Viscoelastic Dynamics Research Articles

Analysis on Coupling of Laminated Elastic Beam Element and the Shock Pressure of Surrounding Rock of Roadway

Based on the rock pressure tunnel support present situation carries on the analysis, the laminated elastic beams of high support ability and impact resistance was designed.Therefore, through assumptions and establishment of mathematical model, and the application of viscoelastic beam dynamics equation, deformation and energy absorption of the laminated elastic beam elements,under the condition of rock burst, was deduced. According to the load - displacement characteristic curve, the coupling of laminated elastic beam elements and rockburst in coal mine roadway was analysed. This can provide a new method in the field of safety production of mining and roadway.

Engineering fibrin polymers through engagement of alternative polymerization mechanisms

Fibrin is an attractive material for regenerative medicine applications. It not only forms a polymer but also contains cryptic matrikines that are released upon its activation/degradation and enhance the regenerative process. Despite this advantageous biology associated with fibrin, commercially available systems (e.g. TISSEEL) display limited regenerative capacity. This limitation is in part due to formulations that are optimized for tissue sealant applications and result in dense fibrous networks that limit cell infiltration. Recent evidence suggests that polymerization knob ‘B’ engagement of polymerization hole ‘b’ activates an alternative polymerization mechanism in fibrin, which may result in altered single fiber mechanical properties. We hypothesized that augmenting fibrin polymerization through the addition of PEGylated knob peptides with specificity to hole ‘b’ (AHRPYAAC-PEG) would result in distinct fibrin polymer architectures with grossly different physical properties. Polymerization dynamics, polymer architecture, diffusivity, viscoelasticity, and degradation dynamics were analyzed. Results indicate that specific engagement of hole ‘b’ with PEGylated knob ‘B’ conjugates during polymerization significantly enhances the porosity of and subsequent diffusivity through fibrin polymers. Paradoxically, these polymers also display increased viscoelastic properties and decreased susceptibility to degradation. As a result, fibrin polymer strength was significantly augmented without any adverse effects on angiogenesis within the modified polymers.

A high-resolution finite-difference method for simulating two-fluid, viscoelastic gel dynamics

An important class of gels are those composed of a polymer network and fluid solvent. The mechanical and rheological properties of these two-fluid gels can change dramatically in response to temperature, stress, and chemical stimulus. Because of their adaptivity, these gels are important in many biological systems, e.g. gels make up the cytoplasm of cells and the mucus in the respiratory and digestive systems, and they are involved in the formation of blood clots. In this study we consider a mathematical model for gels that treats the network phase as a viscoelastic fluid with spatially and temporally varying material parameters and treats the solvent phase as a viscous Newtonian fluid. The dynamics are governed by a coupled system of time-dependent partial differential equations which consist of transport equations for the two phases, constitutive equations for the viscoelastic stresses, two coupled momentum equations for the velocity fields of the two fluids, and a volume-averaged incompressibility constraint. We present a numerical method based on a staggered grid, second order finite-difference discretization of the momentum equations and a high-resolution unsplit Godunov method for the transport equations. The momentum and incompressibility equations are solved in a coupled manner with the Generalized Minimum Residual (GMRES) method using a multigrid preconditioner based on box-relaxation. We present results on the accuracy and robustness of the method together with an illustration of the interesting behavior of this gel model for the four-roll mill problem.

A Decomposition Method for the Analysis of Viscoelastic Structural Dynamics with Time‐Dependent Poisson's Ratio

Abstract: This paper presents a decomposition method for the dynamic analysis of elastic–viscoelastic composite (EVC) structures with time‐dependent Poisson's ratio. The analysis splits the viscoelasticity matrix with time‐dependent Poisson's ratio into two matrices in a simple form in which the time‐dependent Poisson's ratio does not appear. The decomposition simplifies the process of dynamical analysis for EVC structures with time‐dependent Poisson's ratio. The approach also makes it possible to apply existing analysis methods for constant Poisson's ratio structures directly to structures with time‐dependent Poisson's ratio. Based on the numerical results of three case studies, it is found that the time‐dependent Poisson's ratio has little influence on the structure's natural frequencies and damping properties. Therefore, it could be concluded that the effect of time‐dependency in Poisson's ratio may be ignored in the EVC structural dynamic analysis without introducing notable errors.

Catenary shape evolution of spanning structures in direct-write assembly of colloidal gels

This paper proposes a catenary model to describe the shape evolution of spanning filaments created by an extrusion-based, solid freeform fabrication process. Although colloidal gels have excellent self-support properties, their transient viscoelastic dynamics inevitably leads to fast deflection of spanning filaments under gravity. This model is derived from static force analysis of finite spanning filaments by assuming mechanical behavior of colloidal gels to follow a Kelvin-Voigt analogue. This model resembles a viscoelastic catenary to track the dynamic shape of spanning filaments after deposition, and compute their equilibrium shape profiles after long resting time. The model results are compared to published experimental data of lead zirconate titanate (PZT) colloidal inks ( Smay et al., 2002a), which confirm the validity of this model for understanding of shape evolution of spanning features in solid freeform fabrication.

Interface capturing simulations of acoustically driven bubble dynamics in and near tissue.

Tissue injury during therapeutic ultrasound or lithotripsy is thought, in cases, to be due to the action of cavitation bubbles. Assessing this and mitigating it is challenging since bubble dynamics in the complex confinement of tissues or in small blood vessels are challenging to predict. Simulations tools require specialized algorithms to simultaneously represent strong acoustic waves and shocks, topologically complex liquid‐vapor phase boundaries, and the complex viscoelastic material dynamics of tissue. We discuss advances in a simulation tool for such situations. A single‐mesh Eulerian solver is used to solve the governing equations. Special sharpening terms maintain the liquid‐vapor interface in face of the finite numerical dissipation included in the scheme to accurately capture shocks. A recent enhancement to this formulation has significantly improved this interface capturing procedure, which is demonstrated for simulation of the Rayleigh collapse of a bubble. The solver also transports elastic stresses and can thus be used to assess the effects of elastic properties on bubble dynamics. A shock‐induced bubble collapse adjacent to a model elastic tissue is used to demonstrate this and draw some conclusions regarding the injury suppressing role that tissue elasticity might play.

Design and Viscoelasticity Dynamics Modeling of Flexible Driven Unit for Robot's Joint

A flexible driven unit used for joint of robot is designed,whose features are light-duty,convenient,two-way driven and flexible.Dynamics model is deduced based on constitutive equation of viscoelasticity,whose example is shown.A novel method of building cable-pulley system is provided in order to establish model of driven unit and success to simulate based on walking sample of hip with a step at a speed of 2 km/h.The results of dynamics simulation show that the driven unit can be used to robot,which is the foundation for the following experiment.

Nonlinear Fractional Derivative Models of Viscoelastic Impact Dynamics Based on Entropy Elasticity and Generalized Maxwell Law

Two types of models are proposed for describing nonlinear fractional derivative dynamical behavior of viscoelastic materials subject to impulse forces. The models are derived based on the thermodynamic elasticity in terms of entropy and on the “scale-free response of the material” under the basic assumption that the viscoelastic materials consist of stable coils of polymers, which we refer to as blobs. The blobs, which may be connected to each other by chemical bonds or physical bonds, are considered here as the elementary constituent of viscoelastic materials from which the nonlinear fractional derivative models are derived. Responses of individual blobs can determine the net collective response of the viscoelastic material to impulse forces. From the above consideration, two types of models are proposed in which the force elements or the stress elements are connected by the generalized Maxwell law.

Microrheology and dynamics of an associative polymer

We study the microscopic viscoelastic properties and relaxation dynamics of solutions of a side-chain associative polymer, hydrophobically modified hydroxyethyl cellulose (hmHEC). Dynamic light scattering from small tracer particles suspended in the polymer solutions is used to determine their viscous and elastic moduli on the scale of the particles. Bulk-scale viscoelastic properties are measured by shear rheometry. The motion of the tracer particles in hmHEC is diffusive at short times and subdiffusive at intermediate and long times. The long-time subdiffusive motion was not observed in parallel experiments on unmodified HEC solutions, and is explained in terms of hindered reptation of the hydrophobically modified polymer chains in the associative network. Dynamic light scattering from the polymer molecules themselves shows that chain relaxation in hmHEC is dominated by slow concentration-dependent processes due to the large-scale associative network structure, while that in HEC is dominated by fast concentration independent Rouse-like dynamics.

Interpolatory projection methods for structure-preserving model reduction

We present a framework for interpolatory model reduction that treats systems having a generalized coprime factorization C ( s ) ▪ ( s ) − 1 B ( s ) + D . This includes rational Krylov-based interpolation methods as a special case. The broader framework allows retention of special structure in reduced models such as symmetry, second- and higher order structure, state constraints, internal delays, and infinite dimensional subsystems. Two numerical examples are provided for systems associated with viscoelastic dynamics and with an internal state delay that demonstrate the effectiveness and flexibility of the approach.

Nonlinear Viscoelastic Dynamics of Nanoconfined Wetting Liquids

The viscoelastic dynamics of nanoconfined wetting liquids is studied by means of atomic force microscopy. We observe a nonlinear viscoelastic behavior remarkably similar to that widely observed in metastable complex fluids. We show that the origin of the measured nonlinear viscoelasticity in nanoconfined water and silicon oil is a strain rate dependent relaxation time and slow dynamics. By measuring the viscoelastic modulus at different frequencies and strains, we find that the intrinsic relaxation time of nanoconfined water is in the range 0.1-0.0001 s, orders of magnitude longer than that of bulk water, and comparable to the dielectric relaxation time measured in supercooled water at 170-210 K.

Dynamics of wormlike and glassy wormlike chains

The wormlike chain (WLC) is a mathematical minimal model that captures universal aspects of the statistical mechanics and dynamics of stiff and semiflexible fibers. Its applications comprise all kinds of biopolymers from polysaccharides through cytoskeletal proteins to DNA, but also some synthetic polymers, wormlike micelles, and carbon nanotubes. The static force–extension relation of the WLC is today routinely applied to the design and interpretation of single molecule experiments. Its rich predictions for single molecule dynamics and ensuing consequences for networks and entangled solutions, such as those giving strength and power to your own body, are in the focus of ongoing research summarized below. The glassy wormlike chain (GWLC), a recent phenomenological extension of the WLC, aspires to link the highly universal viscoelastic equilbirum dynamics of sticky fiber networks to the physical properties of their microscopic constituents.

Blood Flow in Compliant Arteries: An Effective Viscoelastic Reduced Model, Numerics, and Experimental Validation

The focus of this work is on modeling blood flow in medium-to-large systemic arteries assuming cylindrical geometry, axially symmetric flow, and viscoelasticity of arterial walls. The aim was to develop a reduced model that would capture certain physical phenomena that have been neglected in the derivation of the standard axially symmetric one-dimensional models, while at the same time keeping the numerical simulations fast and simple, utilizing one-dimensional algorithms. The viscous Navier-Stokes equations were used to describe the flow and the linearly viscoelastic membrane equations to model the mechanical properties of arterial walls. Using asymptotic and homogenization theory, a novel closed, "one-and-a-half dimensional" model was obtained. In contrast with the standard one-dimensional model, the new model captures: (1) the viscous dissipation of the fluid, (2) the viscoelastic nature of the blood flow - vessel wall interaction, (3) the hysteresis loop in the viscoelastic arterial walls dynamics, and (4) two-dimensional flow effects to the leading-order accuracy. A numerical solver based on the 1D-Finite Element Method was developed and the numerical simulations were compared with the ultrasound imaging and Doppler flow loop measurements. Less than 3% of difference in the velocity and less than 1% of difference in the maximum diameter was detected, showing excellent agreement between the model and the experiment.

Viscoelastic Properties and Dynamics of Porcine Gastric Mucin

Gastric mucin is a glycoprotein known to undergo a pH-dependent sol-gel transition that is crucial to the protective function of the gastric mucus layer in mammalian stomachs. We present microscope-based dynamic light scattering data on porcine gastric mucin at pH 6 (solution) and pH 2 (gel) with and without the presence of tracer particles. The data provide a measurement of the microscale viscosity and the shear elastic modulus as well as an estimate of the mesh size of the gel formed at pH 2. We observe that the microscale viscosity in the gel is about 100-fold lower than its macroscopic viscosity, suggesting that large pores open up in the gel reducing frictional effects. The data presented here help to characterize physiologically relevant viscoelastic properties of an important biological macromolecule and may also serve to shed light on diffusive motion of small particles in the complex heterogeneous environment of a polymer gel network.

Eigen theory of viscoelastic dynamics based on the Kelvin-Voigt model

Using the eigen theory of solid mechanics, the eigen properties of anisotropic viscoelastic bodies with Kelvin-Voigt model were studied, and the generalized Stokes equation of anisotropic viscoelastic dynamics was obtained, which gives the threedimensional pattern of viscoelastical waves. The laws of viscoelastical waves of different anisotropical bodies were discussed. Several new conclusiones are given.

Analysis of the Viscoelastic Rod Dynamics via Models Involving Fractional Derivatives or Operators of Two different Orders

We present an overview of articles devoted to the analysis of dynamic behavior of viscoelastic rods, whose features are described by rheological models involving fractional derivatives or operators of two different orders. We investigate ten rheological models: the generalized viscoelastic Kelvin-Voigt, Maxwell, Zener models and other models containing fractional derivatives or fractional operators of two different fractional orders. For each of the above-mentioned rheological models, we carry out a comparative analysis between the behavior of its rheological and dynamic characteristics. Vector diagrams are used as the rheological characteristics, but the roots of the characteristic equations in the problems of longitudinal vibrations of rods, the velocities and coefficients of attenuation in the problems of propagation of harmonic waves, and the stress function in the problems of transient wave propagation are considered as the dynamic characteristics. The analysis of the rheological and dynamic characteristics shows that, depending on the relative magnitudes of the orders of the fractional derivatives and fractional operators entering into the rheological model, some of the models considered may describe both the wave and diffusion processes occurring in mechanical systems, but others describe only wave or only diffusion phenomena. The parallels between the behavior of the vector diagrams, the roots of the characteristic equations, the velocities and coefficients of attenuation, and the stress functions are revealed. We also show the analogy in the behavior of viscoelastic rods, whose rheological features are described by the models with fractional time derivatives and ordinary time derivatives.

Viscoelastic dynamics of polymer thin films and surfaces.

The strain relaxation behavior in a viscoelastic material, such as a polymer melt, may be strongly affected by the proximity of a free surface or mobile interface. In this paper, the viscoelastic surface modes of the material are discussed with respect to their possible influence on the freezing temperature and dewetting morphology of thin polymer films. In particular, the mode spectrum is connected with mode coupling theory assuming memory effects in the melt. Based on the idea that the polymer freezes due to these memory effects, surface melting is predicted. As a consequence, the substantial shift of the glass transition temperature of thin polymer films with respect to the bulk is naturally explanied. The experimental findings of several independent groups can be accounted for quantitatively, with the elastic modulus at the glass transition temperature as the only fitting parameter. Finally, a simple model is put forward which accounts for the occurrence of certain generic dewetting morphologies in thin liquid polymer films. It demonstrates that by taking into account the viscoelastic properties of the film, a morphological phase diagram may be derived which describes the observed structures of dewetting fronts. It is demonstrated that dewetting morphologies may also serve to determine nanoscale rheological properties of liquids.

Optical spectroscopy of simple aqueous solutions under extreme conditions

We report the results of an extensive series of Brillouin scattering experiments on simple aqueous solutions with a view to exploring their dynamical properties over a wide range of temperatures and pressures. For all solutes studied that inhibit freezing and allow access to temperatures far below the normal supercooling limit of water, we find clear spectroscopic evidence of GHz-range viscoelastic behavior below ≈−40 °C. This is manifested by a dramatic rise in the Brillouin mode frequencies accompanied by initial broadening and subsequent narrowing of the spectral linewidths on cooling. We find similar behavior in pure compressed (to between 2 and 4 kbar) supercooled water. This suggests that the low-temperature viscoelastic dynamics of these solutions is dominated by the behavior of the aqueous component which evidently exhibits a pronounced decrease in relaxation time though the temperature range over which it occurs is inaccessible unless freezing is suppressed either by pressure or the presence of solutes. No firm conclusion can be drawn concerning the proposed second critical point at these very low temperatures though it is not required for a consistent interpretation of the data. In the high-temperature regime, where the hydrogen bond structure is disrupted, we find considerable chemical sensitivity (even among the three chloride salts NaCl, CsCl, and CaCl2) in the dynamics especially in the vicinity of the liquid–gas critical point. This is in contrast to the low-temperature case where the cooperative dynamics of the water network dominates and appears to remain intact in the presence of a wide variety of solutes.

Completely monotone fading memory relaxation modulii

In linear viscoelasticity, the fundamental model is the Boltzmann caual integral equation which defines how the stress σ(t) at time t depends on the earlier history of the shear rate via the relaxation modulus (kernel) G (t). Physical reality is achieved by requiring that the form of the relaxation modulus G (t) gives the Boltzmann equation fading memory, so that changes in the distant past have less effect now than the same changes in the more recent past. A popular choice, though others have previously been proposed and investigated, is the assumption that G (t) be a completely monotone function. This assumption has much deeper ramifications than have been identified, discussed or exploited in the rheological literature. The purpose of this paper is to review the key mathematical properties of completely monotone functions, and to illustrate how these properties impact on the theory and application of linear viscoelasticity and polymer dynamics. A more general representation of a completely monotone function, known in the mathematical literature, but not the rheological, is formulated and discussed. This representation is used to derive new rheological relationships. In particular, explicit inversion formulas are derived for the relationships that are obtained when the relaxation spectrum model and a mixing rule are linked through a common relaxation modulus.

A Rouse-like model of liquid crystalline polymer melts: Director dynamics and linear viscoelasticity

We describe the linear viscoelastic response and dynamics of director orientation in monodomains of unentangled nematic liquid-crystalline polymers (LCPs), using a Rouse-like model appropriate to polymers with a significant degree of backbone flexibility, such as segmented main-chain thermotropic LCPs and side-chain LCPs. We consider the limits of: (i) main-chain directed polymers, for which the polymer backbone is extended along the director, with no hairpins, but executes a random walk in the plane perpendicular to the director, and (ii) anisotropic Gaussian polymers, for which the backbone executes an anisotropic three-dimensional random walk, as for main-chain LCPs with many hairpins and many side-chain LCPs. The analysis is based upon the assumption that, in fluids of such polymers, the distribution of nematogen orientations relaxes rapidly to a state of local equilibrium, via relatively rapid local rearrangements, which follows the slower evolution of the backbone conformation. We describe the linear response in terms of five independent dynamic moduli, which are time- or frequency-dependent generalizations of the Leslie viscosities. We find that directed chains generally tumble in steady shear flow, and that anistropic Gaussian chains flow align. In transient experiments, the coupling between director rotation and the relaxation of backbone conformations is found to lead to an overshoot of the director orientation following a step shear, and a phenomenon of “director recoil” in response to the temporary application of a magnetic aligning field.