Shear Wave Propagation and Band Gaps in Finitely Deformed Dielectric Elastomer Laminates: Long Wave Estimates and Exact Solution

2017 ◽  
Vol 84 (9) ◽  
Author(s):  
Pavel I. Galich ◽  
Stephan Rudykh
Keyword(s):  
Exact Solution ◽  
Wave Propagation ◽  
Electric Field ◽  
Shear Wave ◽  
Small Amplitude ◽  
Shear Waves ◽  
Dielectric Elastomer ◽  
Band Gaps ◽  
Wave Band ◽  
Long Wave

We analyze small amplitude shear waves (SWs) propagating in dielectric elastomer (DE) laminates subjected to finite deformations and electrostatic excitations. First, we derive long wave estimates for phase and group velocities of the shear waves propagating in any direction in DE laminates subjected to any homogenous deformation in the presence of an electric filed. To this end, we utilize a micromechanics-based energy potential for layered media with incompressible phases described by neo-Hookean ideal DE model. The long wave estimates reveal the significant influence of electric field on the shear wave propagation. However, there exists a configuration, for which electric field does not influence shear waves directly, and can only alter the shear waves through deformation. We study this specific configuration in detail, and derive an exact solution for the steady-state small amplitude waves propagating in the direction perpendicular to the finitely deformed DE layers subjected to electrostatic excitation. In agreement with the long wave estimate, the exact dispersion relation and the corresponding shear wave band gaps (SBGs)—forbidden frequency regions—are not influenced by electric field. However, SBGs in DE laminates with highly nonlinear electroelastic phases still can be manipulated by electric field through electrostatically induced deformation. In particular, SBGs in DE laminates with electroelastic Gent phases widen and shift toward higher frequencies under application of an electric field perpendicular to the layers. However, in laminates with neo-Hookean ideal DE phases, SBGs are not influenced either by electric field or by deformation. This is due to the competing mechanisms of two governing factors: changes in geometry and material properties induced by deformation. In this particular case, these two competing factors entirely cancel each other.

scholarly journals Insights Into Traumatic Brain Injury From MRI of Harmonic Brain Motion

2019 ◽  
Vol 13 ◽  
pp. 117906951984044 ◽  
Author(s):  
Ruth J Okamoto ◽  
Anthony J Romano ◽  
Curtis L Johnson ◽  
Philip V Bayly
Keyword(s):  
Traumatic Brain Injury ◽  
Wave Propagation ◽  
Brain Injury ◽  
Shear Wave ◽  
Relative Motion ◽  
Vector Fields ◽  
Shear Waves ◽  
Mechanical Deformation ◽  
Minor Role ◽  
The Brain

Measurements of dynamic deformation of the human brain, induced by external harmonic vibration of the skull, were analyzed to illuminate the mechanics of mild traumatic brain injury (TBI). Shear wave propagation velocity vector fields were obtained to illustrate the role of the skull and stiff internal membranes in transmitting motion to the brain. Relative motion between the cerebrum and cerebellum was quantified to assess the vulnerability of connecting structures. Mechanical deformation was quantified throughout the brain to investigate spatial patterns of strain and axonal stretch. Strain magnitude was generally attenuated as shear waves propagated into interior structures of the brain; this attenuation was greater at higher frequencies. Analysis of shear wave propagation direction indicates that the stiff membranes (falx and tentorium) greatly affect brain deformation during imposed skull motion as they serve as sites for both initiation and reflection of shear waves. Relative motion between the cerebellum and cerebrum was small in comparison with the overall motion of both structures, which suggests that such relative motion might play only a minor role in TBI mechanics. Strain magnitudes and the amount of axonal stretch near the bases of sulci were similar to those in other areas of the cortex, and local strain concentrations at the gray-white matter boundary were not observed. We tentatively conclude that observed differences in neuropathological response in these areas might be due to heterogeneity in the response to mechanical deformation rather than heterogeneity of the deformation itself.

Reflection of coupled dilatational and shear waves in the generalized micropolar thermoelastic materials

2020 ◽  
Vol 26 (21-22) ◽  
pp. 1948-1955 ◽  
Author(s):  
Rengsi Lianngenga ◽  
Sanasam S Singh
Keyword(s):  
Wave Propagation ◽  
Free Surface ◽  
Boundary Conditions ◽  
Shear Wave ◽  
Shear Waves ◽  
Energy Ratios ◽  
Micropolar Thermoelasticity ◽  
Incident Waves

The problem of wave propagation in the generalized theory of micropolar thermoelasticity under the Green–Lindsay model has been investigated. We have investigated the reflected dilatational and shear waves due to incident waves at a plane-free surface of generalized micropolar thermoelastic materials. The amplitude and energy ratios corresponding to the reflected coupled dilatational and coupled shear waves are derived using boundary conditions at the free surface. These ratios are also computed numerically for a particular model. Note that there are critical angles for the incident shear wave.

scholarly journals The influence of hemodialysis-induced preload changes on the propagation speed of natural shear waves

2021 ◽  
Vol 22 (Supplement_1) ◽  
Author(s):  
S Bezy ◽  
M Orlowska ◽  
A Van Craenenbroeck ◽  
M Cvijic ◽  
J Duchenne ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Shear Wave ◽  
Wave Speed ◽  
Shear Waves ◽  
Propagation Speed ◽  
Left Ventricular ◽  
Frame Rate ◽  
High Frame Rate ◽  
Shear Wave Speed ◽  
Wave Propagation Speed

Abstract Funding Acknowledgements Type of funding sources: Public grant(s) – National budget only. Main funding source(s): Research Foundation - Flanders (FWO) Background Shear wave elastography (SWE) is a novel ultrasound technique based on the detection of transverse waves travelling through the myocardium using high frame rate echocardiography. The propagation speed of these shear waves is dependent on the stiffness of the myocardium. Previous studies have shown the potential of SWE for the non-invasive assessment of myocardial stiffness. It is unclear, however, if preload changes lead to measurable changes in the shear wave propagation speed in the left ventricle. In patients undergoing hemodialysis, the volume status is acutely changed. In this way, the effect of preload changes on shear wave speed can be assessed. Purpose The aim of this study was to explore the influence of preload changes on end-diastolic shear wave propagation speed. Methods Until now, 6 patients (age: 80[53-85] years; female: n = 2) receiving hemodialysis treatment were included. Echocardiographic images were taken before and every hour during a 4 hour hemodialysis session. Left ventricular parasternal long-axis views were acquired with an experimental high frame rate ultrasound scanner (average frame rate: 1016[941-1310] Hz). Standard echocardiography was performed with a conventional ultrasound machine. Shear waves were visualized on tissue acceleration maps by drawing an M-mode line along the interventricular septum. Shear wave propagation speed after mitral valve closure (MVC) was calculated by measuring the slope of the wave pattern on the acceleration maps (Figure A). Results Over the course of hemodialysis, the systolic (141[135-156] mmHg vs. 165[105-176] mmHg; p = 0.35 among groups) and diastolic blood pressure (70[66-75] mmHg vs. 82[63-84] mmHg; p = 0.21 among groups), heart rate (56[54-73] bmp vs. 57[50-67] bpm; p = 0.76 among groups), E/A ratio (1.6[0.7-1.8] vs. 1.2[0.6-1.4]; p = 0.43 among groups) and E/e’ (14[9-15] vs. 9[8-13]; p = 0.24 among groups ) remained the same. The ultra-filtrated volumes are shown in Figure B. The shear wave propagation speed after MVC gradually decreased during hemodialysis (6.7[5.4-9.7] m/s vs. 4.4[3.6-9.0] m/s; p = 0.04 among groups) (Figure C). There was a moderate negative correlation between shear wave speed and the ultra-filtrated volume (r=-0.63; p < 0.01) (Figure D). Conclusion The shear wave propagation speed at MVC significantly decreased over the course of hemodialysis and correlated to the ultra-filtrated volume. These results indicate that alterations in left ventricular preload affect the speed of shear waves at end-diastole. End-diastolic shear wave speed might therefore be a potential novel parameter for the evaluation of the left ventricular filling state. More patients will be included in the future to further explore these findings. Abstract Figure.

scholarly journals Viscoelasticity Imaging of Biological Tissues and Single Cells Using Shear Wave Propagation

2021 ◽  
Vol 9 ◽  
Author(s):  
Hongliang Li ◽  
Guillaume Flé ◽  
Manish Bhatt ◽  
Zhen Qu ◽  
Sajad Ghazavi ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Shear Wave ◽  
Soft Tissues ◽  
Acoustic Radiation ◽  
Single Cells ◽  
Shear Waves ◽  
Mechanical Vibration ◽  
Shear Wave Elastography ◽  
Biomechanical Properties ◽  
Biological Tissues

Changes in biomechanical properties of biological soft tissues are often associated with physiological dysfunctions. Since biological soft tissues are hydrated, viscoelasticity is likely suitable to represent its solid-like behavior using elasticity and fluid-like behavior using viscosity. Shear wave elastography is a non-invasive imaging technology invented for clinical applications that has shown promise to characterize various tissue viscoelasticity. It is based on measuring and analyzing velocities and attenuations of propagated shear waves. In this review, principles and technical developments of shear wave elastography for viscoelasticity characterization from organ to cellular levels are presented, and different imaging modalities used to track shear wave propagation are described. At a macroscopic scale, techniques for inducing shear waves using an external mechanical vibration, an acoustic radiation pressure or a Lorentz force are reviewed along with imaging approaches proposed to track shear wave propagation, namely ultrasound, magnetic resonance, optical, and photoacoustic means. Then, approaches for theoretical modeling and tracking of shear waves are detailed. Following it, some examples of applications to characterize the viscoelasticity of various organs are given. At a microscopic scale, a novel cellular shear wave elastography method using an external vibration and optical microscopy is illustrated. Finally, current limitations and future directions in shear wave elastography are presented.

scholarly journals Shear Wave Propagation and Estimation of Material Parameters in a Nonlinear, Fibrous Material

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Zuoxian Hou ◽  
Ruth J. Okamoto ◽  
Philip V. Bayly
Keyword(s):  
Wave Propagation ◽  
Shear Wave ◽  
Shear Waves ◽  
Material Model ◽  
Model Parameters ◽  
Single Family ◽  
Wave Speeds ◽  
Material Parameters ◽  
Hgo Model

Abstract This paper describes the propagation of shear waves in a Holzapfel–Gasser–Ogden (HGO) material and investigates the potential of magnetic resonance elastography (MRE) for estimating parameters of the HGO material model from experimental data. In most MRE studies the behavior of the material is assumed to be governed by linear, isotropic elasticity or viscoelasticity. In contrast, biological tissue is often nonlinear and anisotropic with a fibrous structure. In such materials, application of a quasi-static deformation (predeformation) plays an important role in shear wave propagation. Closed form expressions for shear wave speeds in an HGO material with a single family of fibers were found in a reference (undeformed) configuration and after imposed predeformations. These analytical expressions show that shear wave speeds are affected by the parameters (μ0, k1, k2, κ) of the HGO model and by the direction and amplitude of the predeformations. Simulations of corresponding finite element (FE) models confirm the predicted influence of HGO model parameters on speeds of shear waves with specific polarization and propagation directions. Importantly, the dependence of wave speeds on the parameters of the HGO model and imposed deformations could ultimately allow the noninvasive estimation of material parameters in vivo from experimental shear wave image data.

The behaviour of natural shear waves under different loading conditions

2020 ◽  
Vol 41 (Supplement_2) ◽  
Author(s):  
S Bezy ◽  
J Duchenne ◽  
M Orlowska ◽  
L Wouters ◽  
A Caenen ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Shear Wave ◽  
Propagation Velocity ◽  
Shear Waves ◽  
Left Ventricular ◽  
Balloon Occlusion ◽  
Frame Rate ◽  
Funding Source ◽  
Preload Reduction ◽  
Propagation Velocities

Abstract Background Shear wave imaging (SWI) is a novel ultrasound technique based on the detection of transverse waves traveling through the myocardium using high frame rate echocardiography. These waves can be naturally induced e.g. by mitral valve closure (MVC). Their propagation velocity is dependent on the stiffness of the myocardium. Previous studies have shown the potential of SWI for the non-invasive assessment of myocardial stiffness. So far, the influence of loading on shear wave propagation velocities has not been extensively investigated. Purpose The aim of this study was to explore how loading changes affect shear wave propagation velocities after MVC. Methods Until now, 5 pigs (weight: 33.5±6.9 kg) were included. Echocardiographic images and left ventricular pressure recordings were simultaneously acquired during acute loading alterations: 1) preload was reduced by balloon occlusion of the vena cava inferior, 2) afterload was increased by balloon occlusion of the descending aorta and 3) preload was increased by intra-venous administration of 500 ml of saline. Left ventricular parasternal long-axis views were acquired with an experimental high frame rate ultrasound scanner (average frame rate: 1247±179 Hz). Shear waves were visualized on tissue acceleration maps by drawing an M-mode line along the interventricular septum. Shear wave propagation velocities after MVC were calculated by measuring the slope of the wave front on the acceleration maps (Figure A). Results The changes in left ventricular end-diastolic pressures (LV EDP) between baseline and each intervention are shown in Figure B. Preload reduction resulted in significantly reduced LV EDP (p<0.01). The shear wave propagation velocities after MVC dropped with preload reduction and increased significantly by increasing afterload as well as preload (both p<0.05) (Figure C). There was a good positive correlation between the change in LV EDP and the change in shear wave velocities (r=0.83; p<0.001) (Figure D). Conclusion The shear wave propagation velocity after MVC was significantly influenced by alterations in left ventricular loading conditions and changes in these velocities were related to changes in LV EDP. These results indicate that shear wave measurements at MVC might be a potential novel parameter for the estimation of left ventricular filling pressures. More pigs will be included in the future to further confirm these findings. Funding Acknowledgement Type of funding source: Public grant(s) – National budget only. Main funding source(s): Fonds Wetenschappelijk Onderzoek - Vlaanderen

scholarly journals Wave Propagation in L-Shape Beams with Piezoelectric Shunting Arrays

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Shengbing Chen ◽  
Yubao Song ◽  
Hao Zhang
Keyword(s):  
Wave Propagation ◽  
Band Gaps ◽  
Flexural Wave ◽  
Wave Band ◽  
Flexural Waves ◽  
Resonant Frequencies ◽  
Numerical Predictions ◽  
Shunting Resistance ◽  
Vibration Transmissibility ◽  
Shunt Damping

Piezoelectric shunting arrays are employed to control the elastic wave propagation in L-shape beams. Unlike straight beams where longitudinal and flexural waves usually propagate independently, these waves are coupled in an L-shape beam. Based on transfer matrix method and Bloch theorem, dispersion curves and vibration transmissibility are evaluated and analyzed. A locally resonant gap is produced on the flexural and longitudinal waves, respectively, whose locations are nonoverlapped if the shunt damping is void. However, the longitudinal wave band gap can be completely overlaid by the flexural one when a proper shunting resistance is involved. With the decreasing of shunting inductance, the locations of longitudinal and flexural wave gaps both go up to higher frequencies which agree with the variation of resonant frequencies, but they are less affected by shunting resistance. As the resistance increases, the width of the band gaps grows, whereas the attainable maximum attenuation within the band gaps shows a significant decrease. Also, finite element simulations are performed to validate the numerical predictions, which demonstrate that the resulting transmissibility of displacements agree well with the band gaps.

Flexural Wave Band Gaps in Phononic Crystal Thick Plates with Defects

2019 ◽  
Author(s):  
Edson Jansen Pedrosa de Miranda Junior ◽  
Jose Maria Campos dos Santos
Keyword(s):  
Phononic Crystal ◽  
Band Gaps ◽  
Flexural Wave ◽  
Wave Band ◽  
Thick Plates
Sign in / Sign up

Export Citation Format

Share Document