Nonlinear Viscoelastic Properties Research Articles

FURTHER EVIDENCE OF FILLER–FILLER MECHANICAL ENGAGEMENT IN RUBBER COMPOUNDS FILLED WITH SILICA TREATED BY LONG-CHAIN SILANE

ABSTRACT The present study discusses that filler–filler mechanical engagement resulting from the grafted long-chain silanes on the silica surface is indeed a reinforcing mechanism in rubber composites, as already speculated by nonlinear viscoelastic properties in our previous study. The existence and severity of such a phenomenon are assessed purely by isolating the energetic contribution of reinforcement from interfering with filler mechanical engagement in the silica network formation and breakdown processes. In a novel approach, the driving force of fillers to flocculate energetically at elevated temperatures was defined using surface energy theories, and it was adjusted to be similar in two composites having silica treated by short- and long-chain silanes. Filler–filler mechanical engagement was monitored by tracking network formation (filler flocculation) in a matrix of styrene–butadiene rubber and also by conducting various dynamic viscoelastic experiments on liquid paraffin suspensions having short- and long-chain silica of similar surface energy. Results consistently confirmed the existence of mechanical engagement between silica particles having the long-chain silane in both rubber compounds and paraffin suspensions. The results may find applications in the rolling resistance of tires, for example, where stabilization of the filler network by displacing the peak energy dissipation of the network breakdown from applied service strains to larger values would be of technical importance.

Mechanical characterization and finite element implementation of the soft materials used in a novel anthropometric test device for simulating underbody blast loading

Soft materials (e.g. polymers) are widely used in biomechanical devices to represent the nonlinear viscoelastic properties inherent in biological soft tissues. Knowledge of their mechanical properties is used to inform design choices and develop accurate finite element (FE) models of human surrogates. The goal of this study was to characterize the behavior of eight polymeric materials used in the design of a novel anthropomorphic test device (ATD) and implement these materials in an FE model of the ATD.Tensile and compressive tests at strain rates ranging from 0.01s−1 to 1000s−1 were conducted on specimens from each material. Stress-strain relationships at discrete strain rates were used to define strain rate-dependent hyper-elastic material models in a commercial finite element solver. Then, the material models were implemented into an FE model of the ATD. The performance of the material models in the FE model was evaluated by simulating experiments that were conducted on the ATD lower limb.The material characterization tests revealed viscoelastic strain rate-dependent properties in the flesh and compliant elements of the ATD. Higher modulus polymers exhibited rate-dependent, strain-hardening properties. A strong agreement was seen between the material model simulations and corresponding experiments. In component simulations, the materials performed well and the model reasonably predicted the forces observed in experiments.

Nonlinear Viscoelasticity and Generalized Failure Criterion for Polymer Gels

Polymer gels behave as soft viscoelastic solids and exhibit a generic nonlinear mechanical response characterized by pronounced stiffening prior to irreversible failure, most often through macroscopic fractures. Here, we describe this scenario for a model protein gel using an integral constitutive equation built upon the linear and the nonlinear viscoelastic properties of the gel. We show that this formalism predicts quantitatively the gel mechanical response in shear start-up experiments, up to the onset of macroscopic failure. Moreover, we couple the computed stress response with Bailey's durability criterion for brittle solids in order to predict the critical values of the stress σc and strain γc at failure. The excellent agreement between theory and experiments suggests that failure in this soft viscoelastic gel is a Markovian process and that Bailey's failure criterion extends beyond hard materials such as metals, glasses, or minerals.

Slip-Spring Model for the Linear and Nonlinear Viscoelastic Properties of Molten Polyethylene Derived from Atomistic Simulations

Atomistic simulations have been very useful for predicting the viscoelastic properties of polymers but face great difficulties in accessing the dynamics of dense, well entangled long-chain melts with relaxation times longer than μs due to the high computational cost required. A plethora of coarse-grained models have been developed to address longer time scales. In this article we present a multiscale simulation strategy that bridges detailed molecular dynamics (MD) simulations to slip-spring based Brownian dynamics/kinetic Monte Carlo (BD/kMC) simulations of long-chain polymer melts. The BD/kMC simulations are based on a mesoscopic Helmholtz energy function incorporating bonded, slip-spring, and nonbonded interaction contributions (Macromolecules 2017, 50, 3004). Bonded contributions are expressed as sums of stretching and bending potentials of mean force derived from detailed MD simulations of shorter-chain melts, while nonbonded interaction contributions in the absence of slip-springs are derived from a...

Recombinant fibrinogen reveals the differential roles of α‐ and γ‐chain cross‐linking and molecular heterogeneity in fibrin clot strain‐stiffening

Background Fibrin plays a crucial role in haemostasis and wound healing by forming strain-stiffening fibrous networks that reinforce blood clots. The molecular origin of fibrin's strain-stiffening behavior remains poorly understood, primarily because plasma fibrinogen is a complex mixture of heterogeneous molecular variants and is often contaminated by plasma factors that affect clot properties. Objectives and methods To facilitate mechanistic dissection of fibrin nonlinear elasticity, we produced a homogeneous recombinant fibrinogen corresponding to the main variant in human plasma, termed rFib610. We characterized the structure of rFib610 clots using turbidimetry, microscopy and X-ray scattering. We used rheology to measure the strain-stiffening behavior of the clots and determined the fiber properties by modeling the clots as semi-flexible polymer networks. Results We show that addition of FXIII to rFib610 clots causes a dose-dependent stiffness increase at small deformations and renders the strain-stiffening response reversible. We find that γ-chain cross-linking contributes to clot elasticity by changing the force-extension behavior of the protofibrils, whereas α-chain cross-linking stiffens the fibers, as a consequence of tighter coupling between the constituent protofibrils. Interestingly, rFib610 protofibrils have a 25% larger bending rigidity than plasma-purified fibrin protofibrils and a delayed strain-stiffening, indicating that molecular heterogeneity influences clot mechanics at the protofibril scale. Conclusions Fibrinogen molecular heterogeneity and FXIII affect the mechanical function of fibrin clots by altering the nonlinear viscoelastic properties at the protofibril and fiber scale. This work provides a starting point to investigate the role of molecular heterogeneity of plasma fibrinogen in fibrin clot mechanics and haemostasis.

Time-domain characterization of the nonlinear viscoelastic memory of rocks with ultrasound waves

The nonlinear elastic response of rocks is known to be caused by internal microstructure, particularly cracks and fluids. In order to quantify this nonlinearity, we describe a new sensitive acoustic method to measure nonlinear viscoelastic properties of rocks directly in the time domain. Our method utilizes co-propagating longitudinal acoustic waves to perturb rocks with dynamically applied strain. Data indicates that rocks have a short period nonlinear viscoelastic memory that is a function of the time history of the loaded strain. We developed a phenomenological model with second and third order nonlinear elastic constants and a memory strength parameter to describe the short period nonlinear viscoelastic memory and the nonlinear elastic behavior of rock. Results of experiments on Crab Orchard sandstone and Lucite samples are presented. We have found both Lucite and Crab Orchard sandstone to be viscoelastic but the sandstone is much more nonlinear. These new observations and methods have significance for quantifying changes in microstructure and pore fluids in rocks and other materials.

Understanding the functionality of lipid‐based materials under large‐amplitude nonlinear deformations

SummaryLipid‐based materials meet many functions such as oil binding, lubricity and rheology. In this article, we focus on their rheological function, specifically in nonlinear viscoelastic properties, which we characterize using a novel approach known as large amplitude oscillatory shear (LAOS). We summarize recent works on this area and show that this technique has potential for providing invaluable insights into the functionality and perception of lipid‐based materials during their application process.

Non-linear Rheological Properties of Soy Protein Isolate Dispersions and Acid-Induced Gels

Abstract This study presents the non-linear viscoelastic properties of soy protein isolate (SPI) dispersions and acid-induced gels to considerable detail. The storage (G′) and loss (G′′) moduli of SPI dispersions showed Type III (week strain overshoot) and Type IV (strong strain overshoot) networks when the strain amplitudes varied between 0.01 and 1.00 and 1.00 to 100.00, respectively. In the case of acid-induced SPI gels the rheological parameters showed the characteristics of Type I (strain thinning) network. Fourier transform rheological experiments showed that the higher harmonic curves obtained u strain sweep test showed quite different shapes for SPI dispersions and gels. In the case of dispersions, the highest I 3/1 (0.101) occurred at the strain amplitude of 0.40 and then decreased to below 0.02. In the case of acid-induced SPI gels, the I 3/1 value began to be appreciable at the strain amplitude of 0.1 increased rapidly to its highest value (I 3/1=0.05).

Reversibility of strain stiffening in silk fibroin gels

We investigate the linear and nonlinear viscoelastic properties as well as the reversibility of strain-stiffening behavior of silk fibroin gels. The gels are prepared from 4.2w/v% fibroin solution in the presence of butanediol diglycidyl ether and N,N,N',N'-tetramethylethylenediamine (TEMED) as a cross-linker and catalyst, respectively. By changing the concentration of TEMED in the gelation system, fibroin gels exhibiting a storage modulus G’ between 10−1–105Pa and a loss factor tan δ between 10−2 and 10° could be obtained. We observe a strong stiffening (up to 900%) in fibroin gels with increasing strain above 10% deformation, but reversibly if the strain is removed, the gel recovers its initial viscoelastic properties. The strain induced formation of transient intermolecular domains acting as reversible cross-links are responsible for the stiffening behavior of fibroin gels. These additional cross-links formed in the hardened fibroin gels have a temporary nature with lifetimes of the order of seconds. The nonlinear behavior of fibroin gels can be reproduced by a wormlike chain model taking into account the entropic elasticity of fibroin molecules and the strain induced increase in the cross-link density of fibroin gels.

EXPERIMENTAL TESTING AND NUMERICAL MODELLING OF STENTS IN THE CORONARY ARTERIES

In this study, experimental and numerical stent modelling with plaque formation and progression for specific patient in the coronary arteries is described. In the method, section experimental stent testing is firstly described. Then numerical methods with finite element methods are given. Blood flow simulation is described with Navier-Stokes and continuity equation. Blood vessel wall is modelled with nonlinear viscoelastic material properties. The coupling of fluid dynamics and solute dynamics at the endothelium was achieved by the Kedem-Katchalsky equations. The inflammatory process is modelled using three additional reaction-diffusion partial differential equations. In the results section, the examples with rigid and deformable arterial wall with stented and unstented arteries are presented. Effective stress analysis results for stent deployment have been shown. These experimental and numerical methods can give better understanding of stent deployment procedure and arterial wall response in everyday clinical practice.

The effect of damping function on extrudate swell

The extrudate swell of an industrial grade high molecular weight high-density polyethylene (HDPE) in capillary dies is studied using the integral K-BKZ constitutive model. The non-linear viscoelastic flow properties of the polymer resin are studied for a broad range of large step shear strains and high shear rates using the cone partitioned plate (CPP) geometry of the stress/strain controlled rotational rheometer. This allowed the determination of the rheological parameters accurately, in particular the damping function, which is proven to be the most important in simulating transient flows such as extrudate swell. A series of simulations performed using the integral K-BKZ Wagner model with different values of the Wagner exponent n, ranging from n=0.15–0.5, demonstrates that the extrudate swell predictions are extremely sensitive to the Wagner damping function exponent. Using the correct n-value resulted in extrudate swell predictions that are in excellent agreement with experimental measurements.

Characterization of linear viscoelastic, nonlinear viscoelastic and damage stages of asphalt mixtures

It has been demonstrated that asphalt mixtures experienced linear viscoelastic stage, nonlinear viscoelastic stage and damage stage when subjected to controlled-strain repeated direct-tension (RDT) tests with increasing strain levels. However, the linear viscoelastic properties of asphalt mixtures are usually muddled up with their nonlinear viscoelastic properties. These confusions directly lead to the incorrect determination of the pseudostrains and dissipated pseudostrain energies (DPSEs) in the nonlinear viscoelastic stage and damage stage. This study investigated the material properties of fine aggregate mixture (FAM) specimens in all three stages. These three stages were differentiated and characterized in terms of the viscoelastic stress, pseudostrain and DPSE. The definitions of viscoelastic stress, reference modulus and pseudostrain were rigorously established to assure that the material properties in the linear viscoelastic stage were the reference properties and that the sole linear viscoelastic effect was eliminated when determining the pseudostrain and DPSE in the three stages. The characteristics of the DPSE in the three stages were found to be: (1) the DPSE of any loading cycle was zero in the linear viscoelastic stage; (2) in the nonlinear viscoelastic stage, the DPSE of each loading cycle remained approximately the same with the growth of the number of loading cycles, and the DPSE increased to a larger value when the strain level of the RDT test increased to a higher level; (3) in the damage stage, the DPSE of the loading cycle increased as the number of loading cycles increased. This study strictly distinguished the linear viscoelasticity from the nonlinear viscoelasticity of the asphalt mixtures, which is critical for the accurate determination of the DPSE spent in overcoming the nonlinear viscoelasticity and in developing damages, such as cracking and permanent deformation, in the asphalt mixtures.

Viscoelastic properties of aqueous guar gum derivative solutions under large amplitude oscillatory shear (LAOS)

The industrial relevant nonlinear viscoelastic properties of aqueous carboxymethyl hydroxypropyl guar gum (CMHPG) and non-ionic hydroxypropyl guar gum (HPG) solutions between semi-dilute and concentrated solution state were investigated by large amplitude oscillatory shear flow (LAOS). Aqueous CMHPG and HPG solutions enter the nonlinear flow regime at deformations γ0>100%. The nonlinear stress waveforms were analyzed by FT-rheology and orthogonal stress decomposition along the MITlaos framework. A rheological fingerprint is generated (Pipkin space) showing that the guar gum derivative solutions undergo a shear-thinning at high strains, which is preceded by a thickening above a minimum strain rate at intermediate strains. The influence and breakup of superstructures/aggregates gives a “rheological fingerprint”, a function of the applied deformation and time scale (Pipkin space). A characteristic process time was found that scales exponentially with the overlap parameter with an exponent of 4/2, and is proposed to represent the relaxation process of the superstructure in solution.

Viscoelasticity of reversibly crosslinked networks of semiflexible polymers.

We present a theoretical framework for the linear and nonlinear viscoelastic properties of reversibly crosslinked networks of semiflexible polymers. In contrast to affine models where network strain couples to the polymer end-to-end distance, in our model strain rather serves to locally distort the network structure. This induces bending modes in the polymer filaments, the properties of which are slaved to the surrounding network structure. Specifically, we investigate the frequency-dependent linear rheology, in particular in combination with crosslink binding-unbinding processes. We also develop schematic extensions to describe the nonlinear response during creep measurements as well as during constant strain-rate ramps.

Compatibilization effectiveness of maleated polypropylene compared to organoclay in PBT/PP blends

The compatibilization efficiency of a conventional compatibilizer (PP-grafted maleic anhydride) is compared with an organoclay of hydrophilic modifier (Cloisite 30B) in poly(butylene terephthalate)/polypropylene (PBT/PP) immiscible polymer blend. Moreover, the effect of PP-grafted maleic anhydride (PP-g-MA) on localization of Cloisite 30B organoclays is investigated, in this research. Accordingly, PBT/PP blends containing PP-g-MA, organoclay and PP-g-MA/organoclay are prepared by melt mixing method. According to morphological analysis, organoclays are more efficient than PP-g-MA in dispersion and distribution of droplets in PBT/PP blend. Additionally, the size of dispersed-droplets in PBT/PP/organoclay nanocomposite is lower than PBT/PP/PP-g-MA/organoclay sample. From X-ray diffractometry (XRD) and transmission electron microscopy illustrations, it is shown that organoclays represent the higher level of intercalation structure in PBT/PP/organoclay compared to PBT/PP/PP-g-MA/organoclay nanocomposite. PBT/PP/Organoclay nanocomposite indicates higher viscosity and elasticity in comparison with PBT/PP/PP-g-MA/organoclay, as well. The present subject can be explained by the role of PP-g-MA in transferring some parts of organoclays from PBT matrix into PP droplets which hinders the break-up of dispersed-droplets. According to non-linear viscoelastic properties, PBT/PP/organoclay sample shows stronger stress overshoots than PBT/PP/PP-g-MA/organoclay in start-up of shear flow. Modified De Kee-Turcotte model is studied to investigate the yield stress and viscoelastic behavior of different samples. PBT/PP/Organoclay nanocomposite shows higher yield stress compared to PBT/PP blend filled by PP-g-MA/organoclay system.

The pH Dependence on the Rheology of Wheat Protein Isolate Suspensions

Linear and non-linear rheological properties of wheat protein isolate (WPI) suspensions were investigated as a function of concentration and pH. Linear dynamic viscoelastic properties for WPI were strongly dependent on concentration and pH. The higher the concentration, the stronger the viscoelasticity of the WPI would be. In the pH range of 4.0-7.0, higher pH resulted in stronger viscoelasticity. WPI suspensions exhibited viscoelastic fluid behavior at lower concentration and/or lower pH. However, at high concentration and high pH, WPI suspensions showed some transition from viscoelastic fluid into viscoelastic solid, and displayed viscoelastic solid behavior at low frequencies. Concentration and pH ranges for the transition were narrow indicating that the property change for the WPI was in evidence. The non-linear shear viscoelastic properties of WPI were also found to depend on concentration and pH. Viscosities of WPI displayed shear-thinning behavior, and fits by a power law constitutive model. Our results indicate that the WPI structure in suspension changes over a small concentration and pH range, which suggest that WPI could be important for adjusting and controlling dough viscoelastic behavior. The information of this work is useful in the development of more and new applications using wheat protein isolate.

Nonlinear and linear viscoelastic properties of a novel type of xanthan gum with industrial applications

The influence of concentration in the viscoelastic properties of an “advanced performance” xanthan gum was studied by means of both techniques, small amplitude oscillatory shear (SAOS) and large amplitude oscillatory shear (LAOS). G′ and G″, within linear viscoelastic range, were demonstrated to be higher than the ones for the conventional xanthan gum pointing out to a less fluid-like behaviour. The combination of the use of both rheological measurements revealed a regime transition within the concentration range studied. Thus, the deviations from the Cox-Merz rule for the concentrations above 0.20 % (m/m) indicate the occurrence of a more development structure. In addition, the analysis of the influence of concentration on the local shear-thickening parameter (T) obtained by LAOS confirmed the modification of the gum structure.

Prediction and verification of the periodic response of a single-degree-of-freedom foam-mass system by using incremental harmonic balance

Vehicle occupants are exposed to low-frequency vibration that can cause fatigue, lower back pain, spine injuries, etc. Understanding the behavior of a seat-occupant system is helpful for minimizing these harmful vibrations. The behavior of a seat-occupant system is strongly affected by the properties of seating foam which exhibits nonlinear viscoelastic properties. Therefore, understanding the foam behavior and the way it affects the occupant response is a prerequisite for any successful and realistic seat-occupant model. The simplest model representing a seat-occupant system is a single-degree-of-freedom foam-mass system, which is also the simplest model representing a seat-occupant system. Here the dynamic response of such a system is studied. The governing equations of the system are developed for three different nonlinear viscoelastic foam models with real system parameters estimated using data from slow cyclic compression tests on a foam sample cut from a car seat. Being highly nonlinear, the local stiffness and hence the dynamic response of the foam-mass system in vertical direction highly depends on the supported mass. The incremental harmonic balance method is used to determine the steady-state behavior of the system subjected to a harmonic base excitation at different excitation levels and frequencies. This method significantly reduces the time required to generate the steady-state response compared to the time required when using direct time integration. The effects of riding mass, base excitation levels, system parameters and damping coefficients on the response are investigated. The predicted system response is seen to depend on the foam model type although each model’s parameters are identified using the same compression test data. To study this dependence on foam constitutive model, experiments are conducted on a single-degree-of-freedom foam-mass system subjected to harmonic base excitation. The simulated response predictions using the three models are found to significantly deviate from the experimental results. One of the foam models is then modified to incorporate rate dependence of foam parameters resulting in response predictions that are in good agreement with experimental results.

Contact forces generated by hailstone impact

Impact by hailstones can cause severe and widespread damage to roofs and many other exposed installations. This research aims at developing a model with which the value of the peak contact force generated by impact of a hailstone can be predicted with good confidence. A custom designed and built experimental setup involving the use of a gas gun for accurate measurement of contact force is first introduced. Some 45 impact experiments were conducted using the device. Meanwhile, an analytical spring connected lumped mass model featuring a non-linear visco-elastic compressive property of the frontal spring has been developed for simulating impact. To ensure that the analytical model is representative of real behaviour values of parameters used for characterising the stiffness properties of the frontal spring were obtained by calibrating with experimental measurements. Moderate changes in the calibrated values of the modelling parameters with increasing velocity of impact have been tracked. Finally, an algebraic expression along with a design chart has been developed to provide a convenient way for designers to estimate the peak contact force in deterministic terms for a range of hailstorm scenarios.

Bond graph model of extensor mechanism of finger based on hook–string mechanism

Biomechanical modeling of a finger is a challenging task especially due to excursion and gliding of tendons along bone geometry, the presence of articular cartilage between mating phalanges, nonlinear viscoelastic properties, load specific change in properties of tendons and complexity of deformable tendinous network (Winslow's rhombus) of the extensor mechanism. In this work, a bond graph model of the extensor mechanism of a finger is developed. Tendons are considered as deformable strings and assumed to pass through hooks fixed at predetermined points on rigid phalanges. This enables them to remain clinging to the phalanx surface while sliding on it, and retain network topology during the movement of phalanges. Word bond graph objects (WBGOs) are developed for dynamics of phalanges, hook–string interaction, normal reaction and frictional forces, and coupling of phalanges in rotation as well as translation, etc. Friction losses and extension of tendons due to applied load are accounted for. Study of motion and tension in tendons, joint variables, location of hooks and characteristics of individual tendons can be conveniently carried out based on the bond graph model. This has been effectively demonstrated through computer simulations.