most reconstruction strategies that have been developed neglect boundary conditions, including quasi-static tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues currently being studied using elastography, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article a configuration, inspired by muscle elastography but generalizable to other applications, is analytically and experimentally studied. A hyperelastic polymer phantom cylinder is statically elongated in the axial direction while its response to transverse-polarized vibratory excitation is measured. We examine the interplay between uniaxial prestress and waveguide effects in this muscle-like tissue phantom using computational finite element simulations and magnetic resonance elastography measurements. Finite deformations caused by prestress coupled with waveguide effects lead to results that are predicted by a coordinate transformation approach that has been previously used to simplify reconstruction of anisotropic properties using elastography. Here, the approach estimates material viscoelastic properties that are independent of the nonhomogeneous prestress conditions without requiring advanced knowledge of those stress conditions.

Biaxial Tensile Prestress and Waveguide Effects on Estimates of the Complex Shear Modulus Using Optical-Based Dynamic Elastography in Plate-Like Soft Tissue Phantoms.

Dynamic elastography attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties altered by disease and injury, by noninvasively measuring mechanical wave motion in the tissue. Most reconstruction strategies that have been developed neglect boundary conditions, including quasi-static tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article a novel configuration, inspired by corneal elastography but generalizable to other applications, is studied. A polymer phantom layer is statically elongated via an in-plane biaxial normal stress while the phantom's response to transverse vibratory excitation is measured. We examine the interplay between biaxial prestress and waveguide effects in this plate-like tissue phantom. Finite static deformations caused by prestressing coupled with waveguide effects lead to results that are predicted by a novel coordinate transformation approach previously used to simplify reconstruction of anisotropic properties. Here, the approach estimates material viscoelastic properties independent of the nonzero prestress conditions without requiring advanced knowledge of those stress conditions.

Comparison of ultrasound elastography, magnetic resonance elastography and finite element model to quantify nonlinear shear modulus.

Objective. The aim of this study is to validate the estimation of the nonlinear shear modulus (A) from the acoustoelasticity theory with two experimental methods, ultrasound (US) elastography and magnetic resonance elastography (MRE), and a finite element method.Approach. Experiments were performed on agar (2%)-gelatin (8%) phantom considered as homogeneous, elastic and isotropic. Two specific setups were built to ensure a uniaxial stress step by step on the phantom, one for US and a nonmagnetic version for MRE. The stress was controlled identically in both imaging techniques, with a water tank placed on the top of the phantom and filled with increasing masses of water during the experiment. In US, the supersonic shear wave elastography was implemented on an ultrafast US device, driving a 6 MHz linear array to measure shear wave speed. In MRE, a gradient-echo sequence was used in which the three spatial directions of a 40 Hz continuous wave displacement generated with an external driver were encoded successively. Numerically, a finite element method was developed to simulate the propagation of the shear wave in a uniaxially stressed soft medium.Main results. Similar shear moduli were estimated at zero stress using experimental methods,µ0US= 12.3 ± 0.3 kPa andµ0MRE= 11.5 ± 0.7 kPa. Numerical simulations were set with a shear modulus of 12 kPa and the resulting nonlinear shear modulus was found to be -58.1 ± 0.7 kPa. A very good agreement between the finite element model and the experimental models (AUS= -58.9 ± 9.9 kPa andAMRE= -52.8 ± 6.5 kPa) was obtained.Significance. These results show the validity of such nonlinear shear modulus measurement quantification in shear wave elastography. This work paves the way to develop nonlinear elastography technique to get a new biomarker for medical diagnosis.

Autonomous Machine Learning Algorithm for Stress Monitoring in Concrete Using Elastoacoustical Effect.

The measurement of stress in concrete structures is a complex issue. This paper presents a new measurement system called a self-acoustic system (SAS), which uses frequency measurements of acoustic waves to determine the condition of concrete structures. The SAS uses a positive feedback loop between ultrasonic heads, which causes excitation to a stable limit cycle. The frequency of this cycle is related to the propagation time of an acoustic wave, which directly depends on stresses in the test object. The coupling mechanism between acoustic wave propagation speed and stress is the elastoacoustic effect described in this paper. Thus, the proposed system enables the coupling between the limit cycle frequency and the stress degree of the concrete structure. This paper presents a machine learning algorithm to analyse the frequency spectrum of the SAS system. The proposed solution is a real-time classifier that enables online analysis of the frequency spectrum from the SAS system. With this approach, an autonomous system for stress condition identification of concrete structures is built and described.

Acousto-elasticity of transversely isotropic incompressible soft tissues: characterization of skeletal striated muscle.

Using shear wave elastography, we measure the changes in the wave speed with the stress produced by a striated muscle during isometric voluntary contraction. To isolate the behaviour of an individual muscle from complementary or antagonistic actions of adjacent muscles, we select theflexor digiti minimimuscle, whose sole function is to extend the little finger. To link the wave speed to the stiffness, we develop an acousto-elastic theory for shear waves in homogeneous, transversely isotropic, incompressible solids subject to an uniaxial stress. We then provide measurements of the apparent shear elastic modulus along, and transversely to, the fibre axis for six healthy human volunteers of different age and sex. The results display a great variety across the six subjects. We find that the slope of the apparent shear elastic modulus along the fibre direction changes inversely to the maximum voluntary contraction (MVC) produced by the volunteer. We propose an interpretation of our results by introducing the S (slow) or F (fast) nature of the fibres, which harden the muscle differently and accordingly, produce different MVCs. A natural follow-up on this study is to apply the method to patients with musculoskeletal disorders or neurodegenerative diseases.

Investigation of thermo-acoustoelastic guided waves by semi-analytical finite element method.

Guided waves are sensitive to variations in propagation environments. Many recent studies have focused on the uniform thermal effect on Lamb waves. However, there is little research on the thermal effect in a more complex situation, such as a nonuniform thermal effect and wave propagation in an arbitrary cross-section. In this study, a thermo-acoustoelastic theory combined with the semi-analytical finite element (TAE-SAFE) method is proposed to investigate both uniform and nonuniform thermal effects on acoustoelastic guided wave propagation. In the TAE-SAFE method, effective thermo-acoustoelastic constants including third-order elastic constants are employed. Then, an acoustoelastic wave equation of the thermal effect is formulated by Hamilton's principle and computed by the semi-analytical finite element (SAFE) method. The phase velocity, group velocity, velocity thermal sensitivity, and displacement mode shape shift can be extracted by the proposed method. To validate this method, numerical results of Lamb waves in an aluminum plate subjected to a uniform thermal effect are compared with the results of a previous theoretical analysis. The results show computational veracity and validity. Two typical cases are investigated: (1) an isotropic aluminum plate under a linear temperature gradient condition; (2) a uniform temperature case in a rail track with a constant irregular cross-section. This study provides an effective numerical method to analyze thermo-acoustoelastic guided wave propagation.

Analysis of multiple shear wave modes in a nonlinear soft solid: Experiments and finite element simulations with a tilted acoustic radiation force.

Tissue nonlinearity is conventionally measured in shear wave elastography by studying the change in wave speed caused by the tissue deformation, generally known as the acoustoelastic effect. However, these measurements have mainly focused on the excitation and detection of one specific shear mode, while it is theoretically known that the analysis of multiple wave modes offers more information about tissue material properties that can potentially be used to refine disease diagnosis. This work demonstrated proof of concept using experiments and finite element simulations in a uniaxially stretched phantom by tilting the acoustic radiation force excitation axis with respect to the material's symmetry axis. Using this unique set-up, we were able to visualize two propagating shear wave modes across the stretch direction for stretches larger than 140%. Complementary simulations were performed using material parameters determined from mechanical testing, which enabled us to convert the observed shear wave behavior into a correct representative constitutive law for the phantom material, i.e. the Isihara model. This demonstrates the potential of measuring shear wave propagation in combination with shear wave modeling in complex materials as a non-invasive alternative for mechanical testing.

Ultrasonic nonlinearity parameter in uniaxial stress condition.

The ultrasonic nonlinearity parameter derived for one-dimensional propagation of a longitudinal wave in an isotropic material has been considered useful in the evaluation of material degradation. To demonstrate this, many researchers have reported on the correlation with the yield strength obtained from a tensile test. However, there is an essential issue with this procedure - which is that the ultrasonic nonlinearity parameter is derived in a state where the lateral strain is restrained, whereas the tensile test to measure the yield strength is carried out under uniaxial stress conditions, where lateral deformation is free. In this study, to address this issue, the authors have defined the ultrasonic nonlinearity parameter under uniaxial stress conditions which were the same as the tensile test, and showed that the correlation with the yield strength was higher than the currently used ultrasonic nonlinearity parameter. To verify the validity of the proposed ultrasonic nonlinearity parameter, experiments were carried out for Al6061-T6 alloy specimens heat-treated with different aging times. Results showed that the proposed ultrasonic nonlinearity parameter exhibited a much higher correlation with yield strength than the currently used nonlinearity parameter.

Analyzing acoustoelastic effect of shear wave elastography data for perfused and hydrated soft tissues using a macromolecular network inspired model.

Shear wave elastography (SWE) has enhanced our ability to non-invasively make in vivo measurements of tissue elastic properties of animal and human tissues. Recently, researchers have taken advantages of acoustoelasticity in SWE to extract nonlinear elastic properties from soft biological tissues. However, most investigations of the acoustoelastic effects of SWE data (AE-SWE) rely on classic hyperelastic models for rubber-like (dry) materials. In this paper, we focus solely on understanding acoustoelasticity in soft hydrated tissues using SWE data and propose a straightforward approach to modeling the constitutive behavior of soft tissue that has a direct microstructural/macromolecular interpretation. Our approach incorporates two constitutive features relevant to biological tissues into AE-SWE: static dilation of the medium associated with nonstructural components (e.g. tissue hydration and perfusion) and finite extensibility derived from an ideal network of biological filaments. We evaluated the proposed method using data from an in-house tissue-mimicking phantom experiment, and ex vivo and in vivo AE-SWE data available in the SWE literature. In conclusion, predictions made by our approach agreed well with measurements obtained from phantom, ex vivo and in vivo tissue experiments.

On the determination of the third-order elastic constants of homogeneous isotropic materials utilising Rayleigh waves.

This paper presents a new method for determining the third-order elastic constants (TOECs) of a homogeneous isotropic material utilising the acoustoelastic effect associated with Rayleigh waves. It is demonstrated that the accuracy of the evaluation of TOECs can be substantially improved by supplementing the classical equations of acoustoelasticity, which describe the effect of applied stress on bulk wave speeds, with the nonlinear characteristic equation for the propagation of Rayleigh waves in pre-stressed media. The developed method can be readily implemented for Structural Health Monitoring applications; for example, the measurement of applied stresses based on the acoustoelastic effect, or the monitoring of near-surface microstructural damage based on the change in magnitude of the TOECs.

Shear wave elastography can assess the in-vivo nonlinear mechanical behavior of heel-pad.

This study combines non-invasive mechanical testing with finite element (FE) modelling to assess for the first time the reliability of shear wave (SW) elastography for the quantitative assessment of the in-vivo nonlinear mechanical behavior of heel-pad. The heel-pads of five volunteers were compressed using a custom-made ultrasound indentation device. Tissue deformation was assessed from B-mode ultrasound and force was measured using a load cell to calculate the force - deformation graph of the indentation test. These results were used to design subject specific FE models and to inverse engineer the tissue's hyperelastic material coefficients and its stress - strain behavior. SW speed was measured for different levels of compression (from 0% to 50% compression). SW speed for 0% compression was used to assess the initial stiffness of heel-pad (i.e. initial shear modulus, initial Young's modulus). Changes in SW speed with increasing compressive loading were used to quantify the tissue's nonlinear mechanical behavior based on the theory of acoustoelasticity. Statistical analysis of results showed significant correlation between SW-based and FE-based estimations of initial stiffness, but SW underestimated initial shear modulus by 64%(±16). A linear relationship was found between the SW-based and FE-based estimations of nonlinear behavior. The results of this study indicate that SW elastography is capable of reliably assessing differences in stiffness, but the absolute values of stiffness should be used with caution. Measuring changes in SW speed for different magnitudes of compression enables the quantification of the tissue's nonlinear behavior which can significantly enhance the diagnostic value of SW elastography.

Higher order longitudinal guided wave modes in axially stressed seven-wire strands.

This paper investigates the effect of axial stress on higher order longitudinal guided modes propagating in individual wires of seven-wire strands. Specifically, an acoustoelastic theory for a rod is used to predict the effect of stress on the phase velocity of guided modes in a strand. To this end, the exact acoustoelastic theory for an axially stressed rod is adapted for small deformations. Aside from the exact theory, approximate phase velocity changes (derived from both theory and experiment) are proposed, without the need to solve for dispersion curves. To validate the use of rod theories for strands, a custom-built prestressing bed was designed to apply axial load (up to 50% of yield) to a strand while conducting guided wave measurements. Higher order modes were excited in individual wires, and their phase velocity change under stress is compared to the exact acoustoelastic theory. Furthermore, it is shown that the proposed approximate phase velocity changes derived from theory and experiment only differ by roughly 2% from their exact counterparts. Higher order modes are shown to have stable stress dependence near their peak group velocity, which is beneficial for stress measurement. Additionally, linear stress dependence is observed, which is predicted by rod theories. Due to the unavailability of third order elastic constants for the steel strand, constants for a steel with similar Carbon content (0.6% C Hecla 17) were used as representative values in the theory. Using the Hecla 17 constants, roughly 15% mismatch in the slope of the linear stress dependence was observed when compared to the measurements on a steel strand.

Nonlinear waves in solids with slow dynamics: an internal-variable model.

In heterogeneous solids such as rocks and concrete, the speed of sound diminishes with the strain amplitude of a dynamic loading (softening). This decrease, known as 'slow dynamics', occurs at time scales larger than the period of the forcing. Also, hysteresis is observed in the steady-state response. The phenomenological model by Vakhnenko et al. (2004 Phys. Rev. E 70, 015602. (doi:10.1103/PhysRevE.70.015602)) is based on a variable that describes the softening of the material. However, this model is one dimensional and it is not thermodynamically admissible. In the present article, a three-dimensional model is derived in the framework of the finite-strain theory. An internal variable that describes the softening of the material is introduced, as well as an expression of the specific internal energy. A mechanical constitutive law is deduced from the Clausius-Duhem inequality. Moreover, a family of evolution equations for the internal variable is proposed. Here, an evolution equation with one relaxation time is chosen. By construction, this new model of the continuum is thermodynamically admissible and dissipative (inelastic). In the case of small uniaxial deformations, it is shown analytically that the model reproduces qualitatively the main features of real experiments.

Effect of pressurization on helical guided wave energy velocity in fluid-filled pipes.

The effect of pressurization stresses on helical guided waves in a thin-walled fluid-filled pipe is studied by modeling leaky Lamb waves in a stressed plate bordered by fluid. Fluid pressurization produces hoop and longitudinal stresses in a thin-walled pipe, which corresponds to biaxial in-plane stress in a plate waveguide model. The effect of stress on guided wave propagation is accounted for through nonlinear elasticity and finite deformation theory. Emphasis is placed on the stress dependence of the energy velocity of the guided wave modes. For this purpose, an expression for the energy velocity of leaky Lamb waves in a stressed plate is derived. Theoretical results are presented for the mode, frequency, and directional dependent variations in energy velocity with respect to stress. An experimental setup is designed for measuring variations in helical wave energy velocity in a thin-walled water-filled steel pipe at different levels of pressure. Good agreement is achieved between the experimental variations in energy velocity for the helical guided waves and the theoretical leaky Lamb wave solutions.