Complex Elastic Modulus Research Articles

Comparison analysis of four processing methods employed in dynamic elastography to estimate viscoelastic parameters of a medium: tests using computational simulation and experiment

Dynamic ultrasound elastography is a method commonly used to quantify the mechanical parameters, such as shear elasticity modulus, and shear viscosity modulus, of biological tissues. Basically, the method employs four processing techniques, in order to estimate the mentioned parameters, denominated: phase velocity dispersion, PVD, attenuation-velocity, AV, complex shear elasticity modulus, CSM, and shear wave velocity, SV. The accuracy and precision of estimated values for and depend on the processing technique and the purpose of this paper is to compare the results obtained with PVD, AV, CSM and SV processing techniques by means of two cases: computer simulation and experiments. In the first case, the processing techniques were evaluated, via simulation, at different conditions for the signal-to-noise-ratio of the ultrasound RF echo signal used to probe the medium with vibrations due to the propagation of shear wave, the vibration amplitude and the viscoelastic properties of the medium itself. The corresponding results are expressed as the magnitudes of the mean and standard deviation of the relative error. In the second case, experiments were conducted based on a dynamic elastographic system with a cylindrical shear wave induced by a repetitive acoustic radiation force, with pulse repetition frequency of 50 Hz. A 4.98 MHz pulse-echo ultrasound system was used to probe the medium, a 3% gelatin phantom, traversed by the shear wave and the received RF echo signals were processed using the four techniques to yield the phantom values of and The results from computer simulation indicate that, in general, the CSM and AV techniques presented highest accuracy and precision. The experimental results obtained in this study are consistent with the values reported in the literature and the values of the shear elasticity modulus estimated by the four processing techniques did not differ significantly.

An Investigation of Vibrational Power Flow in One-Dimensional Dissipative Phononic Structures

Owing to their ability to block propagating waves at certain frequencies, phononic materials of self-repeating cells are widely appealing for acoustic mitigation and vibration suppression applications. The stop band behavior achieved via Bragg scattering in phononic media is most commonly evaluated using wave propagation models which predict gaps in the dispersion relations of the individual unit cells for a given frequency range. These models are in many ways limited when analyzing phononic structures with dissipative constituents and need further adjustments to account for viscous damping given by complex elastic moduli and frequency-dependent loss factors. A new approach is presented which relies on evaluating structural intensity parameters, such as the active vibrational power flow in finite phononic structures. It is shown that the steady-state spatial propagation of vibrational power flow initiated by an external disturbance reflects the wave propagation pattern in the phononic medium and can thus be reverse engineered to numerically predict the stop band frequencies for different degrees of damping via a stop band index (SBI). The treatment is shown to be very effective for phononic structures with viscoelastic components and provides a clear distinction between Bragg scattering effects and wave attenuation due to material damping. Since the approach is integrated with finite element methods, the presented analysis can be extended to two-dimensional lattices with complex geometries and multiple material constituents.

Comparison of complex modulus and elasticity modulus of bitumen bonded materials

The European standards for asphalt mixture testing are mainly focused on empirical parameters of asphalt mixtures. On the other hand, functional parameters (e.g. fatigue, stiffness) of asphalt mixtures describe real behavior of the material in-situ. These parameters are used for design of road construction according to the Slovak design method where the elasticity modulus is used instead of the complex modulus. The problem is that no standard for elasticity modulus measurement exists in the collection of the European standards. In this study complex modulus measurement was performed according to the European standard, and for comparison elasticity modulus measurement was also done according to the Australian standard.

Determination of mechanical properties of some glass fiber reinforced plastics suitable to Wind Turbine Blade construction

The control of wind turbine's components is very rigorous, while the tower and gearbox have more possibility for revision and repairing, the rotor blades, once they are deteriorated, the defects can rapidly propagate, producing failure, and the damages can affect large regions around the wind turbine. This paper presents the test results, performed on glass fiber reinforced plastics (GFRP) suitable to construction of wind turbine blades (WTB). The Young modulus, shear modulus, Poisson's ratio, ultimate stress have been determined using tensile and shear tests. Using Dynamical Mechanical Analysis (DMA), the activation energy for transitions that appear in polyester matrix as well as the complex elastic modulus can be determined, function of temperature.

Rheology of the Active Cell Cortex in Mitosis

The cell cortex is a key structure for the regulation of cell shape and tissue organization. To reach a better understanding of the mechanics and dynamics of the cortex, we study here HeLa cells in mitosis as a simple model system. In our assay, single rounded cells are dynamically compressed between two parallel plates. Our measurements indicate that the cortical layer is the dominant mechanical element in mitosis as opposed to the cytoplasmic interior. To characterize the time-dependent rheological response, we extract a complex elastic modulus that characterizes the resistance of the cortex against area dilation. In this way, we present a rheological characterization of the cortical actomyosin network in the linear regime. Furthermore, we investigate the influence of actin cross linkers and the impact of active prestress on rheological behavior. Notably, we find that cell mechanics values in mitosis are captured by a simple rheological model characterized by a single timescale on the order of 10 s, which marks the onset of fluidity in the system.

Fast blood-flow simulation for large arterial trees containing thousands of vessels

Blood flow modelling has previously been successfully carried out in arterial trees to study pulse wave propagation using nonlinear or linear flow solvers. However, the number of vessels used in the simulations seldom grows over a few hundred. The aim of this work is to present a computationally efficient solver coupled with highly detailed arterial trees containing thousands of vessels. The core of the solver is based on a modified transmission line method, which exploits the analogy between electrical current in finite-length conductors and blood flow in vessels. The viscoelastic behaviour of the arterial-wall is taken into account using a complex elastic modulus. The flow is solved vessel by vessel in the frequency domain and the calculated output pressure is then used as an input boundary condition for daughter vessels. The computational results yield pulsatile blood pressure and flow rate for every segment in the tree. This solver is coupled with large arterial trees generated from a three-dimensional constrained constructive optimisation algorithm. The tree contains thousands of blood vessels with radii spanning ~1 mm in the root artery to ~30 μm in leaf vessels. The computation takes seconds to complete for a vasculature of 2048 vessels and less than 2 min for a vasculature of 4096 vessels on a desktop computer.

Anti-ageing properties of styrene–butadiene–styrene copolymer-modified asphalt combined with multi-walled carbon nanotubes

This paper presents the findings from a study conducted to evaluate the potential impact of Carbon Nanotubes (CNTs) on the anti-ageing properties of styrene–butadiene–styrene copolymer-modified asphalt (SBS PMA). Ageing Indexes (AIs) of conventional parameters, rheological parameters, and structural changes were employed to capture the changes in asphalt samples before and after ageing. For conventional parameters, AIs of viscosity at 60°C, penetration, and ductility were significantly decreased by the addition of CNTs. Rheological parameters were performed by Master curves and Han curves, including complex modulus (G*), elastic modulus (G′), viscous modulus (G″), and phase angle (δ). When the amount of CNTs below 0.5 wt.%, the AIs of G* in the low-frequency zone of mater curves for SBS PMA was smaller than the one without CNTs. On the other hand, when the amount of CNTs surpass 0.5 wt.%, the AIs of G* in high-frequency zone of mater curves for SBS PMA was large. CNTs provided unaged SBS PMA with lower slopes of log (G′) versus log (G″) plots and higher elastic modulus in the terminal region of the plot attributable to the deformation and relaxation of SBS and CNT particles. For structural changes, AI of carbonyl functions and butadiene functions for SBS PMA were larger than that of samples with CNTs; thus, SBS degradation was decreased by adding CNTs. Furthermore, the oxygen-uptake amount of blends combined with SBS and CNTs was lower than that of neat SBS modifiers, demonstrating its important effect on the anti-ageing properties of SBS-modified asphalt.

On the nontrivial wave-vector dependence of the elastic modulus of glasses

Recent theoretical models for the vibrations in glasses assume that the complex elastic modulus depends on frequency but not on the wave vector, $q$. This assumption translates in a simple $q$ dependence of the dynamic structure factor, which can be experimentally tested. Following the suggestion of a recent paper [U. Buchenau, Phys. Rev. E 90, 062319 (2014)], we present here a new analysis, performed in $q$ space, of inelastic x-ray scattering data of supercooled silica. The outcome of the analysis is compared to the more common approach in the frequency domain and indicates that the mentioned theoretical assumption is consistent with the data only below the boson peak frequency. At higher frequencies it gives rise to a breakdown of the classical second moment sum rule. This violation arises from the underlying assumption of the presence of a single excitation in the spectra. A comparison with the vibrational dynamics of $\ensuremath{\alpha}$-cristobalite suggests, on the contrary, that in the terahertz frequency domain the inelastic spectrum of the glass gains contributions from both acousticlike and opticlike modes. A microscopic theory of the vibrations in glasses cannot neglect the medium range order in their structure, which gives rise to dispersion curves within a pseudo-Brillouin zone.

Rheological and Mechanical Properties of Ultra-fine Cellulose-Filled Thermoplastic Epoxy Composites

Thermoplastic epoxy resin (TPER)-based composites containing different amounts of ultra-fine cellulose (UFC) were prepared via melt compounding and injection molding. The effect of UFC loading on the mechanical properties and dynamic rheological behavior of the UFC-filled TPER composites was analyzed. The UFC-filled composites displayed higher complex viscosities than those of the neat TPER composites, especially at low frequencies. The elastic modulus of the 20 wt.% UFC-filled composite was up to 6- and 2-fold higher than that of TPER at 0.1 and 100 Hz, respectively. The loss factor decreased over the entire frequency range with the incorporation of UFC. The tensile modulus of elasticity (TMOE) of neat TPER was 3.13 GPa, and it increased as a function of UFC loading. The neat TPER exhibited the lowest flexural strength (108.1 MPa), and the flexural strength increased by 14% with the incorporation of 20 wt.% UFC. The results of the TMOE and the flexural modulus of elasticity (FMOE) were in agreement with rheological data on complex viscosity, elastic modulus, and viscous modulus. Ultra-fine cellulose-filled TPER composites may provide special capabilities for automotive applications and may also meet requirements for end-of-life vehicle (ELV) directives.

Active Elastomer Components Based on Dielectric Elastomers

A new design concept developed at the Fraunhofer LBF allows dielectric elastomers to be integrated efficiently as load-bearing components, serving as both actuator and sensor at the same time. Since the concept is based on perforated metal electrodes with high electrical conductivities, it can also be used for highly dynamic and acoustic applications to which dielectric elastomers would not usually lend themselves. This article focuses on the adaptive properties of these elastomer components. By applying a static voltage, the effective complex elastic modulus and the loss angle of the composite material can be adjusted within certain limits and varied as required. Experimental results are provided to illustrate this approach and the potential of this new technology for innovative solutions is discussed.

Rheological study of mudflows at Lianyungang in China

An experimental study of the rheological properties of mudflows at Lianyungang in China was carried out by the RS6000 rheometer, including steady and dynamic measurements. Five samples with the range of mud volume concentration from 0.058 to 0.179 were investigated. Based on the experimental data, a Dual-Herschel–Bulkley model was developed to analyze the flow curve and interpolate the static and dynamic yield stresses. The results show that in the steady measurement, the consolidation time and the system temperature show some effects on the rheogram and the yield stress for the sample with low sediment volume concentration, and the effects are strengthened gradually with the sediment volume concentration increasing. Under a shear stress sweep, two linear visco-elastic regions, showing the viscous and the elastic behaviors respectively, were discovered. Complex viscosity, elastic modulus and loss modulus in the elastic region are several orders of magnitude larger than those in the viscous region. Furthermore, the analysis of experimental data show that both steady and dynamic rheological properties can be expressed as appropriate exponential functions of the sediment volume concentration.

Fibrillation of chain branched poly (lactic acid) with improved blood compatibility and bionic structure

Highly-oriented poly (lactic acid) (PLA) with bionic fibrillar structure and micro-grooves was fabricated through solid hot drawing technology for further improving the mechanical properties and blood biocompatibility of PLA as blood-contacting medical devices. In order to enhance the melt strength and thus obtain high orientation degree, PLA was first chain branched with pentaerythritol polyglycidyl ether (PGE). The branching degree as high as 12.69mol% can be obtained at 0.5wt% PGE content. The complex viscosity, elastic and viscous modulus for chain branched PLA were improved resulting from the enhancement of molecular entanglement, and consequently higher draw ratio can be achieved during the subsequent hot stretching. The stress-induced crystallization of PLA occurred during stretching, and the crystal structure of the oriented PLA can be attributed to the α′ crystalline form. The tensile strength and modulus of PLA were improved dramatically by drawing. Chain branching and orientation could significantly enhance the blood compatibility of PLA by prolonging clotting time and decreasing hemolysis ratio, protein adsorption and platelet activation. Fibrous structure as well as micro-grooves can be observed for the oriented PLA which were similar to intimal layer of blood vessel, and this bionic structure was considered to be beneficial to decrease the activation and/or adhesion of platelets.

Destructive and nondestructive evaluations of the effect of moisture absorption on the mechanical properties of polyester-based composites

In this study the effect of moisture absorption on the mechanical properties of glass-reinforced polyester composites is evaluated using both destructive and nondestructive tests. The composite resins were produced with two different production processes, while the mechanical properties of the composite materials were measured using DMA destruction tests. According to the DMA tests, the dependency in terms of temperature for the real component of the complex elastic modulus (E′), the imaginary component of the complex elastic modulus (E″), as well as tan(δ) can be traced. For a more efficient use of the composite materials, the compliance tensor was obtained with nondestructive tests based on ultrasound. A method for the generation and reception of Lamb waves in plates of composite materials is described, based on using air-coupling, low-frequency, ultrasound transducers in a pitch–catch configuration. The results of the nondestructive measurements made in this study are in good agreement with those obtained when using the DMA destructive tests.

Anomalous glass transition behavior of SBR–Al2O3 nanocomposites at small filler concentrations

Elastomers filled with hard nanoparticles are of great technical importance for the rubber industry. In general, fillers improve mechanical properties of polymer materials, e.g. elastic moduli, tensile strength etc. The smaller the size of the particles, the larger is the interface where interactions between polymer molecules and fillers can generate new properties. Using temperature-modulated differential scanning calorimetry and dynamic mechanical analysis, we investigated the properties of pure styrene-butadiene rubber (SBR) and SBR/alumina nanoparticles. Beside a reinforcement effect seen in the complex elastic moduli, small amounts of nanoparticles of about 2 wt% interestingly lead to an acceleration of the relaxation modes responsible for the thermal glass transition. This leads to a minimum in the glass transition temperature as a function of nanoparticle content in the vicinity of this critical concentration. The frequency dependent elastic moduli are used to discuss the possible reduction of the entanglement of rubber molecules as one cause for this unexpected behavior.

Experimental and numerical investigations on the use of polymer Hopkinson pressure bars

Split Hopkinson pressure bar (SHPB) testing has traditionally been carried out using metal bars. For testing low stiffness materials such as rubbers or low strength materials such as low density cellular solids considered primarily herein, there are many advantages to replacing the metal bars with polymer bars. An investigation of a number of aspects associated with the accuracy of SHPB testing of these materials is reported. Test data are used to provide qualitative comparisons of accuracy using different bar materials and wave-separation techniques. Sample results from SHPB tests are provided for balsa, Rohacell foam and hydroxyl-terminated polybutadiene. The techniques used are verified by finite-element (FE) analysis. Experimentally, the material properties of the bars are determined from impact tests in the form of a complex elastic modulus without curve fitting to a rheological model. For the simulations, a rheological model is used to define the bar properties by curve fitting to the experimentally derived properties. Wave propagation in a polymer bar owing to axial impact of a steel bearing ball is simulated. The results indicate that the strain histories can be used to determine accurately the viscoelastic properties of polymer bars. An FE model of the full viscoelastic SHPB set-up is then used to simulate tests on hyperelastic materials.

WE‐E‐9A‐01: Ultrasound Elasticity

Principles and techniques of ultrasound‐based elasticity imaging will be presented, including quasistatic strain imaging, shear wave elasticity imaging, and their implementations in available systems. Deeper exploration of quasistatic methods, including elastic relaxation, and their applications, advantages, artifacts and limitations will be discussed. Transient elastography based on progressive and standing shear waves will be explained in more depth, along with applications, advantages, artifacts and limitations, as will measurement of complex elastic moduli. Comparisons will be made between ultrasound radiation force techniques, MR elastography, and the simple A mode plus mechanical plunger technique. Progress in efforts, such as that by the Quantitative Imaging Biomarkers Alliance, to reduce the differences in the elastic modulus reported by different commercial systems will be explained.Dr. Hall is on an Advisory Board for Siemens Ultrasound and has a research collaboration with them, including joint funding by R01CA140271 for nonlinear elasticity imaging.Learning Objectives: Be reminded of the long history of palpation of tissue elasticity for critical medical diagnosis and the relatively recent advances to be able to image tissue strain in response to an applied force. Understand the differences between shear wave speed elasticity measurement and imaging and understand the factors affecting measurement and image frame repletion rates. Understand shear wave propagation effects that can affect measurements, such as essentially lack of propagation in fluids and boundary effects, so important in thin layers. Know characteristics of available elasticity imaging phantoms, their uses and limitations. Understand thermal and cavitational limitations affecting radiation force‐based shear wave imaging. Have learning and references adequate to for you to use in teaching elasticity imaging to residents and technologists. Be able to explain how elasticity measurement and imaging can contribute to diagnosis of breast and prostate cancer, staging of liver fibrosis, age estimation of deep veinous fhrombosis, confirmation of thermal lesions in the liver after RF ablation.

Modeling the high-frequency complex modulus of silicone rubber using standing Lamb waves and an inverse finite element method.

To gain an understanding of the high-frequency elastic properties of silicone rubber, a finite element model of a cylindrical piezoelectric element, in contact with a silicone rubber disk, was constructed. The frequency-dependent elastic modulus of the silicone rubber was modeled by a fourparameter fractional derivative viscoelastic model in the 100 to 250 kHz frequency range. The calculations were carried out in the range of the first radial resonance frequency of the sensor. At the resonance, the hyperelastic effect of the silicone rubber was modeled by a hyperelastic compensating function. The calculated response was matched to the measured response by using the transitional peaks in the impedance spectrum that originates from the switching of standing Lamb wave modes in the silicone rubber. To validate the results, the impedance responses of three 5-mm-thick silicone rubber disks, with different radial lengths, were measured. The calculated and measured transitional frequencies have been compared in detail. The comparison showed very good agreement, with average relative differences of 0.7%, 0.6%, and 0.7% for the silicone rubber samples with radial lengths of 38.0, 21.4, and 11.0 mm, respectively. The average complex elastic moduli of the samples were (0.97 + 0.009i) GPa at 100 kHz and (0.97 + 0.005i) GPa at 250 kHz.

Master curve of viscoelastic solid: Using causality to determine the optimal shifting procedure, and to test the accuracy of measured data

Viscoelastic solids such as rubber exhibit a complex elastic modulus E(ω), which depends on the frequency ω of the applied stress or strain. The modulus E(ω) can often be determined in a wide frequency range by performing measurements in a limited frequency range for many different temperatures, and then shift the frequency segments horizontally along the frequency axis to obtain a continuous master curve. We show that one can use the spectral representation of E(ω) (or 1/E(ω)), which obeys causality, to determine the optimal shifting procedure, and to test the accuracy of the measured data and the calculated master curve.

Rayleigh wave propagation method for the characterization of a thin layer of biomaterials

An experimental method based on Rayleigh wave propagation was developed for quantifying the frequency-dependent viscoelastic properties of a small volume of expensive biomaterials over a broad frequency range. Synthetic silicone rubber and gelatin materials were fabricated and tested to evaluate the proposed method. Planar harmonic Rayleigh waves at different frequencies, from 80 to 4000 Hz, were launched on the surface of a sample composed of a substrate with known material properties coated with a thin layer of the soft material to be characterized. A transfer function method was used to obtain the complex Rayleigh wavenumber. An inverse wave propagation problem was solved and a complex nonlinear dispersion equation was obtained. The complex shear and elastic moduli of the sample materials were then calculated through the numerical solution of the obtained dispersion equation using the measured wavenumbers. The results were in good agreement with those of a previous independent study. The proposed method was found to be reliable and cost effective for the measurement of viscoelastic properties of a thin layer of expensive biomaterials, such as phonosurgical biomaterials, over a wide frequency range.

Modified hysteretic damping model applied to Timoshenko timber beams

The present study deals with prediction of material damping in Timoshenko beams. Complex elastic moduli and complex stiffness are defined to derive an analytical model that predicts the hysteretic system damping for the whole structure. The prediction model comprises two parts, the first related to bending, and the second related to shear. Reliable experimental damping evaluations on overhanging timber beams are used to calibrate the model and obtain fitted values of loss factors for two types of wood. The good agreement of the derived model with experimental data reveals an efficient approach in the prediction of material damping.