Viscoelastic Dynamics Research Articles

A Comparison between Elastic and Viscoelastic Asymmetric Dynamics of Elastically Supported AFG Beams

This investigation compares the dynamic simulation results of perfect, elastically-supported, axially-functionally-graded (AFG) beams between viscoelastic and elastic models. When modeling and simulating the dynamics of AFG beams, the elastic model is commonly assumed so as to simplify calculations. This investigation shows how the dynamics varies if viscosity is present. The nonlinear continuous/discretized, axial/transverse motion derivation procedure is explained briefly based on Hamilton’s principle for energy/energy-loss, Kelvin–Voigt viscosity, elastic foundation assumption, and exponential functions for material and geometric variations along the axial axis. A comparison between elastic and Kelvin–Voigt viscoelastic AFG beams on an elastic foundation shows that the viscosity influences the asymmetric dynamics of AFG beams; the viscosity effects become more dominant for larger motion amplitudes, for example.

Control of MIMO mechanical systems interacting with actuators through viscoelastic linkages

This paper proposes a new method for control of nonlinear multi input – multi output (MIMO) mechanical systems that incorporate viscoelastic dampers (VED) for reducing undesired vibrations of actuators. To this end, a control algorithm is proposed based on considering various characteristics of the described dynamical systems (namely mechanical dynamics, viscoelasticity and actuator dynamics) in generation of control inputs guaranteeing convergence of system response to desired reference signals. This procedure features three consecutive parts within the control loop which are conducted iteratively at each control sample. At each sample, initially necessary forces and moments exerted to mechanical system are calculated as virtual control inputs generated based on a MIMO discrete-time sliding mode control (DSMC) algorithm. As the aim of control model is obtaining a closed-loop system without resulting in notable vibrational effects, undesired chattering effects should be eliminated from inputs generated by DSMC. This objective is attained by calculation of appropriate input bounds. Next, an additional virtual input is assigned corresponding to viscoelastic strain such that virtual mechanical input from previous part of the control loop is generated. To this end, Maxwell model for viscoelastic material is considered. Finally, actual controller input is generated such that all virtual control objectives are satisfied. The effectiveness of control procedure is numerically illustrated for a 3-PRR manipulator.

Linear viscoelastic dynamics in holography

We study the mechanical response under time-dependent sources of a simple class of holographic models that exhibit viscoelastic features. The ratio of viscosity over elastic modulus defines an intrinsic relaxation time scale -- the so-called Maxwell relaxation time $\tau_M$, which has been identified traditionally with the relaxation time scale. We compute explicitly the relaxation time in our examples and that it differs from $\tau_M$. At high temperatures $\tau_M$ over-estimates the actual relaxation time, although not by much and moreover it still captures reasonably well the temperature behaviour. At sufficiently low temperatures the situation is reversed: $\tau_M$ underestimates the actual relaxation time, in some cases quite drastically. Moreover, when $\tau_M$ under-estimates the real-time response exhibits an overshoot phenomenon before relaxation. We comment on the $T = 0$ limit, where the relaxation is power-law because our models exhibit criticality.

A Finite Element Model for the Vibration Analysis of Sandwich Beam with Frequency-Dependent Viscoelastic Material Core.

In this work, a finite element model was developed for vibration analysis of sandwich beam with a viscoelastic material core sandwiched between two elastic layers. The frequency-dependent viscoelastic dynamics of the sandwich beam were investigated by using finite element analysis and experimental validation. The stiffness and damping of the viscoelastic material core is frequency-dependent, which results in complex vibration modes of the sandwich beam system. A third order seven parameter Biot model was used to describe the frequency-dependent viscoelastic behavior, which was then incorporated with the finite elements of the sandwich beam. Considering the parameters identification, a strategy to determine the parameters of the Biot model has been outlined, and the curve fitting results closely follow the experiment. With identified model parameters, numerical simulations were carried out to predict the vibration and damping behavior in the first three vibration modes, and the results showed that the finite model presented here had good accuracy and efficiency in the specific frequency range of interest. The experimental testing on the viscoelastic sandwich beam validated the numerical predication. The experimental results also showed that the finite element modeling method of sandwich beams that was proposed was correct, simple and effective.

Vortex generation by viscoelastic sheath flow in flow-focusing microchannel

Microfluidics-based technologies have attracted much attention since the fluid flow can be controlled precisely and only small sample volumes are required. Viscoelastic non-Newtonian fluids such as polymer solution and biofluids are frequently used in microfluidic analyses, and it is essential to understand the small-scale flow dynamics of such viscoelastic fluids. In this work, we report on vortex generation at the junction region of a flow-focusing microchannel, where a central flow stream of a Newtonian fluid meets two sheath flows of a non-Newtonian poly (ethylene oxide) aqueous solution. We elucidated the vortex-generation mechanism by the backward-flow component induced by the first normal stress difference in the viscoelastic sheath fluid. We systematically investigated the effects of polymer concentration, total flow rate, and total to central-stream flow-rate ratio, on the vortex generation. In addition, we demonstrated that this phenomenon can be engineered to enhance the mixing in the flow-focusing microchannel. We expect this work to be helpful for the understanding of viscoelastic flow dynamics in microscale flows and also for the development of microfluidic mixers.

OR21-6 Diabetic Cardiac Hypertrophy Is Associated With Viscoelastic Changes In Myocardial Contraction: Role Of Hsa-mir-122-5p On Extracellular Matrix.

Background. Diabetic cardiomyopathy, evolving into heart failure, dramatically affects patients morbidity and mortality. Cardiac magnetic resonance (CMR) is the gold standard to assess cardiac remodeling. Aim. The aim of this study was to follow the long-term progression of diabetic cardiomyopathy by CMR. A secondary outcome was to highlight changes of circulating miRNAs and relative targets. Methods and Results. A longitudinal 5-years prospective study was undertaken in 71 subjects: all diabetic men completing the a registered trial (NCT number anonimized) and 20 non-diabetic matched controls. CMR with tagging was performed at baseline and after 4.6±0.2 years in 51/59 of enrolled diabetic men (age 64.6 ± 8.15 years). A significant increase in ventricular mass (∆LVMi= 13.47±29.66 g/m2; p=0.014) and a borderline increase in end-diastolic volume (∆EDVi= 5.16±14.71 ml/m2; p=0.056) was found at follow-up time point in diabetic men. Circumferential strain worsened (∆σ=1.52 ± 3.85%; p=0.033) without significant changes in torsion (∆θ=0.24 ±4.04°; p=0.737) revealing a loss of the adaptive uncoupling between strain and torsion. Contraction dynamics showed a significant decrease in time to systolic peak (∆TtP= -35.18±28.81 ms; p=0.000) and in early diastolic recoil rate (∆RR=-20.01±19.07 s-1; p=0.000). Cardiac performance and metabolic control were preserved. Micro-array analysis documented up-regulation of circulating hsa-miR-122-5p, hsa-miR-193a-5p, hsa-miR-4707-5p, hsa-miR-4749-3p, and down-regulation of hsa-miR-3148, miR-3149, miR-32-3p, miR-595, but only the longitudinal change of hsa-miR-122-5p, hsa-miR-3148 and miR-595 correlated with CMR. Target-scan predicted metalloproteinases (MMP2, MMP16) and their regulators (TIMP1) as converging targets in network analysis. Using Db/Db mouse model we confirmed that miR-122-5p expression is associated with diabetic cardiomiopathy and that cardiac tissue can be considered its main source. In vitro analysis showed that MMP2 is a direct hsa-miR-122-5p target and its expression is altered in diabetic endothelial cells model. Moreover, we found that hsa-miR-122-5p overexpression affects extracellular matrix genes likely through MMP2 modulation. Conclusion. Within five years, independently from glycemic control, increasing cardiac hypertrophy is associated with a progressive impairment in strain, exhaustion of the compensatory role of torsion and changes in viscoelastic contraction dynamics that are paralleled by specific changes in circulating miRNA targeting the extracellular matrix.

Impedance-based viscoelastic flow cytometry.

Elastic nature of the viscoelastic fluids induces lateral migration of particles into a single streamline and can be used by microfluidic based flow cytometry devices. In this study, we investigated focusing efficiency of polyethylene oxide based viscoelastic solutions at varying ionic concentration to demonstrate their use in impedimetric particle characterization systems. Rheological properties of the viscoelastic fluid and particle focusing performance are not affected by ionic concentration. We investigated the viscoelastic focusing dynamics using polystyrene (PS) beads and human red blood cells (RBCs) suspended in the viscoelastic fluid. Elasto-inertial focusing of PS beads was achieved with the combination of inertial and viscoelastic effects. RBCs were aligned along the channel centerline in parachute shape which yielded consistent impedimetric signals. We compared our impedance-based microfluidic flow cytometry results for RBCs and PS beads by analyzing particle transit time and peak amplitude at varying viscoelastic focusing conditions obtained at different flow rates. We showed that single orientation, single train focusing of nonspherical RBCs can be achieved with polyethylene oxide based viscoelastic solution that has been shown to be a good candidate as a carrier fluid for impedance cytometry.

Viscoelastic dynamics of axially FG microbeams

A viscoelastic axially functionally graded (FG) imperfect microbeam is considered and the complex nonlinear dynamics is analysed for the first time. The distribution of the material properties from beam's left end to the right one is of an exponential form. The small nature of the system is incorporated using the couple stress theory (CST) in a modified form. The viscosity between microbeam's infinitesimal elements is incorporated through the Kelvin-Voigt scheme. The elastic part of the energy is formulated via the elastic component of the stress and its couple; the viscous parts are incorporated via a negative work. The energy of kinetic type is also formulated. Without ignoring the axial displacement/inertia, Hamilton's principle of energy is used to formulate the viscoelastic mechanical model of the microsystem. A high-dimensional truncation/discretisation is conducted and numerical simulations are performed based upon it. The complex nonlinear dynamics of the axially FG imperfect beam is analysed in the presence/absence of viscosity.

Engineering hydrogel viscoelasticity

The aim of this study was to identify a method for modifying the time-dependent viscoelastic properties of gels without altering the elastic component. To this end, two hydrogels commonly used in biomedical applications, agarose and acrylamide, were prepared in aqueous solutions of dextran with increasing concentrations (0%, 2% and 5% w/v) and hence increasing viscosities. Commercial polyurethane sponges soaked in the same solutions were used as controls, since, unlike in hydrogels, the liquid in these sponge systems is poorly bound to the polymer network. Sample viscoelastic properties were characterised using the epsilon-dot method, based on compression tests at different constant strain-rates. Experimental data were fitted to a standard linear solid model. While increasing the liquid viscosity in the controls resulted in a significant increase of the characteristic relaxation time (τ), both the instantaneous (Einst) and the equilibrium (Eeq) elastic moduli remained almost constant.However, in the hydrogels a significant reduction of both Einst and τ was observed. On the other hand, as expected, Eeq – an indicator of the equilibrium elastic behaviour after the occurrence of viscoelastic relaxation dynamics – was found to be independent of the liquid phase viscosity.Therefore, although the elastic and viscous components of hydrogels cannot be completely decoupled due to the interaction of the liquid and solid phases, we show that their viscoelastic behaviour can be modulated by varying the viscosity of the aqueous phase. This simple-yet-effective strategy could be useful in the field of mechanobiology, particularly for studying cell response to substrate viscoelasticity while keeping the elastic cue (i.e. equilibrium modulus, or quasi-static stiffness) constant.

Direct Mapping of Nanoscale Viscoelastic Dynamics at Nanofiller/Polymer Interfaces

The mobility gradient of polymer chains near a solid interface plays an important role in explaining a complex behavior of relaxation dynamics and thermodynamic properties observed for various poly...

Effects of Surfactant and Urea on Dynamics and Viscoelastic Properties of Hydrophobically Assembled Supramolecular Hydrogel.

Physically associated hydrogels based on strong hydrophobic interactions often have attractive mechanical properties that combine processability with elasticity. However, there is a need to study such interactions and understand their relation to the macroscopic hydrogel properties. Therefore, we use the surfactant sodium dodecyl sulfate (SDS) and urea as reagents that disrupt hydrophobic interactions. The model hydrogel is based on a segmented copolymer between poly(ethylene glycol) (PEG) and hydrophobic dimer fatty acid (DFA). We show that both agents influence viscoelastic properties, dynamics, and relaxation processes of the model hydrogel. In particular, the relaxation time is significantly reduced by urea, as compared to SDS, whereas the surfactant causes a decrease of the modulus of the hydrogel more efficiently. The reversibility of the effects of SDS and urea can be exploited, for instance, by using an injectable sol that solidifies when the SDS or urea diffuses out of the sample. Surfactant-induced processability may be advantageous in future applications of hydrophobically assembled physical hydrogels.

Dynamics of networks in a viscoelastic and active environment.

We investigate the dynamics of fractals and other networks in a viscoelastic and active environment. The viscoelastic dynamics is modeled based on the generalized Langevin equation, where the activity is introduced to it by means of the exponentially correlated noise. The intramolecular interactions are taken into account by the bead-spring picture. The microscopic connectivity (studied in the form of Vicsek fractals, of dual Sierpiński gaskets, of NTD trees, and of a family of deterministic small-world networks) reveals itself in the multiscale monomeric dynamics, which shows vastly different behaviors in the active and passive baths. In particular, the dynamics under active forces leads to a swelling that is characterized through power laws which are not present in the passive case. In all cases, the dynamics reflects the broad scaling behavior of the density of states and not necessarily the maximal relaxation time of the structures in a passive bath, as it is exemplified on the NTD trees.

A Stable and Convergent Finite Difference Scheme for 2D Incompressible Nonlinear Viscoelastic Fluid Dynamics Problem

In this study, a stable and convergent finite difference (FD) scheme based on staggered meshes for two-dimensional (2D) incompressible nonlinear viscoelastic fluid dynamics problem including the velocity vector field and the pressure field as well as the deformation tensor matrix is established in order to find numerical solutions for the problem. The stability, convergence, and errors of the FD solutions are analyzed. Some numerical experiments are presented to show that the FD scheme is feasible and efficient for simulating the phenomena of the velocity and the pressure as well as the deformation tensor in an estuary.

On one problem of viscoelastic fluid dynamics with memory on an infinite time interval

In the present paper we establish the existence of weak solutions of one boundary value problem for one model of a viscoelastic fluid with memory along the trajectories of the velocity field on an infinite time interval. We use solvability of related approximating initial-boundary value problems on finite time intervals and responding pass to the limit.

Viscoelasticity and Dynamics of Confined Polyelectrolyte/Layered Silicate Nanocomposites: The Influence of Intercalation and Exfoliation

AbstractThe influence of different confinement regimes on the linear viscoelastic properties of a polyelectrolyte, the protonated poly‐[(dimethylamino) ethyl methacrylate] (PDMAEMAH), is investigated. PDMAEMAH is reinforced with the layered silicate montmorillonite (MMT). Neat MMT and MMT treated with sulfobetaine and ammonia‐based surfactants (MMT/SB and MMT/NH, respectively) are utilized. Transmission electron microscopy and X‐ray scattering show that MMT and MMT/NH produce intercalated morphology, whereas MMT/SB produces an exfoliated morphology. Thus, the polyelectrolyte is under different confinement regimes. The confinement produces the increase of glass transition temperature Tg; however, the increase is larger for the (highly confined) intercalated morphology. Master curves are constructed applying time–temperature superposition. Strikingly, the viscoelastic spectra evidence that the intercalated morphology produces twofold increase of rubber‐like modulus, whereas the exfoliated morphology produces over fourfold reduction of rubber‐like modulus, both at 3 wt% clay concentration. The reduction of rubber‐like modulus suggests that an exfoliated morphology produces disruption of the entanglement density. Analysis in the segmental relaxation regime shows that the intercalated morphology induces longer relaxation times, that is, more dynamics retardation, in correlation with the increase of glass transition temperature. This research paves the road for better understanding of viscoelastic behavior and dynamics of molten polyelectrolytes under confinement.

Novel discrete element modeling coupled with finite element method for investigating ballasted railway track dynamics

A quadruple discrete element method (QDEM) was developed for viscoelastic multi-body dynamics. The sleeper motion modeled using QDEM was coupled with the rail motion modeled using a finite element method (FEM). The traffic impact response of a ballast particle and a sleeper was analyzed. The three-dimensional spatial distribution of ballast particle displacement was clearly revealed. Moreover, the ballast layer absorbed the low frequency vibration of the sleeper more effectively than its high frequency vibration. This study suggests that the proposed QDEM-FEM can provide greater insight into the impact response of ballasted railway tracks.

Stability of gravito-coupled complex gyratory astrofluids

We analyze the gravitational instability of complex rotating astrofluids in the presence of dynamic role of dark matter in a homogeneous hydrostatic equilibrium framework. The effects of the lowest-order fluid viscoelasticity, Coriolis force, fluid turbulence and inter-layer frictional coupling dynamics are concurrently considered in spatially-flat geometry. The Coriolis rotation is relative to the center of the entire fluid mass distribution, contributed by both the gyratory bright (visible) and dark (invisible) sectors, conjugated via the mutual gravitational interaction. The turbulence effects are included via the modified Larson equation of state. We use a regular Fourier-based linear perturbation analysis over the rotating fluid field equations to obtain a unique form of quartic dispersion relation with variable coefficients. We numerically carry out the dispersion analysis in two extreme limits: hydrodynamic (low-frequency) and kinetic (high-frequency) regimes. It is demonstrated that, in the former regime, the gas as well as dark matter rotations have stabilizing effects on the Jeans instability of the bi-fluidic admixture. In contrast, in the latter, the rotations play destabilizing roles on the instability. An interesting feature noted here is that the magnitude of the group velocity of the fluctuations throughout increases with both the gas and dark matter rotation frequencies, and vice-versa. We, finally, hope that the obtained results could be helpful in understanding the top-down kinetic mechanisms of bounded structure formation via gravitational collapse dynamics.

Unified Space–Time Finite Element Methods for Dissipative Continua Dynamics

Based upon the extended framework of Hamilton’s principle, unified space–time finite element methods for viscoelastic and viscoplastic continuum dynamics are presented, respectively. For numerical efficiency, mixed time-step algorithm in time- and displacement-based algorithm in space are adopted. Through analytical investigation, we demonstrate that the Newmark’s constant average acceleration method and the present method are the same for viscoelasticity. With spatial eight-node brick elements, some numerical simulations are undertaken to validate and investigate the performance of the present non-iterative space–time finite element method for viscoplasticity.

Application of Microrheology in Food Science.

Microrheology provides a technique to probe the local viscoelastic properties and dynamics of soft materials at the microscopic level by observing the motion of tracer particles embedded within them. It is divided into passive and active microrheology according to the force exerted on the embedded particles. Particles are driven by thermal fluctuations in passive microrheology, and the linear viscoelasticity of samples can be obtained on the basis of the generalized Stokes-Einstein equation. In active microrheology, tracer particles are controlled by external forces, and measurements can be extended to the nonlinear regime. Microrheology techniques have many advantages such as the need for only small sample amounts and a wider measurable frequency range. In particular, microrheology is able to examine the spatial heterogeneity of samples at the microlevel, which is not possible using traditional rheology. Therefore, microrheology has considerable potential for studying the local mechanical properties and dynamics of soft matter, particularly complex fluids, including solutions, dispersions, and other colloidal systems. Food products such as emulsions, foams, or gels are complex fluids with multiple ingredients and phases. Their macroscopic properties, such as stability and texture, are closely related to the structure and mechanical properties at the microlevel. In this article, the basic principles and methods of microrheology are reviewed, and the latest developments and achievements of microrheology in the field of food science are presented.

Rapid dynamics of cell-shape recovery in response to local deformations.

It is vital that cells respond rapidly to mechanical cues within their microenvironment through changes in cell shape and volume, which rely upon the mechanical properties of cells' highly interconnected cytoskeletal networks and intracellular fluid redistributions. While previous research has largely investigated deformation mechanics, we now focus on the immediate cell-shape recovery response following mechanical perturbation by inducing large, local, and reproducible cellular deformations using AFM. By continuous imaging within the plane of deformation, we characterize the membrane and cortical response of HeLa cells to unloading, and model the recovery via overdamped viscoelastic dynamics. Importantly, the majority (90%) of HeLa cells recover their cell shape in <1 s. Despite actin remodelling on this time scale, we show that cell-shape recovery time is not affected by load duration, nor magnitude for untreated cells. To further explore this rapid recovery response, we expose cells to cytoskeletal destabilizers and osmotic shock conditions, which uncovers the interplay between actin and osmotic pressure. We show that the rapid dynamics of recovery depend crucially on intracellular pressure, and provide strong evidence that cortical actin is the key regulator in the cell-shape recovery processes, in both cancerous and non-cancerous epithelial cells.