Nonlinear Viscoelastic Behavior Research Articles

Nanomechanics of actin filament: A molecular dynamics simulation.

Actin is known as the most abundant essentially protein in eukaryotic cells. Actin plays a crucial role in many cellular processes involving mechanical forces such as cell motility, adhesion, muscle contraction, and intracellular transport. However, little is known about the mechanical properties of this protein when subjected to mechanical forces in cellular processes. In this article, a series of large-scale molecular dynamics simulations are carried out to elucidate nanomechanical behavior such as elastic and viscoelastic properties of a single actin filament. Here, we used two individual methods namely, all-atoms and coarse-grained molecular dynamics, to evaluate elastic properties of a single actin filament. In the other word, based on Brownian motions of the filament and using the principle of the equipartition theorem, in aqueous solution, tensile stiffness, torsional rigidity, and bending rigidity of the single actin filament are studied. The results revealed that increasing the sampling window time leads to convergence of obtained mechanical properties to the experimental values. Moreover, in order to investigate viscoelastic properties of a single actin filament, constant force steered molecular dynamics method is used to apply different external tensile loads and perform five individual creep tests on the molecule. The strain-time response of the filament for each creep test is obtained. Based on the Kelvin-Voigt model, the results reveal that a single actin filament shows a nonlinear viscoelastic behavior, with a Young's modulus of 2.85 GPa, a viscosity of 4.06 GPa.ns, and a relaxation time in the range of 1.42 ns which were measured here for the first time at the single filament level. The findings of this article suggest that molecular dynamics simulations could also be a useful tool for investigating the mechanical behavior of bio-nanomaterials.

Influence of mechanically-induced dilatation on the shape memory behavior of amorphous polymers at large deformation

In this study, we explore the influence of mechanically-induced dilatation on the thermomechanical and shape memory behavior of amorphous shape memory polymers (SMPs) at large deformation. The uniaxial tension, glass transition, stress relaxation and free recovery behaviors are examined with different strain levels (up to 340% engineering strain). A multi-branched constitutive model that incorporates dilatational effects on the polymer relaxation time is established and applied to assist in discussions and understand the nonlinear viscoelastic behaviors of SMPs. It is shown that the volumetric dilatation results in an SMP network with lower viscosity, faster relaxation, and lower $T_{g}$ . The influence of the dilatational effect on the thermomechanical behaviors is significant when the polymers are subject to large deformation or in a high viscosity state. The dilation also increases the free recovery rate of SMP at a given recovery temperature. Even though the tested SMPs are far beyond their linear viscoelastic region when a large programming strain is applied, the free recovery behavior still follows the time-temperature superposition (TTSP) if the dilatational effect is considered during the transformation of time scales; however, if the programming strain is different, TTSP fails in predicting the recovery behavior of SMPs because the network has different entropy state and driving force during shape recovery. Since most soft active polymers are subject to large deformation in practice, this study provides a theoretical basis to better understand their nonlinear viscoelastic behaviors, and optimize their performance in engineering applications.

Dielectrophoresis Testing of Nonlinear Viscoelastic Behaviors of Human Red Blood Cells.

Dielectrophoresis in microfluidics provides a useful tool to test biomechanics of living cells, regardless of surface charges on cell membranes. We have designed an experimental method to characterize the nonlinear viscoelastic behaviors of single cells using dielectrophoresis in a microfluidic channel. This method uses radio frequency, low voltage excitations through interdigitated microelectrodes, allowing probing multiple cells simultaneously with controllable load levels. Dielectrophoretic force was calibrated using a triaxial ellipsoid model. Using a Kelvin–Voigt model, the nonlinear shear moduli of cell membranes were determined from the steady-state deformations of red blood cells in response to a series of electric field strengths. The nonlinear elastic moduli of cell membranes ranged from 6.05 µN/m to up to 20.85 µN/m, which were identified as a function of extension ratio, rather than the lumped-parameter models as reported in the literature. Value of the characteristic time of the extensional recovery of cell membranes initially deformed to varied extent was found to be about 0.14 s. Shear viscosity of cell membrane was estimated to be 0.8–2.9 (µN/m)·s. This method is particularly valuable for rapid, non-invasive probing of mechanical properties of living cells.

Understanding the structural evolution under the oscillatory shear field to determine the viscoelastic behavior of nanorod filled polymer nanocomposites

By taking advantage of the classic coarse-grained molecular dynamics simulation, we have examined the effect of oscillatory shear strain amplitude on the viscoelastic behavior of nanorod (NR) filled polymer nanocomposites (PNCs) by tuning the interfacial interaction between polymer and NRs. We have observed the Payne effect (referred to the nonlinear viscoelastic behavior) at strong interfacial interaction. Payne-effect magnitude gradually increases with the interfacial interaction and the NR volume fraction. To understand the origin of Payne-effect, we examine the NR microstructures and their evolution during the shear field. We find that at low interfacial interaction, the probability of forming NR network is nearly unchanged with the shear strain amplitude; while at strong interfacial interaction, on the contrary the probability significantly decreases with the shear strain amplitude. We infer that various interfacial interactions change the NR network, influencing their evolution behavior under the shear flow. Meanwhile, we calculate the main cluster size and the total number of clusters for the NR network at different shear strain amplitudes, which is consistent with the probability of forming NR network. Thus, the original NR microstructure is significantly broken down under the external shear field, which can also be reflected by the number for polymer-mediated NR network bridged by glassy chains and the connected polymer beads between NRs. In addition, the polymer chains can slip on the filler surface under the shear field. As a result, the observed Payne effect comes from the slippage of the interfacial chains and breakage of the polymer-mediated NR network bridged by glassy chains at strong interfacial interaction. While at low interfacial interaction, it exhibits a weak non-linear behavior. Additionally, both reinforcement and Payne-effect magnitude exhibit a linear dependence on the inverse of the aspect ratio of the NRs. At last, different contributions to reinforcement due to hydrodynamic effects, “occluded rubber”, and “filler network” are quantified where the “filler network” is the main contribution. In summary, this work provides some interesting results to help further understand the relationship between the viscoelastic behavior and the NR network under the shear flow.

The application of large amplitude oscillatory stress in a study of fully formed fibrin clots

The suitability of controlled stress large amplitude oscillatory shear (LAOStress) for the characterisation of the nonlinear viscoelastic properties of fully formed fibrin clots is investigated. Capturing the rich nonlinear viscoelastic behaviour of the fibrin network is important for understanding the structural behaviour of clots formed in blood vessels which are exposed to a wide range of shear stresses. We report, for the first time, that artefacts due to ringing exist in both the sample stress and strain waveforms of a LAOStress measurement which will lead to errors in the calculation of nonlinear viscoelastic properties. The process of smoothing the waveforms eliminates these artefacts whilst retaining essential rheological information. Furthermore, we demonstrate the potential of LAOStress for characterising the nonlinear viscoelastic properties of fibrin clots in response to incremental increases of applied stress up to the point of fracture. Alternating LAOStress and small amplitude oscillatory shear measurements provide detailed information of reversible and irreversible structural changes of the fibrin clot as a consequence of elevated levels of stress. We relate these findings to previous studies involving large scale deformations of fibrin clots. The LAOStress technique may provide useful information to help understand why some blood clots formed in vessels are stable (such as in deep vein thrombosis) and others break off (leading to a life threatening pulmonary embolism).

The effect of storage temperature on blue cheese mechanical properties.

The results of this work can be used by blue cheese manufacturers to better understand the impact of storage time and temperature on blue cheese end quality. Manufacturers can take advantage of the effects of storage time on blue cheese mechanical behaviors to determine how long to age blue cheese to achieve the desired texture.

Non-linear viscoelastic behavior and damping factor of polypropylene/clay nanocomposites

The non-linear viscoelastic properties of pure polypropylene and its clay nanocomposites are studied to establish structure–property relationship in conjunction with clay concentrations. First, flow birefringence is performed through a slit-die to obtain centerline principal stress difference during elongational flow for clay nanocomposites. The centerline stress profile of clay nanocomposite reveals additional viscoelastic nature even at low silicate concentrations, while similar short-time chain relaxation is observed. The effects of higher clay concentrations are further examined during the simple shearing flow to consider damping properties of the clay nanocomposites. The step strain, dynamic shear and steady shear are performed. All the samples show time-strain separable melt flow behavior adequately demonstrated through Wagner’s exponential damping function. The damping coefficient is found to be strongly dependent on clay percentage revealing viscoelastic differences therein. We have also used a time-strain separable Kaye-Bernstein Kearsley Zapas (K-BKZ) type constitutive equation to predict steady shear stress. The suggested constitutive model satisfies simple shear at lower fractions of clay while the damping function behaves similar to pure polymer thought to result from the absence of filler–filler interactions and chain length degradation. The unusual rheological behavior for maximum clay concentration studied is explained on experimental as well as theoretical basis. Thus, the results of this investigation would improve the theoretical understanding of possible molecular orientations at different clay concentrations during elongational and shearing flows.

Non-linear stress response of non-gap-spanning magnetic chains suspended in a Newtonian fluid under oscillatory shear test: A direct numerical simulation

A direct numerical simulation approach is used to investigate the effective non-linear viscoelastic stress response of non-gap-spanning magnetic chains suspended in a Newtonian fluid. The suspension is confined in a channel and the suspended clusters are formed under the influence of a constant external magnetic field. Large amplitude oscillatory shear (LAOS) tests are conducted to study the non-linear rheology of the system. The effect of inertia on the intensity of non-linearities is discussed for both magnetic and non-magnetic cases. By conducting magnetic sweep tests, the intensity and quality of the non-linear stress response are studied as a function of the strength of the external magnetic field. The Chebyshev expansion of the stress response is used to quantify the non-linear intra-cycle behaviour of the suspension. It is demonstrated that the system shows a strain-softening behaviour while the variation of the dynamic viscosity is highly sensitive to the external magnetic field. In a series of strain sweep tests, the overall non-linear viscoelastic behaviour of the system is also investigated for both a constant frequency and a constant strain-rate amplitude. It is shown that the intra-cycle behaviour of the system is different from its inter-cycle behaviour under LAOS tests.

Preparation of magnetorheological elastomers and their slip-free characterization by means of parallel-plate rotational rheometry

A systematic study is presented to highlight a methodology of sample preparation and subsequent slip-free characterization of magnetorheological (MR) elastomers in parallel-plate rotational rheometry. Focusing on the magnetic field-dependent nonlinear viscoelastic behavior an array of oscillatory strain sweep measurements is conducted with samples cured within the rheometer. The examined nonlinear material response (i.e. the amplitude dependence of the storage and loss moduli) as a function of the applied magnetic field is found to be qualitatively similar to the amplitude dependence of particle reinforced elastomers (i.e. the Payne effect). Therefore, the experimental data (both moduli) is decomposed similar to that for reinforced elastomers and a phenomenological model is formulated for both the storage and loss modulus to account for the physical mechanisms governing the nonlinear material characteristics. Parameter identification suggests that the material response at low magnetic fields is dominated by the polymeric network whereas the strong magneto-reinforced microstructure governs the linear and nonlinear viscoelastic behavior at high magnetic fields. The overall experimental outcome further suggests that the underlying concept of the phenomenological model for particle reinforced elastomers (i.e. destruction and reformation of the filler network) can be transfered to MR materials. Consequently, the proposed phenomenological model can be applied to quantify and further analyze the nonlinear response characteristics of MR elastomers (i.e. the amplitude dependence of the storage and loss modulus as a function of the applied magnetic field) that is closely linked to microstructural changes of the magnetizable particle network.

Creep behaviour of plane frame structures made of GFRP profiles

A methodology is presented for analytical calculation of creep behavior of plane frames made of glass fiber reinforced polymer (GFRP) profiles and an experimental study is carried out in order to evaluate the analytical calculation results. In order to account nonlinear viscoelastic material behavior, stress – strain – time relationship of plane frame is given and creep behavior of plane frame structure is investigated. Material coefficients for the creep functions are determined using three point beam bending test results. In order to validate the analytical approach, a plane frame made of GFRP profiles is tested under sustained loads for 100 days and displacements, strains are monitored. Strain and displacement values that are calculated using analytical method show good agreement with the full-scale test data. DOI: http://dx.doi.org/10.5755/j01.mech.23.3.14029

On the nonlinear viscoelastic behavior of rubber-like materials: Constitutive description and identification

The main concern of this paper is the development of a three dimensional viscoelastic model at finite strain to describe nonfactorizable behavior of rubber-like materials. The model is developed within the framework of rational thermodynamics and internal state variable approach such that the second law of thermodynamics in the form of Clausius–Duhem inequality is satisfied. The nonfactorizable aspect of the behavior is introduced via a strain dependent relaxation times. The model is applied to describe the response of the isotropic Pipkin multi-integral viscoelastic model and the Bromobutyl (BIIR) material, several parameters involved are then identified using quasi-static and dynamic experiments thanks to a least-square minimization procedure. The proposed model is able to reproduce quasi-static response and show a good ability to predict the dynamic response of nonfactorizable rubber-like materials (BIIR) and the multi-integral model of Pipkin in a wide range of strain.

Viscoelastic behaviour of flocculated silica sediments in concentrated monovalent chloride salt solutions

Silica sand and quartz represent the second most common mineral in the earth's crust. The silica-water interface is central to the processing of a large number of mineral systems and the flow properties of particulate suspensions. In particular, these flow properties define the upper limit to processing of tailings suspensions in the mining industry and, ultimately, the recovery of water. In some regions of the world, the scarcity of fresh water has pushed this industry to use seawater, either as is or partially desalinated. Here we analyze the impact of monovalent alkali metal chlorides that are typical of seawater on the viscoelastic behaviour of flocculated silica sediments at concentrations typical of thickening systems. The sediment samples were subject to creep-recovery tests. All sediments exhibit nonlinear viscoelastic behaviour, deduced from the compliance-applied stress relationship. Interestingly, creep recovery was observed to be related to the Hofmeister series, Cs+<K+<Na+<Li+, with Cs+ producing lower recoveries than Li+. The yield stress, critical strain, and critical strain energy of the sediments were observed to be higher in maker salts (Na+ and Li+) compared with breaker salts (Cs+ and K+), due to stronger bonds in the particle networks. Our model of viscoelastic behaviour (Goñi et al., 2015) satisfactorily reproduces all experimental strain-time curves. The work provides novel input to decisions about the use of seawater or partially desalinated seawater in minerals processing with direct implications for tailings transportation, handling and water recovery.

Constitutive modelling of the strain-rate dependency of fabric reinforced polymers

Among the various mechanisms which occur during impact, the strain rate effect plays a significant role on the mechanical response of layered carbon fibre reinforced polymer structure. In this work, the viscoelastic behaviour of the material is studied to introduce a strain-rate dependency. To preserve numerical efficiency the generalised Maxwell model, formulated in the strain-space, is taken as a basis. The non-linear viscoelastic behaviour is introduced by coupling the generalised Maxwell model with a pre-existing intralaminar matrix continuum damage model. The fact that the Maxwell model preserves the explicit scheme of the damage model leads to an efficient material model for impact simulations. This paper proposes a complete framework to implement the strain-rate sensitive damage model in an explicit finite element code (for low-speed impact simulations). For this purpose, the procedure of parameter identification, based on DynamicMechanical Analysis, is given. Furthermore, a challenging experimental procedure on high-speed jack device with a particular attention paid to the consistency of the results is proposed to validate the developed model.

Modeling short- and long-term time-dependent nonlinear behavior of polyethylene

ABSTRACTA new methodology for developing macromechanical constitutive formulations for time-dependent materials is presented in this article. In particular, two phenomenological constitutive models for polymer materials are illustrated, describing time-dependent and nonlinear mechanical behavior. In this new approach, short-term creep test data are used for modeling both short-term and long-term responses. The differential form of a model is used to simulate typical nonlinear viscoelastic polymeric behavior using a combination of springs and dashpots. Unified plasticity theory is then used to develop the second model, which is a nonlinear viscoplastic one. Least squares fitting is applied for the determination of material parameters for both models, based on experimental results. Due to practical constraints, experimental data are usually available for short-term time-frames. In the presented proposed formulation, the material parameters determined from short-term testing are used to obtain material parameter relationships for predicting the long-term material response. This is done by extending short-term information for longer time frames. Finally, theoretical and experimental results of tensile tests on polyethylene subjected to various load levels and test times are compared and discussed. Very good agreement of the modeling results with experimental data shows that the developed formulation provides a flexible and reliable framework for predicting load responses of polymers.

A nonlinear model of cell interaction with an acoustic field

A theoretical and experimental nonlinear analysis of cellular response/displacement to ultrasound excitations is presented. Linear cell models can predict the resonant frequency (fR∼5MHz), but only a nonlinear analysis can reveal the amount of mechanical energy that couples into the cell and the bifurcation behavior of the cell when it is excited near resonance. The cell dynamics is described by the nonlinear viscoelastic constitutive behavior of the cytoplasm, nucleus and their respective membranes, in the presence of a fluid with an oscillating pressure field. The method of multiple scales is used to derive the amplitude of oscillation of the cytoplasm and nucleus as a function of frequency. A major finding is the existence of multiple solutions for a range of sub-resonant frequencies. At positive detuning (f>fR), the mechanical energy that couples into the cell is small, it is higher at resonance but significantly higher at sub-resonant frequencies in the multiplicity range. Experimentally it was shown when 3.5MHz is approached sub- and supra-resonance and 6.5MHz is approached sub-resonance, gene expression was statistically higher than that when stimulated directly. Thus, there exists an optimal range of frequencies for ultrasound treatment – in the region of multiplicity where deformation and thus mechanical energy coupling is maximized. The ultrasound protocol must be designed to operate at the solution associated with the higher mechanical energy – thus the start-up conditions should be in the domain of attraction of the high energy solution.

Road Load Identification and Accelerated Life Testing of Engine Mounts

Internal combustion engine mounts in a ground vehicle experience a very complicated loading situation. The loads mainly depend on the combination of engine vibration, engine torque, and vehicle motion especially in irregular road and maneuver conditions. Fatigue life estimation of rubber components is more complicated than metal components because of nonlinear viscoelastic behavior of rubber. Hence, analytical and numerical methods to estimate the loading and fatigue life of engine mount rubber components are not employed as often as in metal components. A new approach has been proposed to validate engine mount rubber components using accelerated fatigue life testing. Accurate identification of service loads is the key factor for a successful engine mount development and validation process. A multi-axial load sensor was developed to measure the engine mount loading in six degrees of freedom for a rear wheel drive heavy duty truck. Developed load sensors were installed onto a heavy duty truck and engine mount loading was measured during vehicle durability test. Measured loading data were processed using rainflow cycle counting technique to generate the accelerated fatigue life test profile. Failure of the engine mount rubber observed in vehicle durability test was successfully replicated in accelerated life test. This approach can also be employed for validation of different rubber components available in suspension and driveline sub-systems.

Correlation between Numerical and Experimental Tests of Laminated Glass Panels with Visco-elastic Interlayer

Present research is focused on numerical and experimental investigation of glass laminate structure consolidated with ethylene vinyl acetate film. The European wide industry standard for laminate glass panels is considered polyvinyl butyral interlayer film where ethylene vinyl acetate layer is particular out of autoclave manufacturing process related. Conducted numerical and experimental research worldwide rarely consider this type of polymer in lamination process even though in Baltic‘s this is industry standard. So far such glass laminate products are not mechanically characterised to the level that experimental results correlation with numerical predictions to give an engineers required confidence. Therefore current research initially characterise post cured ethylene vinyl acetate film then integration of viscoelastic material properties in numerical four point bending analysis and finally verification with non-contact measurements of natural frequencies to assess mechanical response of laminate glass panels. It was shown that by introducing non-linear viscoelastic behaviour of ethylene vinyl acetate film for depicting mechanical behaviour in 4-point bending the discrepancy between numerical and experimental results was less than 5% whereas assuming the interlayer as isotropic material only obtained discrepancy reached up to 50%.

Rheological Behavior of Tough PVP-in Situ-PAAm Hydrogels Physically Cross-Linked by Cooperative Hydrogen Bonding

Rheology studies were performed on tough PVP-in situ-PAAm hydrogels physically cross-linked by cooperative hydrogen bonding to understand their viscoelastic response and, hence, the interactions and microstructure. The viscoelasticity of the PVP-in situ-PAAm hydrogels was strongly affected by the monomer ratio (CAAm/CVP). Hydrogels prepared with a high monomer ratio exhibited weak time, temperature and frequency dependence of the viscoelastic properties, similar to those of chemically cross-linked hydrogels. The storage modulus (G′) of the gels was much greater than the loss moduli (G″) and low loss factor (tan δ < ∼ 0.1), which indicated that they were solid-like, and mostly elastic. These supramolecular gels exhibited a strain- and CAAm/CVP-dependent reversible gel (solid) to viscoelastic liquid transition due to the dynamic nature of the cooperative hydrogen bonds. That transition also coincided with the onset of nonlinear viscoelastic behavior. The addition of a low molecular weight compound, urea, th...

A novel methodology to characterize the constitutive behaviour of polyethylene terephthalate for the stretch blow moulding process

The stretch blow moulding (SBM) process is the main method for the mass production of PET containers. And understanding the constitutive behaviour of PET during this process is critical for designing the optimum product and process. However due to its nonlinear viscoelastic behaviour, the behaviour of PET is highly sensitive to its thermomechanical history making the task of modelling its constitutive behaviour complex. This means that the constitutive model will be useful only if it is known to be valid under the actual conditions of interest to the SBM process. The aim of this work was to develop a new material characterization method providing new data for the deformation behaviour of PET relevant to the SBM process. In order to achieve this goal, a reliable and robust characterization method was developed based on an instrumented stretch rod and a digital image correlation system to determine the stress-strain relationship of material in deforming preforms during free stretch-blow tests. The effect of preform temperature and air mass flow rate on the deformation behaviour of PET was also investigated.

Characterization of anaerobic granular sludge using a rheological approach

High-rate anaerobic granular sludge reactors have been developed and are widely used for wastewater treatment. An accurate estimate of sludge rheological properties is required for the design and efficient operation of the digestion process. The present work determined the rheological behavior of anaerobic granular sludge obtained from a full-scale bioreactor at different solid concentrations, operation temperatures and particle sizes, and highlighted common features in flow and dynamic measurements. The granular sludge showed a shear-thinning behavior with a yield stress under flow measurements and a viscoelastic property in dynamic measurements. The structure of granules was nearly temperature-independent in the range of operational temperature (20–70 °C), but the total solid concentration and particle size had significant effects on not only the rheological properties, but also the operation of the bioreactors. In addition, anaerobic granular sludge could cross over from the strong-link regime to the weak-link regime as the solid concentration increased. Furthermore, we adopted a Wagner-type constitutive model to describe the time-dependent and non-linear viscoelastic behaviors of anaerobic granular sludge, and then evaluated its validity and limitation.