Viscoelastic Dynamics Research Articles

Viscoelastic liquid flow dynamics in small porous-medium channels under pressure and velocity forces

Viscoelastic liquid flow dynamics in small porous-medium channels under pressure and velocity forces

Sequence-specific interactions determine viscoelasticity and aging dynamics of protein condensates.

Biomolecular condensates are viscoelastic materials. Here, we investigate the determinants of sequence-encoded and age-dependent viscoelasticity of condensates formed by the prion-like low-complexity domain of the protein hnRNP A1 and its designed variants. We find that the dominantly viscous forms of the condensates are metastable Maxwell fluids. A Rouse-Zimm model that accounts for the network-like organization of proteins within condensates reproduces the measured viscoelastic moduli. We show that the strengths of aromatic inter-sticker interactions determine sequence-specific amplitudes of elastic and viscous moduli, and the timescales over which elastic properties dominate. These condensates undergo physical ageing on sequence-specific timescales. This is driven by mutations to spacer residues that weaken the metastability of dominantly viscous phases. The ageing of condensates is accompanied by disorder-to-order transitions, leading to the formation of non-fibrillar, beta-sheet-containing, semi-crystalline, elastic, Kelvin-Voigt solids. Our results suggest that sequence grammars, which refer to amino acid identities of stickers versus spacers in prion-like low-complexity domains, have evolved to afford control over metastabilities of dominantly viscous fluid phases of condensates. This selection is likely to render barriers for conversion from metastable fluids to globally stable solids insurmountable on functionally relevant timescales.

Investigation of Viscoelastic Guided Wave Properties in Anisotropic Laminated Composites Using a Legendre Orthogonal Polynomials Expansion-Assisted Viscoelastodynamic Model.

This study investigates viscoelastic guided wave properties (e.g., complex-wavenumber-, phase-velocity-, and attenuation-frequency relations) for multiple modes, including different orders of antisymmetric, symmetric, and shear horizontal modes in viscoelastic anisotropic laminated composites. To obtain those frequency-dependent relations, a guided wave characteristic equation is formulated based on a Legendre orthogonal polynomials expansion (LOPE)-assisted viscoelastodynamic model, which fuses the hysteretic viscoelastic model-based wave dynamics and the LOPE-based mode shape approximation. Then, the complex-wavenumber-frequency solutions are obtained by solving the characteristic equation using an improved root-finding algorithm, which leverages coefficient matrix determinant ratios and our proposed local tracking windows. To trace the solutions on the dispersion curves of different wave modes and avoid curve-tracing misalignment in regions with phase-velocity curve crossing, we presented a curve-tracing strategy considering wave attenuation. With the LOPE-assisted viscoelastodynamic model, the effects of material viscosity and fiber orientation on different guided wave modes are investigated for unidirectional carbon-fiber-reinforced composites. The results show that the viscosity in the hysteresis model mainly affects the frequency-dependent attenuation of viscoelastic guided waves, while the fiber orientation influences both the phase-velocity and attenuation curves. We expect the theoretical work in this study to facilitate the development of guided wave-based techniques for the NDT and SHM of viscoelastic anisotropic laminated composites.

On the Weak Solvability of High-order Viscoelastic Fluid Dynamics Model

On the Weak Solvability of High-order Viscoelastic Fluid Dynamics Model

Error estimates for finite element approximations of viscoelastic dynamics: The generalized Maxwell model

We prove error estimates for a finite element approximation of viscoelastic dynamics based on continuous Galerkin in space and time, both in energy norm and in L2 norm. The proof is based on an error representation formula using a discrete dual problem and a stability estimate involving the kinetic, elastic, and viscoelastic energies. To set up the dual error analysis and to prove the basic stability estimates, it is natural to formulate the problem as a first-order-in-time system involving evolution equations for the viscoelastic stress, the displacements, and the velocities. The equations for the viscoelastic stress can, however, be solved analytically in terms of the deviatoric strain velocity, and therefore, the viscoelastic stress can be eliminated from the system, resulting in a system for displacements and velocities.

CN ADI fast algorithm on non-uniform meshes for the three-dimensional nonlocal evolution equation with multi-memory kernels in viscoelastic dynamics

This paper proposes a Crank-Nicolson alternating direction implicit (CN-ADI) finite difference scheme for solving the three-dimensional nonlocal evolution equation with multi-memory kernels in viscoelastic dynamic for the first time. Due to the weakly singular behavior of the exact solution near the initial time t=0, we use the non-uniform meshes to capture the rapid change of the solution at t=0. The Crank-Nicolson method and product-integration (PI) rule are proposed to approximate temporal derivative and the Riemann-Liouville (R-L) fractional integral term, respectively. The fully discrete scheme is obtained by the standard central finite difference method (FDM) in space. The stability in L2-norm and convergence of the CN-ADI difference scheme are strictly proved, where the convergence reached O(τ2+hx2+hy2+hz2). The ADI algorithm greatly reduces the computational cost of the three-dimensional problems in viscoelastic dynamics. At last, the results of numerical examples verify the correctness of the theoretical analysis and prove the effectiveness of the proposed method.

Viscoelastic Dynamics of Photothermal‐Responsive Liquid Crystal Elastomer Fibers

AbstractLiquid crystal elastomers (LCEs) with photo‐responsive properties, typically driven by either photochemical or photothermal mechanisms, have found extensive applications as, for example, actuators in soft robots. However, intricate temperature‐dependent viscoelasticity of LCEs poses a challenge, leading to a notable gap in the domain of dynamic models for photothermal‐responsive LCE (PTR‐LCE) fibers. Here, a fundamental framework is proposed for accurate modeling and real‐time simulations of PTR‐LCE fiber dynamics. The PTR‐LCE fiber is described as a one‐dimensional (1D) string model that decomposes the fiber deformation into active and passive parts, which are characterized by an order parameter and a temperature‐dependent linear viscoelasticity model, respectively. Then, independent experimental measurements of model parameters are conducted, and a numerical algorithm is developed to solve the model, which is validated for convergence, time efficiency, and accuracy. Finally, the model is employed to simulate both open‐loop and Proportional‐Integral‐Derivative (PID) control of actuators made of PTR‐LCE fibers. The results confirm the advantages of this model over previous models. This work not only reveals the physical mechanisms underlying the PTR‐LCE fiber dynamic behaviors but also provides inspirations for more efficient and precise soft robotic applications.

Numerical modelling of the viscoelastic polymer melt flow in material extrusion additive manufacturing

ABSTRACT In material extrusion (MEX), it is challenging to accurately predict the steady and transient feeding forces at various polymer extrusion rates when printing island and thin-walled structures involving rapid start/stop or acceleration/deceleration, especially for semi-crystalline polymers. This research presents a non-isothermal viscoelastic Computational Fluid Dynamics model to investigate the steady and transient feeding forces, as well as the phase transition process and viscoelastic behaviour of polylactic acid (PLA), a semi-crystalline polymer, during the extrusion process. The study establishes a relationship between polymer flow and viscoelastic stress, demonstrating that the elastic effect during extrusion is more significant than the viscous effect, particularly at higher feeding rates. Furthermore, the study uncovers critical aspects of PLA melt flow behaviour during the MEX process, laying the foundation for future research and optimisation of MEX printing processes.

Viscoelastic dynamics of a soft strip subject to a large deformation.

To produce sounds, we adjust the tension of our vocal folds to shape their properties and control the pitch. This efficient mechanism offers inspiration for designing reconfigurable materials and adaptable soft robots. However, understanding how flexible structures respond to a significant static strain is not straightforward. This complexity also limits the precision of medical imaging when applied to tensioned organs like muscles, tendons, ligaments and blood vessels among others. In this article, we experimentally and theoretically explore the dynamics of a soft strip subject to a substantial static extension, up to 180%. Our observations reveal a few intriguing effects, such as the resilience of certain vibrational modes to a static deformation. These observations are supported by a model based on the incremental displacement theory. This has promising practical implications for characterizing soft materials but also for scenarios where external actions can be used to tune properties.

The Acute Effects of Theragun™ Percussive Therapy on Viscoelastic Tissue Dynamics and Hamstring Group Range of Motion

Handheld percussive therapy (PT) massage guns have seen a rapid rise in use and with-it increased attention within injury prevention and sport performance settings. Early studies have proposed beneficial effects upon range of motion (ROM), however the mechanism behind these increases remains unreported. This study aimed to determine the influence of a minimal frequency PT dose upon ROM and myotonometry outcomes. Twenty participants (N = 20; 13 males and 7 females, height 1.78cm ± 9.62; weight 77.35kg ± 8.46) participants were allocated to either a PT group receiving 2 x 60-seconds (plus 30-seconds rest) via a Theragun™ Pro4 to the hamstrings covering a standardised 20 lengths from proximal to distal via the standard ball attachment at 1 bar of pressure or a control group (CON) of 2-minutes 30-seconds passive supine rest. Pre and post intervention outcomes were measured for ROM via passive straight leg raise (PSLR) and tissue dynamics via MyotonPro (Tone, Stiffness, Elasticity, Relaxation Time). Results showed significant within-group increases (p < 0.0001, ηp2 0.656, +11.4%) in ROM following PT and between group difference against CON (P < 0.026). Significant within-group differences in stiffness (p < 0.016, ηp2 0.144, -6%), tone (p < 0.003, ηp2 0.213, +2%) and relaxation time (p < 0.002, ηp2 0.232, +6.3%) were also reported following PT. No significant difference was reported in elasticity (P > 0.05) or any other between group outcomes. PT therapy can provide an acute increase in hamstring group ROM following a resultant decrease in tissue stiffness.

The Acute Effects of Theragun™ Percussive Therapy on Viscoelastic Tissue Dynamics and Hamstring Group Range of Motion.

Handheld percussive therapy (PT) massage guns have seen a rapid rise in use and with-it increased attention within injury prevention and sport performance settings. Early studies have proposed beneficial effects upon range of motion (ROM), however the mechanism behind these increases remains unreported. This study aimed to determine the influence of a minimal frequency PT dose upon ROM and myotonometry outcomes. Twenty participants (N = 20; 13 males and 7 females, height 1.78cm ± 9.62; weight 77.35kg ± 8.46) participants were allocated to either a PT group receiving 2 x 60-seconds (plus 30-seconds rest) via a Theragun™ Pro4 to the hamstrings covering a standardised 20 lengths from proximal to distal via the standard ball attachment at 1 bar of pressure or a control group (CON) of 2-minutes 30-seconds passive supine rest. Pre and post intervention outcomes were measured for ROM via passive straight leg raise (PSLR) and tissue dynamics via MyotonPro (Tone, Stiffness, Elasticity, Relaxation Time). Results showed significant within-group increases (p < 0.0001, ηp2 0.656, +11.4%) in ROM following PT and between group difference against CON (P < 0.026). Significant within-group differences in stiffness (p < 0.016, ηp2 0.144, -6%), tone (p < 0.003, ηp2 0.213, +2%) and relaxation time (p < 0.002, ηp2 0.232, +6.3%) were also reported following PT. No significant difference was reported in elasticity (P > 0.05) or any other between group outcomes. PT therapy can provide an acute increase in hamstring group ROM following a resultant decrease in tissue stiffness.

Nonequilibrium diffusion of active particles bound to a semiflexible polymer network: Simulations and fractional Langevin equation.

In a viscoelastic environment, the diffusion of a particle becomes non-Markovian due to the memory effect. An open question concerns quantitatively explaining how self-propulsion particles with directional memory diffuse in such a medium. Based on simulations and analytic theory, we address this issue with active viscoelastic systems where an active particle is connected with multiple semiflexible filaments. Our Langevin dynamics simulations show that the active cross-linker displays superdiffusive and subdiffusive athermal motion with a time-dependent anomalous exponent α. In such viscoelastic feedback, the active particle always exhibits superdiffusion with α = 3/2 at times shorter than the self-propulsion time (τA). At times greater than τA, the subdiffusive motion emerges with α bounded between 1/2 and 3/4. Remarkably, active subdiffusion is reinforced as the active propulsion (Pe) is more vigorous. In the high Pe limit, athermal fluctuation in the stiff filament eventually leads to α = 1/2, which can be misinterpreted with the thermal Rouse motion in a flexible chain. We demonstrate that the motion of active particles cross-linking a network of semiflexible filaments can be governed by a fractional Langevin equation combined with fractional Gaussian noise and an Ornstein-Uhlenbeck noise. We analytically derive the velocity autocorrelation function and mean-squared displacement of the model, explaining their scaling relations as well as the prefactors. We find that there exist the threshold Pe (Pe∗) and crossover times (τ∗ and τ†) above which active viscoelastic dynamics emerge on timescales of τ∗≲ t ≲ τ†. Our study may provide theoretical insight into various nonequilibrium active dynamics in intracellular viscoelastic environments.

Viscoelastic response of confined powder under large strain oscillations, characterized by its noise temperature

We report a study on granular matter with and without small additions of silicon oil, under low-frequency and large amplitude oscillatory shear strain under constant normal pressure, by running experiments with a rotational rheometer with a cup-and-plate geometry. We analysed the expansion with the Chebyshev polynomials of the orthogonal decomposition of stress–strain Lissajous–Bowditch loops. We found the onset of the strain amplitude for the yielding regime indicated a regime change from filament-like structures of grains to grain rearrangements for the dry granulate and from oscillations to the breaking and regeneration of liquid bridges for wet granulates. We have shown that this viscoelastic dynamics can be characterized by a noise temperature following Sollich et al. (Phys Rev Lett https://doi.org/10.1103/PhysRevLett.78.2020, 1997). The analysis of the first harmonics of the Chebyshev expansion showed that the state of disorder of dry and wet granular matter in pre-yielding and yielding regimes involved ensembles of different inherent states; thus, each of them was governed by a different noise temperature. The higher-order harmonics of the Chebyshev expansion revealed a proportionality between the viscous nonlinearity and the variation in the elastic nonlinearity induced by the deformation, which shows the coupling between the elastic deformation and the viscous flow of mesoscopic-scale structures.Graphic abstract

Rational understanding of viscoelastic drop impact dynamics on porous surfaces considering rheological properties

Understanding of viscoelastic drop impact on porous solid surfaces emerges as the essential physics for broad industrial and biological systems. However, there have been few studies concerning the post-drop impact transition considering rheological properties and dynamics. Here, we report the post-impact dynamics of viscoelastic drops on porous mesh surfaces using experimental and theoretical analyses. Five concentrations of highly viscous polymer solutions with shear-thinning and viscoelastic characteristics exhibit different rheological properties (viscosity, storage, loss moduli, etc.). These changes in the rheological features result in four distinguishable impact dynamics on two-dimensional mesh surfaces. Viscoelastic drops that exhibit viscoelastic solid properties (storage modulus &amp;gt; loss modulus) resulted in combined elastic solid-like motions and viscous fluid-like motions depending on the impact velocity and anti-penetration effects (such as capillary pressure and yield stress). Meanwhile, decreases in the viscoelastic fluid properties resulted in monotonous viscosity-dominant behaviors. A pressure-balance equation was proposed to theoretically predict the filament column penetration length of viscoelastic solid drops. The theoretical results correlated with the experimentally measured values until necking occurred in the filament column. We believe that this study on viscoelastic drop impact dynamics can shed light on future applications that involve various mechanical behaviors of non-Newtonian fluid drops, such as 3D printing, coating, bio-fluid treatments, and polymeric solutions.

Mixed [Formula: see text]-synthesis tracking control and disturbance rejection in a robotic digit of an impaired human hand for anthropomorphic coordination.

In a partially impaired anthropomorphic hand, maintaining the movement coordination of the robotic digits with the central nervous system (CNS) and natural digits is crucial for robust performance. A challenge in the control perspective of movement coordination of a human hand is finding methods robust to the disturbances in a well-posed control problem of a biomechanical model. We use visco-elastic dynamics in the human palm frame of reference to explore the biomechanics of movement coordination to solve this control problem. Our biomechanical model incorporates the time delay due to actuation force, parametric uncertainty, exogenous disturbances, and sensory noise to constitute a 21-degree of freedom model. A mixed [Formula: see text]-synthesis controller, considering the real parametric uncertainty, represents the CNS in the control paradigm. We consider the robotic finger's flexion movement when perturbed from the initial equilibrium. The controller provides feedback force at the joints to regulate the robotic finger movement. The index finger follows a reference trajectory of the joint angular position profile and stabilizes at a flexion angle of 1 rad/s at a time of 1 s. The main control objective is to keep the angular displacement of the finger joint constant when a disturbance force acts. We simulate the modeling scheme in MATLAB/ Simulink. The results demonstrate that our controller scheme is robust against the worst-case disturbance and achieves the desired performance value. Developing a biologically inspired neurophysiological controller with robust performance has many applications, including assistive rehabilitation devices, hand movement disorder diagnosis, and robotic manipulators.

Three parametric Prabhakar fractional derivative-based thermal analysis of Brinkman hybrid nanofluid flow over exponentially heated plate

Fractional calculus yields numerous implementations in different fields such as biological materials, physical memory, oscillation, wave propagation, and viscoelastic dynamics. Due to the significant applications of fractional calculus, the current study deals with the fractional derivative base study of a Brinkman hybrid nanofluid with an inclined magnetic field. A three-parametric Prabhakar fractional derivative with the involvement of the Mittag-Leffler function is implemented. A vertical plate moving with exponential velocity is considered to be the source of the flow mechanism. Moreover, the effects of exponential heating are incorporated into the thermal analysis. An appropriate group of dimensionless ansatz is adopted to get the dimensionless setup of equations. The Prabhakar fractional operator is implemented in the dimensionless equations which are further tackled by an effectual Laplace transform technique. An inverse Stehfest method and Tzou's method are implemented to tackle the inversion of the Laplace transform. This study exhibits that the fractional constraints minimize both the fields of temperature and velocity. Moreover, the velocity distribution deteriorates corresponding to the improved Brinkman parameter. The Brinkman parameter and the fluid's viscosity are directly related to each other. With the improved Brinkman parameter, the viscosity of the fluid increases. As a result, the fluid motion decreases.

Mechanical Properties and Synergistic Interfacial Interactions of ZnO Nanorod-Reinforced Polyamide–Imide Composites

Metal oxide nanoparticle -reinforced polymers have received considerable attention due to their favorable mechanical properties compared to neat materials. However, the effect of nanoscale reinforcements of the interface on the composites' mechanical properties has not been investigated in-depth to reach their optimal performance in structural applications. Aiming at revealing the effect of synergistic interfacial interactions on the mechanical properties of polymer composites, using a nanoscale reinforcement, herein, a series of zinc oxide nanorod-reinforced polyamide-imide (PAI)/ZnO) composites were fabricated and their mechanical properties and viscoelastic responses were investigated. The composite prepared by reinforcing them with 5 wt % ZnO nanorods resulted in improved elastic modulus, stiffness, and hardness values by 32%, 14% and 35%, respectively, compared to neat polymer thin films. The viscoelastic dynamics of the composites revealed that there was an 11% increase in elastic wave speed in the composite, containing 5 wt % ZnO nanorods, indicating better response to high impacts. Delayed viscoelastic response decreased by 67% spatially and 51% temporally, with a corresponding decrease in the creep rate, for the 5 wt % ZnO nanorod- containing composite, evidencing its potential applicability in high strength lightweight structures. The improved mechanical properties with respect to the filler concentration evidence strong particle-polymer interfacial interactions, creating "chain-bound" clusters, providing clear reinforcement and polymer chain mobility retardation. However, hypervelocity impact testing revealed that all the composites' films were vulnerable to hypervelocity impact, but the spallation region of the composite films reinforced with 2.5 wt % and 5 wt % ZnO nanorods exhibited a cellular-like matrix with shock-induced voids compared to a rather hardened spallation region with cracks in the neat film.

Microscale mechanics of actin-vimentin composite networks.

Most eukaryotic cells contain a complex network of cytoskeletal proteins comprised of filamentous actin, microtubule, and intermediate filaments. The ability of cells to resist mechanical deformation, transport cargo, and change shape during movement depends on these cytoskeletal proteins. Several previous studies have mainly focused on exploring the mechanics of in vitro reconstituted networks consisting of only one of these components, which may not be able to predict the properties of composite networks. Thus, investigating the interplay between the components as a composite is central to understanding the underlying biophysical principles. Here, we couple optical tweezers microrheology with confocal imaging to measure the viscoelastic response and structural dynamics of in vitro reconstituted filamentous actin (F-actin) and vimentin intermediate filaments (VIFs) composite networks by varying the relative concentration of the proteins. Our measurements shed new light on how VIFs and F-actin work synergistically during the various cellular processes.

Fractional‐order dynamics and adaptive dynamic surface control of flexible‐joint robots

AbstractThis paper establishes a novel fractional‐order model for n‐links flexible‐joint (FJ) robots and proposes an adaptive dynamic surface control (DSC) scheme to address the tracking control problem. The fractional‐order FJ model is built by fractional‐order viscoelastic dynamics model to have a more concise form. An adaptive DSC strategy is proposed to address the tracking control problem based on backstepping method. By selecting the appropriate orders for fractional filters, the controller could solve the “explosion of complexity” problem. The unknown nonlinearities of FJ robot systems are approximated by Radial basis function (RBF) neural networks (NNs). Based on the Lyapunov stability theory, the bounds of all signals in the closed‐loop system are achieved. The simulation results confirm the effectiveness of the presented control scheme.

Modeling the viscoelastic relaxation dynamics of soft particles via molecular dynamics simulation-informed multi-dimensional transition-state theory.

Viscoelastic soft colloidal particles have been widely explored in mechanical, chemical, pharmaceutical and other engineering applications due to their unique combination of viscosity and elasticity. The characteristic viscoelastic relaxation time shows an Arrhenius-type (or super-Arrhenius due to temperature-dependent transition attempts) thermally-activated behavior, but a holistic explanation from the relevant transition-state theory remains elusive. In this paper, the viscoelastic relaxation times of Lennard-Jones soft colloidal particle systems, including a single particle type system and a binary particle mixture based on the Kob-Andersen model, are determined using molecular dynamics (MD) simulations as the benchmark. First, the particle systems show a non-Maxwellian behavior after comparing the MD-predicted viscoelastic relaxation time and dynamic moduli (storage and loss modulus) to the classic Maxwell viscoelastic model and the recent particle local connectivity theory. Surprisingly, neither the Maxwell relaxation time τMaxwell (obtained from the static shear viscosity η and the high-frequency shear modulus G∞) nor the particle local connectivity lifetime τLC can capture the super-Arrhenius temperature-dependent behavior in the MD-predicted relaxation time τMD. Then, the particle dissociation and association transition kinetics, fractal dimensions of the particle systems, and neighbor particle structure (obtained from the radial distribution functions) are shown to collectively determine the viscoelastic relaxation time. These factors are embedded into a new multi-dimensional transition kinetics model to directly estimate the viscoelastic relaxation time τModel, which is found to agree with the MD-predicted τMD remarkably well. This work highlights the microscopic origin of viscoelastic relaxation dynamics of soft colloidal particles, and theoretically connects rheological dynamics and transition kinetics in soft matters.