Viscoelastic Shell Research Articles

Nonlinear three-dimensional modeling for encapsulated microbubble dynamics subject to ultrasound

Encapsulated microbubbles (EMBs) stabilized by thin coatings have been used as contrast agents for ultrasound sonography as well as having been demonstrated as a promising new technology for targeted drug delivery. The dynamics of EMBs is three-dimensional (3D) because EMBs within micro-vessels inevitably interact with boundaries, but the theoretical and numerical studies are limited to spherical, weakly non-spherical, and/or axisymmetric EMBs. Here, we have developed physical, mathematical, and numerical models for nonlinear 3D EMB dynamics. The liquid flow is evaluated using the boundary integral method. The EMB coating is modeled as a thin viscoelastic shell including stretching, bending, and shear effects and simulated using the finite element method. These models are coupled through the kinematic and dynamic boundary conditions at the interface. The model is in good agreement with the Hoff equation for spherical EMBs and the asymptotic theory for weakly non-spherical deformation of EMBs. Using this model, a numerical study for EMB dynamics near a rigid boundary subject to an ultrasonic wave is performed. The migration, non-spherical oscillation, resonant oscillation, and jetting of EMBs are displayed and analyzed systematically. If the ultrasound wave is strong, a high-speed liquid jet forms at the final stage of the collapse, orientated between the directions of the wave and toward the wall. The EMB jet is weaker and slower and has less momentum, as the non-spherical deformation of the coating and the jetting are suppressed by the viscoelastic property of the coating. If the ultrasound is not strong, the EMB remains spherical for many cycles of oscillation but the EMB undergoes resonant oscillation and becomes significantly non-spherical after several oscillation cycles, when the wave frequency is equal to its natural frequency. The numerical capability has the potential to be developed for the optimization of sonography or drug delivery.

Are monodisperse phospholipid-coated microbubbles “mono-acoustic?”

Phospholipid-coated microbubbles with a uniform acoustic response are a promising avenue for functional ultrasound sensing. A uniform acoustic response requires both a monodisperse size distribution and uniform viscoelastic shell properties. Monodisperse microbubbles can be produced in a microfluidic flow focusing device. Here, we investigate whether such monodisperse microbubbles have uniform viscoelastic shell properties and thereby a uniform “mono-acoustic” response. To this end, we visualized phase separation of the DSPC and DPPE-PEG5000 lipid shell components and measured the resonance curves of nearly 2000 single and freely floating microbubbles using a high-frequency acoustic scattering technique. The results demonstrate inhomogeneous phase-separated shell microdomains across the monodisperse bubble population, which may explain the measured inhomogeneous viscoelastic shell properties. The shell viscosity varied over an order of magnitude and the resonance frequency by a factor of two indicating both a variation in shell elasticity and in initial surface tension despite the relatively narrow size distribution.

Topology optimization design of frequency- and temperature-dependent viscoelastic shell structures under non-stationary random excitation

Topology optimization design of frequency- and temperature-dependent viscoelastic shell structures under non-stationary random excitation

Creep instability analysis of viscoelastic sandwich shell panels

Creep instability analysis of viscoelastic sandwich shell panels

$ H^1 $ solutions for a modified Korteweg-de Vries-Burgers type equation

<p>This paper modeled the dynamics of microbubbles coated with viscoelastic shells using the modified Korteweg-de Vries-Burgers equation, a nonlinear third-order partial differential equation. This study focused on the well-posedness of the Cauchy problem associated with this equation.</p>

Shape recovery simulation of viscoelastic thin-ply composite coilable booms

Coilable booms made of thin-ply composites provide mass and volume efficiency for deploying large structures in space. The recovered shape of the booms after being stowed in the coiled configuration is critical to the deployed stiffness and shape precision of the spacecraft, but is heavily influenced by the viscoelasticity of the polymer composites. A numerical study of coiling, stowing, uncoiling and shape recovery of a viscoelastic thin-ply composite coilable boom is presented in this paper. The formulation of two micromechanics-based viscoelastic shell models and their numerical implementation in structural simulations are presented. The shape recovery of a composite boom coiled for two years, replicating the typical timeline for deployable structures used in solar sail missions, has been simulated. The demonstrated modeling and simulation capability is useful for designing deployable spacecraft structures.

A 3D time-domain solution for the bending of viscoelastic shells

This article presents a time domain analysis of viscoelastic doubly curved shallow shells employing 3D solution based on equilibrium equations. The constitutive equation is transformed into Laplace domain in order to avoid the time domain integration. The partial differential equations are solved for the mid-surface variables by applying the Navier Technique. The thickness equations are solved using the differential quadrature method (DQM). Lagrange interpolation polynomial are employed as basis functions. Each layer of the panel is discretized by the Chebyshev–Gauss–Lobatto grid distribution. The time-domain displacements are obtained by using the inverse Laplace transformation in an approximate numerical manner. The 3D solution is compared with references in the literature. Given the inclusion of comprehensive 3D time domain solutions, these results can be considered as a benchmark for reference.

Mixed MITC and interface shell element formulation for multi-part viscoelastic shell structures

This study presents a novel approach for constitutive modeling of multi-part viscoelastic shell structures using a combination formulation of mixed MITC (MITC3 and MITC4) and interface shell elements with reduced computational cost. It focuses on accurate viscoelastic analysis, considering the time-dependent behavior of the multi-part shell structures. The use of the Laplace transform simplifies the integral-form constitutive equation, enabling efficient and accurate viscoelastic analysis. Moreover, by combining the advantages of MITC shell elements and interface shell elements, this approach comprehensively represents multi-part shell structures with non-matching interfaces. Hence, it allows the meshing of each component part independently when assembled. Furthermore, these methods also provide better resistance to shear and membrane locking, which can be problematic when modeling thin shell structures. In numerical examples, to validate the accuracy of the current study, we meticulously analyze multi-part shell models such as an elastic U-shaped beam and the viscoelastic propeller subjected to creep bending loads. This research contributes to improving the design and performance of shell structures in various engineering fields.

Phase transition reversible 3D printing of magnetic thixotropic fluid

Advances in 3D and 4D printing technologies enable the combined design of structure and function in soft robotics. The reversibility of the phase transition in smart materials can provide removable support for the fabrication of thin viscoelastic shells and realize amoeboid locomotion. Here we show that a new dimension of design space can be exploited by controlling the magnetorheological properties of printed structures. A series of magnetic thixotropic fluids (MTFs) was prepared and characterized. Using a specially designed direct ink writing device, the phase transition reversible 3D printing using MTF was first presented. The printability of the MTF was investigated through an insight into its macroscopic and microscopic mechanism within the overall printing process. Multi-material printing of core-shell structures was carried out through an optimized strategy, presenting a prototype of amoeboid locomotion under high magnetic field gradients. This work could contribute to many future applications, such as bionic robots for space exploration, post-disaster search, and even in vivo treatment and drug delivery.

A study on dynamic characteristics of the flutter for three-layer plates and shells flown around by a gas flow

The nonlinear flutter of viscoelastic three-layer plates and shallow shells with a structure asymmetrical in thickness, flown around by a supersonic gas flow is studied in this paper. Mathematical models of problems on the flutter of viscoelastic three-layer plates, cylindrical panels, and shells with a structure asymmetrical in thickness, flown around by a supersonic gas flow are developed. The flutter of viscoelastic three-layer plates is studied in linear and nonlinear formulations. The critical flutter velocities of elongated plates are compared with the results obtained in previously published studies, where the solutions were obtained in an elastic formulation. The flutter of viscoelastic three-layer plates, cylindrical panels with a rigid filler that resists transverse shear, flown from the outside by a supersonic flow, was studied. It is shown that an increase in the geometric parameter characterizing the flexural rigidity of the bearing layers of three-layer structures leads to an increase in the flutter velocity by 25–40%.

Wave Propagation in the Viscoelastic Functionally Graded Cylindrical Shell Based on the First-Order Shear Deformation Theory.

Based on the first-order shear deformation theory (FSDT) and Kelvin-Voigt viscoelastic model, one derives a wave equation of longitudinal guide waves in viscoelastic orthotropic cylindrical shells, which analytically solves the wave equation and explains the intrinsic meaning of the wave propagation. In the numerical examples, the velocity curves of the first few modes for the elastic cylindrical shell are first calculated, and the results of the available literature are compared to verify the derivation and programming. Furthermore, the phase velocity curves and attenuation coefficient curves of the guide waves for a functionally graded (FG) shell are calculated, and the effects of viscoelastic parameters, material gradient patterns, material volume fractions, and size ratios on the phase velocity curves and attenuation curves are studied. This study can be widely used to analytically model the wave propagating in inhomogeneous viscoelastic composite structures and present a theoretical basis for the excellent service performance of composite structures and ultrasonic devices.

The characterization of disruptive combustion of organic gellant-laden ethanol fuel droplets

The future of high-performance rocket propulsion systems depends on superior burn rates, shorter ignition delay times, and eco-friendly nature. Gelled fuel propellants are such candidates which are pivotal to achieving these performance parameters. Gel fuels are multi-component fuels, and their combustion behavior is different from conventional solid and liquid propellants. To develop a fundamental understanding of the vaporization and combustion of gel fuels, single droplet experiments in a pendant mode setup are performed for ethanol-based organic gel fuels by capturing high-speed video data. Primarily, two gel fuel combinations are taken for experiments. The gel fuels are non-metalized ethanol-based fuels containing organic gellants Hydroxypropyl methylcellulose (HPMC) and methylcellulose (MC). Both fuels have shown three distinct combustion stages namely transient heat up (stage I), disruptive burning (stage II), and carbonization (stage III). The demarcation of the stages is done by visual evidence backed by high-fidelity high-speed video data. In stage I, phase separation occurs which leads to the formation of gellant shells. Organic gellants tend to form viscoelastic shells which significantly influence the jetting behavior during the disruptive burning (stage II). The combustion of gel droplets in stage II exhibits characteristic differences in bursting mechanism, for instance, oscillatory and transient bursting in HPMC and transient bursting in MC. Moreover, droplet-bursting behaviors influence jetting attributes and burn rates. Besides, the bursting of gel droplets during combustion is also dependent on the thickness of the gellant shells, the thin and weak shells are prone to bulk droplet motion due to active jetting, whereas the thick and rigid shells act as kinetic energy dampeners and thereby inhibit the bulk motion of droplets. Apart from disruptive burning, carbonization is a significant part of the combustion during which the suppressed jetting behavior is seen due to the traces of fuel trapped in the gellant shells. A significant rise in burn rate is observed due to jetting during the disruptive burning stage in contrast to the other two stages of combustion for both the gel fuels under study. Furthermore, combustion residue analysis is carried out to assess the variation in shell morphology across the stages. Overall, the current study provides detailed insights into the combustion characterization of organic gel fuels, which can help in fabricating gel fuel compositions.

An isogeometric FSDT approach for the study of nonlinear vibrations in truncated viscoelastic conical shells

An isogeometric FSDT approach for the study of nonlinear vibrations in truncated viscoelastic conical shells

Spin–orbit coupling of Europa’s ice shell and interior

Europa is an icy ocean world, differentiated into a floating ice shell and solid interior, separated by a global ocean. The classical spin–orbit coupling problem considers a satellite as a single rigid body, but in the case of Europa, the existence of the subsurface ocean enables independent motion of the ice shell and solid interior. This paper explores the spin–orbit coupling problem for Europa from a dynamical perspective, yielding illuminating analytical and numerical results. We determine that the spin behavior of Europa is influenced by processes not captured by the classical single rigid body spin–orbit coupling analysis. The tidal locking process for Europa is governed by the strength of gravity-gradient coupling between the ice shell and solid interior, with qualitatively different behavior depending on the scale of this effect. In this coupled rigid model, the shell can potentially undergo large angular displacements from the solid interior, and the coupling plays an outsize role in the dynamical evolution of the moon, even without incorporating the dissipative effects of shell non-rigidity. We additionally discuss the effects of a realistic viscoelastic shell, and catalogue other torques that we expect to be sub-dominant in Europa’s spin dynamics, or whose importance is unknown. Finally, we explore how the choice of tidal model affects the resulting equilibrium spin state.

Damped response of porous functionally graded viscoelastic cylindrical shells

In this article, the behavior of viscoelastic porous functionally graded (FG) shells regarding the free and damped forced vibration analysis is investigated. The differential equations are derived by using higher order shear deformation theory. Using Hamilton’s principle and the energy method, the equations of motion are obtained and solved using Navier’s method. The damping effect is implemented into the analysis by means of Kelvin and linear standard viscoelastic models. With the correspondence principle, the transition from elastic material properties to viscoelastic material properties is achieved. First, a free vibration analysis is performed to verify the accuracy of the developed algorithm and obtained results are compared with the existing studies in the literature. Afterwards, a parametric study considering two different viscoelasticity models is performed. In the first parametric example, damped forced vibration analysis is performed for simply supported FG cylindrical shell using linear standard viscoelastic model as the viscoelastic model. Then, damped forced analysis is performed using Kelvin viscoelastic model for simply supported FG cylindrical shell. Analyses are performed in Laplace domain. The obtained results are transferred to time domain using Durbin’s inverse Laplace transform method. The displacement graphs are given for the damped forced vibration examples. In the performed parametric studies, the effects of various porosity coefficients, ratios of instantaneous value, retardation times of the relaxation function and damping ratios on the analysis are investigated.

Effect of Prestresses on the Resonant Vibrations and Heating of a Cylindrical Viscoelastic Shell*

Effect of Prestresses on the Resonant Vibrations and Heating of a Cylindrical Viscoelastic Shell*

Nonlinear ultrasound in liquid containing multiple coated microbubbles: effect of buckling and rupture of viscoelastic shell on ultrasound propagation

With promising applications in medical diagnosis and therapy, the behavior of shell-encapsula-ted ultrasound contrast agents (UCAs) has attracted considerable attention. Currently, second-generation contrast agents stabilized by a phospholipid membrane are widely used and studies have focused on the dynamics of single phospholipid shell-encapsulated microbubbles. To improve the safety and the efficiency of the methods using the propagation or targeted ultrasound, a better understanding of the propagation of ultrasound in liquids containing multiple encapsulated microbubbles is required. By incorporating the Marmottant–Gompertz model into the multiple scale analysis of two-phase model, this study derived a Korteweg–de Vries–Burgers equation as a weakly nonlinear wave equation for one-dimensional ultrasound in bubbly liquids. It was found that the wave propagation characteristics changed with the initial surface tension, highlighting two notable features of the phospholipid shell: buckling and rupture. These results may provide insights into the suitable state of microbubbles, and better control of ultrasound for medical applications, particularly those that require high precision.

Time-Varying Oscillatory Response of Burning Gel Fuel Droplets.

Gel fuel droplets exhibit disruptive burning due to the rupture of their gellant shell, which causes the release of unreacted fuel vapors from the droplet interior to the flame in the form of jets. In addition to pure vaporization, this jetting allows convective transport for fuel vapors, which accelerates gas-phase mixing and is known to improve droplet burn rates. Using high-magnification and high-speed imaging, this study found that the viscoelastic gellant shell at the droplet surface evolves during the droplet's lifetime, which causes the droplet to burst at different frequencies, thereby triggering a time-varying oscillatory jetting. In particular, the continuous wavelet spectra of the droplet diameter fluctuations show that the droplet bursting exhibits a nonmonotonic (hump-shaped) trend, where the bursting frequency first increases and then decreases to a point where the droplet stops oscillating. The changes in the shell structure are captured by tracking the temporal variation of the area of rupture sites, spatial movement of their centroid, and the degree of overlap between the rupture areas of successive cycles. During the initial period (immediately following its formation) when the shell is newly formed, it is weak and flexible, which causes it to burst at increasingly high frequencies. This is because the area at and around the rupture site becomes progressively weaker with each rupture in an already weak shell. This is shown by a high degree of overlap between the areas of successive ruptures. On the other hand, the shell flexibility during the initial period is demonstrated by a reversal in the motion of rupture site centroids. However, at later stages when the droplet has undergone multiple ruptures, the depletion of the fuel vapor causes accumulation of gellant on the shell, thus causing the shell to become strong and rigid. This thick, strong, and rigid shell suppresses droplet oscillations. Overall, this study provides a mechanistic understanding of how the gellant shell evolves during the combustion of a gel fuel droplet and causes the droplet to burst at different frequencies. This understanding can be used to devise gel fuel compositions that result in gellant shells with tailored properties, and therefore, control the jetting frequencies to tune droplet burn rates.

Pseudo-bistability of viscoelastic shells.

Viscoelastic shells subjected to a pressure loading exhibit rich and complex time-dependent responses. Here we focus on the phenomenon of pseudo-bistability, i.e. a viscoelastic shell can stay inverted when pressure is removed, and snap to its natural shape after a delay time. We model and explain the mechanism of pseudo-bistability with a viscoelastic shell model. It combines the small strain, moderate rotation shell theory with the standard linear solid as the viscoelastic constitutive law, and is applicable to shells with arbitrary axisymmetric shapes. As a case study, we investigate the pseudo-bistable behaviour of viscoelastic ellipsoidal shells. Using the proposed model, we successfully predict buckling of a viscoelastic ellipsoidal shell into its inverted configuration when subjected to an instantaneous pressure, creeping when the pressure is held, staying inverted after the pressure is removed, and eventually snapping back after a delay time. The stability transition of the shell from a monostable, temporarily bistable and eventually back to the monostable state is captured by examining the evolution of the instantaneous pressure-volume change relation at different time of the holding and releasing process. A systematic parametric study is conducted to investigate the effect of geometry, viscoelastic properties and loading history on the pseudo-bistable behaviour. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Nonlinear acoustic theory on flowing liquid containing multiple microbubbles coated by a compressible visco-elastic shell: Low and high frequency cases

Microbubbles coated by visco-elastic shells are important for ultrasound diagnosis using contrast agents, and the dynamics of single coated bubbles has been investigated in the literature. However, although a high number of contrast agents are used in practical situations, there has long been an absence of a nonlinear acoustic theory for multiple coated bubbles, except for our recent work by Kikuchi and Kanagawa [“Weakly nonlinear theory on ultrasound propagation in liquids containing many microbubbles encapsulated by visco-elastic shell,” Jpn. J. Appl. Phys. 60, SDDD14 (2021)], under several assumptions to be excluded. Aiming for generalization, in this study, we theoretically investigate weakly nonlinear propagation of ultrasound in liquid containing multiple bubbles coated by a visco-elastic shell with compressibility. Leveraging the method of multiple scales, both the Korteweg–de Vries–Burgers (KdVB) equation for a low-frequency long wave and nonlinear Schrödinger (NLS) equation for a high-frequency short wave are derived from the volumetric averaged equations for bubbly liquids based on a two-fluid model and the up-to-date model for single coated bubbles with shell compressibility. Neglected factors in our previous paper, i.e., compressibility of the shell and liquid, drag force acting on bubbles, bubble translation, and thermal conduction, are incorporated in the present KdVB and NLS equations; the proposed model will be regarded as a generic physico-mathematical model. The results show that shell compressibility attenuated ultrasound strongly and decreased nonlinearity of ultrasound. Finally, we compared the magnitudes of six dissipation factors (shell compressibility, shell viscosity, liquid compressibility, liquid viscosity, thermal effect, and drag force) for five typical ultrasound contrast agents, and a similar tendency between KdVB and NLS equations was revealed.