Viscoelastic Contribution Research Articles

Continuous transition between traveling mass and traveling oscillator using mixed variables

The interaction between cars or trains and bridges has been often described by means of a simplified model consisting of a beam loaded by a traveling mass, or by a traveling oscillator.Among others, two aspects are essential when dealing with masses traveling along flexible vibrating supports: (i) a complete relative kinematics; and (ii) a continuous transition between a traveling mass, rigidly coupled, and a traveling oscillator, elastically coupled with the support.The kinematics is governed by normal and tangential components—with respect to the curved trajectory—of the acceleration. However in literature these parts are oriented with reference to the undeformed beam configuration. This model is improved here by a non-linear second-order enriched contribution.The transition between a traveling oscillator and a traveling mass is governed by the stiffness k of the elastic or viscoelastic coupling which, in the latter case (i.e. rigid coupling), has to tend towards infinity.However, very large stiffness values cause high frequencies and significant problems are mentioned in the literature in order to establish numerically stable and reliable results and in order to realize a continuous evolution between absolute and relative formulations.By using mixed state variables, generalized displacements and coupling forces, the contribution from the stiffness changes from k to its inverse 1/k, the coupling force itself becomes a member of the solution-space and the problems, which have been mentioned in the literature, disappear. As a matter of fact, the coupling force can also take into account a viscoelastic contribution; moreover, a larger number of traveling oscillators can be considered, too.Finally, for a periodic sequence of moving oscillators the dynamic stability is treated in the time-domain along several periods, as well as in the spectral domain, by using Floquet׳s theorem.

Fluid physico-chemical properties influence capture and diet in Nepenthes pitcher plants.

Nepenthes pitcher plants have evolved modified leaves with slippery surfaces and enzymatic fluids that trap and digest prey, faeces and/or plant detritus. Although the fluid's contribution to insect capture is recognized, the physico-chemical properties involved remain underexplored and may vary among species, influencing their diet type. This study investigates the contributions of acidity and viscoelasticity in the fluid's capture efficiency of two ant and two fly species in four Nepenthes species with different nutrition strategies. Four Nepenthes species were studied, namely N. rafflesiana, N. gracilis, N. hemsleyana and N. ampullaria. Fluid was collected from pitchers of varying ages from plants growing in the field and immediately transferred to glass vials, and individual ants (tribe Campotini, Fomicinae) and flies (Calliphora vomitoria and Drosophila melanogaster) were dropped in and observed for 5 min. Water-filled vials were used as controls. Survival and lifetime data were analysed using models applied to right-censored observations. Additional laboratory experiments were carried out in which C. vomitoria flies were immersed in pH-controlled aqueous solutions and observed for 5 min. Pitcher fluid differed among Nepenthes species as regards insect retention capacity and time-to-kill, with differences observed between prey types. Only the fluids of the reputedly insectivorous species were very acidic and/or viscoelastic and retained significantly more insects than the water controls. Viscoelastic fluids were fatal to flies and were able to trap the broadest diversity of insects. Younger viscoelastic fluids showed a better retention ability than older fluids, although with less rapid killing ability, suggesting that a chemical action follows a mechanical one. Insect retention increased exponentially with fluid viscoelasticity, and this happened more abruptly and at a lower threshold for flies compared with ants. Flies were more often retained if they fell into the traps on their backs, thus wetting their wings. Insect retention and death rate increased with fluid acidity, with a lower threshold for ants than for flies, and the time-to-kill decreased with increasing acidity. The laboratory experiments showed that fewer flies escaped from acidic solutions compared with water. In addition to viscoelasticity, the pitcher's fluid acidity and wetting ability influence the fate of insects and hence the diet of Nepenthes. The plants might select the prey that they retain by manipulating the secretion of H(+) ions and polysaccharides in their pitcher fluid. This in turn might participate in possible adaptive radiation of this genus with regard to nutrient sequestration strategy. These plants might even structurally influence insect fall-orientation and capture-probability, inspiring biomimetic designs for pest control.

The poro-viscoelastic properties of trabecular bone: a micro computed tomography-based finite element study

Bone is a porous structure with a solid phase that contains hydroxyapatite and collagen. Due to its composition, bone is often represented either as a poroelastic or as a viscoelastic material; however, the poro-viscoelastic formulation that allows integrating the effect of both the fluid flow and the collagen on the mechanical response of the tissue, has not been applied yet. The objective of this study was to develop a micro computed tomography (µCT)-based finite element (FE) model of trabecular bone that includes both the poroelastic and the viscoelastic nature of the tissue. Cubes of trabecular bone (N=25) from human distal tibia were scanned with µCT and stress relaxation experiments were conducted. The µCT images were the basis for sample specific FE models, and the stress relaxation experiments were simulated applying a poro-viscoelastic formulation. The model considers two scales of the tissue: the intertrabecular pore and the lacunar-canalicular pore scales. Independent viscoelastic and poroelastic models were also developed to determine their contribution to the poro-viscoelastic model. All the experiments exhibited a similar relaxation trend. The average reaction force before relaxation was 9.28×102N (SD±5.11×102N), and after relaxation was 4.69×102N (SD±2.88×102N). The slope of the regression line between the force before and after relaxation was 1.92 (R2=0.96). The poro-viscoelastic models captured 49% of the variability of the experimental data before relaxation and 33% after relaxation. The relaxation predicted with viscoelastic models was similar to the poro-viscoelastic ones; however, the poroelastic formulation underestimated the reaction force before relaxation. These data suggest that the contribution of viscoelasticity (fluid flow-independent mechanism) to the mechanical response of the tissue is significantly greater than the contribution of the poroelasticity (fluid flow-dependent mechanism).

Lateral migration of a viscoelastic drop in a Newtonian fluid in a shear flow near a wall.

Wall induced lateral migration of a viscoelastic (FENE-MCR) drop in a Newtonian fluid is investigated. Just like a Newtonian drop, a viscoelastic drop reaches a quasi-steady state where the lateral velocity only depends on the instantaneous distance from the wall. The drop migration velocity and the deformation scale inversely with the square and the cube of the distance from the wall, respectively. The migration velocity varies non-monotonically with increasing viscoelasticity (increasing Deborah number); initially increasing and then decreasing. An analytical explanation has been given of the effects by computing the migration velocity as arising from an image stresslet field due to the drop. The semi-analytical expression matches well with the simulated migration velocity away from the wall. It contains a viscoelastic stresslet component apart from those arising from interfacial tension and viscosity ratio. The migration dynamics is a result of the competition between the viscous (interfacial tension and viscosity ratio) and the viscoelastic effects. The viscoelastic stresslet contribution towards the migration velocity steadily increases. But the interfacial stresslet-arising purely from the drop shape-first increases and then decreases with rising Deborah number causing the migration velocity to be non-monotonic. The geometric effect of the interfacial stresslet is caused by a corresponding nonmonotonic variation of the drop inclination. High viscosity ratio is briefly considered to show that the drop viscoelasticity could stabilize a drop against breakup, and the increase in migration velocity due to viscoelasticity is larger compared to the viscosity-matched case.

Electromechanical behavior of polyaniline/poly (vinyl alcohol) blend films under static, dynamic and time-dependent strains

We report on the experimentally observed electrical conductivity enhancement in polyaniline/poly (vinyl alcohol) blend films under uniaxial tensile loading. Polyaniline (PANI) is an intrinsically conducting polymer, which does not form stretchable free-standing films easily and hence its electromechanical characterization is a challenge. Blending of PANI with other insulating polymers is a good choice to overcome the processability problem. We report the electromechanical response of solution blended and HCl doped PANI/PVA blends subjected to uniaxial, static, dynamic and time-dependent tensile loading. The demonstrated viscoelastic and morphological contributions of the component polymers to the electrical conductivity behavior in these blends could lead to interesting applications in strain sensors and flexible electronics. The reversibility of the electromechanical response under dynamic strain is found to increase in blends with higher PANI content. Time-dependent conductivity studies during mechanical stress relaxation reveal that variations in the micro-domain ordering and the relative relaxation rate of the individual polymer phases can give rise to interesting electrical conductivity changes in PANI blends. From morphological and electrical conductivity studies, we show that PANI undergoes primary and secondary agglomeration behavior in these blends that contributes to the changes in conductivity behavior during the deformation. A 3D variable range hopping (VRH) process, which uses a deformable core and shell concept based on blend morphology analysis, is used to explain the experimentally observed electromechanical behavior.

Measurement of the evolution of rigid and viscoelastic mass contributions from fibrin network formation during plasma coagulation using quartz crystal microbalance

The coagulation of blood plasma and the effect of fibrinogen concentration were studied with a quartz crystal microbalance (QCM), where frequency and half-width at half-maximum (bandwidth) values measured from the conductance spectrum near resonant frequency were used. Bandwidth change is an indicator of energy dissipation, allowing for an understanding of qualitative changes occurring during fibrin clot formation. Both frequency shift (Δf) and bandwidth shift (ΔΓ) were dependent on the concentration of fibrinogen in plasma. We defined a sum of squares function α (=Δf2/1000+ΔΓ2/1000) that measures absolute changes in QCM resonant characteristics to semi-quantitatively include an overall contribution of adsorbed mass and elastic modulus components and a function β (=1−ΔΓ/Δf) that indicates qualitatively the nature of response based on its deviation from ideal Newtonian behaviour. Increasing concentration of fibrinogen resulted in an increase in the value of α, showing that a larger amount of fibrinogen results in larger amount of coupled viscoelastic mass. Changes in β indicated that the nature of changes occurring was very similar to Newtonian and that coupling of rigid-mass dominates the overall response in the early stage of coagulation and in the later stage growing elastic mass compensates some of the response.

Creep behaviour of sandwich panels with rigid polyurethane foam core and glass-fibre reinforced polymer faces: Experimental tests and analytical modelling

This paper presents experimental and analytical investigations about the creep behaviour of sandwich panels comprising glass-fibre reinforced polymer faces and rigid polyurethane foam core for civil engineering applications. A full-scale sandwich panel was tested in bending for a period of 3600 h, in a simply supported configuration, subjected to a uniformly distributed load corresponding to 20% of the panel’s flexural strength. Additionally, specimens of polyurethane foam core were tested in shear for a period of 1200 h, for three different load levels corresponding to 10%, 20% and 30% of the foam’s shear strength. Experimental results were fitted using Findley’s power law formulation. Creep coefficients, shear modulus reduction factors and time-dependent shear moduli were obtained for the polyurethane foam in shear. A composed creep model is proposed to simulate the sandwich panel’s long-term creep deformations by considering the individual viscoelastic contributions from (1) the core material in shear and (2) the glass-fibre reinforced polymer faces in tension/compression. The composed creep model predictions adequately reproduced the full-scale panel’s experimental results. In addition, a good agreement was found between the composed creep model predictions and the extrapolation of the power law fitting obtained from the full-scale panel test, for a 50-year period.

Nonlinear viscoelastic contribution to the cyclic accommodation of high density polyethylene in tension: Experiments and modeling

Viscous polymers tackle the prediction of the accommodated cycle from which fatigue criterion parameters should be computed, within a formalism adapted to structure calculation. This work focuses on viscoelasticity, shown to be predominant in the high cycle fatigue stress range. Stress-controlled cyclic, recovery and creep tensile tests in polyethylene at room temperature allow characterizing the frequency and the stress ratio effect on the ratcheting strain and the loop parameters. An isothermal nonlinear viscoelastic model is derived for small strains in a Thermodynamics of Irreversible Processes framework. Nonlinearity arises from the description of the relaxed state towards which viscous internal variables evolve. Both the short (loop) and long (1000cycles) time scales are captured, with a ratcheting strain globally underestimated but features of the accommodated loop satisfyingly predicted.

Adhesion: role of bulk viscoelasticity and surface roughness

We study the adhesion between smooth polydimethylsiloxane (PDMS) rubber balls and smooth and rough poly(methyl methacrylate) (PMMA) surfaces, and between smooth silicon nitride balls and smooth PDMS surfaces. From the measured viscoelastic modulus of the PDMS rubber we calculate the viscoelastic contribution to the crack-opening propagation energy γeff(v,T) for a wide range of crack tip velocities v and for several temperatures T. The Johnson–Kendall–Roberts (JKR) contact mechanics theory is used to analyze the ball pull-off force data, and γeff(v,T) is obtained for smooth and rough surfaces. We conclude that γeff(v,T) has contributions of similar magnitude from both the bulk viscoelastic energy dissipation close to the crack tip, and from the bond-breaking process at the crack tip. The pull-off force on the rough surfaces is strongly reduced compared to that of the flat surface, which we attribute mainly to the decrease in the area of contact on the rough surfaces.

A novel methodology to predict sliding and rolling friction of viscoelastic materials: Theory and experiments

In this paper we propose a novel methodology to numerically investigate the steady-state sliding or rolling contact of viscoelastic materials, and in particular to calculate the viscoelastic contribution to friction. The implemented boundary element method relies on a very general mathematical formulation, able to deal either with rolling or sliding contact, and more importantly, able to handle real viscoelastic materials with a large number of relaxation times (e.g. tire rubber), thus overcoming the limitations of other analytical and numerical techniques. The proposed methodology is, then, employed to study the steady state rolling of a smooth rigid sphere on a standard linear viscoelastic solid, and to investigate the rolling contact of a rigid sphere moving on a styrene butadiene rubber. Numerical predictions are compared with existing theoretical investigations and with experiments. In both cases we find an almost perfect agreement.

On the skin friction coefficient in viscoelastic wall-bounded flows

Analysis of the skin friction coefficient for wall bounded viscoelastic flows is performed by utilizing available direct numerical simulation (DNS) results for viscoelastic turbulent channel flow. The Oldroyd-B, FENE-P and Giesekus constitutive models are used. First, we analyze the friction coefficient in viscous, viscoelastic and inertial stress contributions, as these arise from suitable momentum balances, for the flow in channels and pipes. Following Fukagata et al. (Phys. Fluids, 14, p. L73, 2002) and Yu et al. (Int. J. Heat. Fluid Flow, 25, p. 961, 2004) these three contributions are evaluated averaging available numerical results, and presented for selected values of flow and rheological parameters. Second, based on DNS results, we develop a universal function for the relative drag reduction as a function of the friction Weissenberg number. This leads to a closed-form approximate expression for the inverse of the square root of the skin friction coefficient for viscoelastic turbulent pipe flow as a function of the friction Reynolds number involving two primary material parameters, and a secondary one which also depends on the flow. The primary parameters are the zero shear-rate elasticity number, El0, and the limiting value for the drag reduction at high Weissenberg number, LDR, while the secondary one is the relative wall viscosity, μw. The predictions reproduce both types A and B of drag reduction, as first introduced by Virk (Nature, 253, p. 109, 1975), corresponding to partially and fully extended polymer molecules, respectively. Comparison of the results for the skin friction coefficient against experimental data shows good agreement for low and moderate drag reduction which is the region covered by the simulations.

Study of Instability of Streaming Rivlin-Ericksen Fluid in Porous Medium

There are many elastoviscous fluids that can be characterised neither by Maxwell’s constitutive relations nor by Oldroyd’s constitutive relations. One such class of viscoelastic fluids is the Rivlin– Ericksen’s fluid. RIVLIN and ERICKSEN] have proposed a theoretical model for such viscoelastic fluid. The behaviour of surface waves propagating between two Rivlin–Ericksen elastico-viscous fluids is examined. The investigation is made in the presence of a vertical electric field and a relative horizontal constant velocity. The influence of both surface tension and gravity force is taken into account. Due to the inclusion of streaming flow a mathematical simplification is considered. The viscoelastic contribution is demonstrated in the boundary conditions. From this point of view the approximation equations of motion are solved in the absence of viscoelastic effects. The solutions of the linearized equations of motion under nonlinear boundary conditions lead to derivation of a nonlinear equation governing the interfacial displacement and having damping terms with complex coefficients.

Defects and Glassy Dynamics in Solid 4He: Perspectives and Current Status

We review the anomalous behavior of solid He-4 at low temperatures with particular attention to the role of structural defects present in solid. The discussion centers around the possible role of two level systems and structural glassy components for inducing the observed anomalies. We propose that the origin of glassy behavior is due to the dynamics of defects like dislocations formed in He-4. Within the developed framework of glassy components in a solid, we give a summary of the results and predictions for the effects that cover the mechanical, thermodynamic, viscoelastic, and electro-elastic contributions of the glassy response of solid He-4. Our proposed glass model for solid He-4 has several implications: (1) The anomalous properties of He-4 can be accounted for by allowing defects to freeze out at lowest temperatures. The dynamics of solid He-4 is governed by glasslike (glassy) relaxation processes and the distribution of relaxation times varies significantly between different torsional oscillator, shear modulus, and dielectric function experiments. (2) Any defect freeze-out will be accompanied by thermodynamic signatures consistent with entropy contributions from defects. It follows that such entropy contribution is much smaller than the required superfluid fraction, yet it is sufficient to account for excess entropy at lowest temperatures. (3) We predict a Cole-Cole type relation between the real and imaginary part of the response functions for rotational and planar shear that is occurring due to the dynamics of defects. Similar results apply for other response functions. (4) Using the framework of glassy dynamics, we predict low-frequency yet to be measured electro-elastic features in defect rich He-4 crystals. These predictions allow one to directly test the ideas and very presence of glassy contributions in He-4.

Joint strength measurements of individual fiber-fiber bonds: An atomic force microscopy based method

We are introducing a method to measure tensile strength of individual fiber-fiber bonds within a breaking force range of 0.01 mN-1 mN as well as the energy consumed during breaking. Until now, such a method was not available. Using a conventional atomic force microscope and a specifically designed sample holder, the desired force and the breaking behavior can be analyzed by two different approaches. First, dynamic loading can be applied, where force-versus-distance curves are employed to determine the proportions of elastic energy and energy dissipated in the bond. Second, static loading is utilized to study viscoelastic behavior and calculate viscoelastic energy contributions. To demonstrate the capability of the proposed method, we are presenting results for breaking strength of kraft pulp fiber-fiber bonds in tensile opening mode. The procedure is by no means restricted to cellulose fibers, it has the potential to quantify joint strength of micrometer-sized fibers in general.

On the nature of the coefficient of friction of diamond-like carbon films deposited on rubber

In this paper, the nature of the coefficient of friction (CoF) of diamond-like carbon (DLC)-protected rubbers is studied. The relative importance of the viscoelastic and adhesive contributions to the overall friction is evaluated experimentally by modifying the contact load and the adhesive strength between the surface and the counterpart. The results indicate that the increase of CoF during the tribotests under non-lubricated conditions is caused by the increase of the adhesive contribution to friction motivated by the growth of the contact area during the test. In the case of oil lubricating condition, the adhesive force is minimized and the CoF is observed to decrease during the tribotest. This is caused by the reduction of the viscoelastic contribution due to the variation of the shape of the contact area. The role of the microstructure of the DLC film on the efficiency of the oil lubrication is also discussed.

Direct numerical simulation of surfactant-stabilized emulsions

A 3D lattice Boltzmann model for two-phase flow with amphiphilic surfactant was used to investigate the evolution of emulsion morphology and shear stress in starting shear flow. The interfacial contributions were analyzed for low and high volume fractions and varying surfactant activity. A transient viscoelastic contribution to the emulsion rheology under constant strain rate conditions was attributed to the interfacial stress. For droplet volume fractions below 0.3 and an average capillary number of about 0.25, highly elliptical droplets formed. Consistent with affine deformation models, gradual elongation of the droplets increased the shear stress at early times and reduced it at later times. Lower interfacial tension with increased surfactant activity counterbalanced the effect of increased interfacial area, and the net shear stress did not change significantly. For higher volume fractions, co-continuous phases with a complex topology were formed. The surfactant decreased the interfacial shear stress due mainly to advection of surfactant to higher curvature areas. Our results are in qualitative agreement with experimental data for polymer blends in terms of transient interfacial stresses and limited enhancement of the emulsion viscosity at larger volume fractions where the phases are co-continuous.

The Non-Equilibrium Thermodynamics and Kinetics Governing Coupled Stress Fiber and Focal Adhesion Dynamics

We consider the coupled mechano-chemistry governing the cytoskeletal force in cells with stress fibers and focal adhesions. Our studies include published experimental work in which we monitor the cytoskeletal forces in cells on elastomeric substrates of micron-sized posts. These experiments demonstrate complex dynamics involving substrate strain as well as the binding/unbinding of cytoskeletal and focal adhesion proteins. Our model explains these dynamics, which underlie force generation and motility of, especially, mesenchymal cells. The broader motivation for this research comes from our ongoing work on cancer cell motility and invasion. Guided by our experiments, our model considers a single stress fiber, the focal adhesion by which it is attached to a micropost, the cell reservoir of cytoskeletal and focal adhesion proteins, the deforming micropost and underlying substrate. The complex mechano-chemistry that controls these sub-systems' interaction is itself governed by non-equilibrium thermodynamics: The binding/unbinding of proteins is driven by free energy changes due to chemistry, elasticity and mechanical work done. The stress fibers' mechanical response has viscoelastic and active contributions, the latter due to myosin contractility. Our model, an extension of our recently published work, generates a very rich range of responses depending on the mechanical and chemical boundary conditions, and parameter values (which are obtained from our experiments, and well-established estimates from the literature). This range of model responses includes every case observed in our experiments. We find that while applied strain and acto-myosin contractility dictate the increase of force in stress fibers over the short to medium time scale (∼600 sec.), the longer time scale response (∼1000-10000 sec) is dominated by the growth and disassembly of focal adhesions. These findings have direct implications for published and ongoing work on cancer cell locomotion in our group.

Performance of diamond-like carbon-protected rubber under cyclic friction. II. Influence of substrate viscoelasticity on the friction evolution

In this paper, the influence of the mechanical properties of rubber substrate on frictional behavior of DLC-protected rubber is studied by numerical methods. The viscoelastic contribution to the friction during a tribotest was simulated according to a “mattress” approach composed by Voigt or standard linear solid units. The latter approach demonstrated more accurate predictions. In both cases, the results show an increase of the contact depth, which is in agreement with the experimental observations. The simulations also show a progressive reduction of the viscoelastic contribution of the coefficient of friction (CoF) with the number of laps due to the elongation of the front part of the contact area. This prediction does not agree with the experimentally observed increase of CoF, and suggests a dominant contribution of the adhesive component to the friction under real conditions.

A result of existence and uniqueness for an integro-differential system in magneto-viscoelasticity

We prove the existence and uniqueness of solution to a one-dimensional hyperbolic–parabolic system arising in the study of magneto-viscoelasticity. Specifically, the local existence and uniqueness result is proved on application of the fixed point theorem; then, a uniform a priori estimate of the solution is established. The latter, via a continuation method, allows as to obtain the global result. A crucial tool to achieve such a result is a technical lemma concerning the only viscoelastic contribution; it relies on the assumptions that the memory kernel is positive, monotonically non-increasing and convex.

Viscoelastic fracture of biological composites

Soft constituent materials endow biological composites, such as bone, dentin and nacre, with viscoelastic properties that may play an important role in their remarkable fracture resistance. In this paper we calculate the scaling properties of the quasi-static energy release rate and the viscoelastic contribution to the fracture energy of various biological composites, using both perturbative and non-perturbative approaches. We consider coarse-grained descriptions of three types of anisotropic structures: (i) liquid-crystal-like composites, (ii) stratified composites, (iii) staggered composites, for different crack orientations. In addition, we briefly discuss the implications of anisotropy for fracture criteria. Our analysis highlights the dominant lengthscales and scaling properties of viscoelastic fracture of biological composites. It may be useful for evaluating crack velocity toughening effects and structure-dissipation relations in these materials.