Viscoelastic Functions Research Articles

Closed-form solution for horizontal and vertical shiftings of viscoelastic material functions in frequency domain

The closed-form shifting (CFS) algorithm is a simple mathematical methodology which determines the unique solution in the process of constructing master curves at selected reference temperature and pressure conditions. In a previous paper, the CFS algorithm has been fully described for monotonically increasing or monotonically decreasing functions only. This paper presents detailed steps of the generalized CFS methodology for non-monotonic functions, like the loss tangent. Performing shifting on the loss tangent, which does not require vertical shifting, is particularly important for materials which require vertical adjustment of dynamic viscoelastic functions, i.e., loss and storage moduli. Thus, based on horizontal shifting of the loss tangent, the CFS-based procedure of consecutive horizontal-vertical superposition for the storage modulus is proposed and analyzed. The analysis is done on the example of two synthetically generated non-monotonic tan delta segments and corresponding storage modulus segments in respect to different experimental parameters. It has been shown that the error brought by the shifting method into non-monotonic loss tangent and storage modulus master curves is twice smaller than the corresponding experimental noise level.

Application of a fractional model for simulation of the viscoelastic functions of polymers

ABSTRACTIn the present work the dynamic behavior of two representative polymeric materials, experimentally studied in previous works, has been analyzed by a fractional derivative model. It is shown that the well‐known fractional derivative Zener model, in its simplest form as a four‐parameter model is capable of capturing the main features of the dynamic moduli of the polymeric structures examined. Furthermore, the time dependent viscoelastic functions, namely the compliance and the relaxation modulus could be simulated with the same model parameter values, indicating this way that the fractional model can provide a method of interconversion between viscoelastic material functions. The model's inadequacy of describing the loss modulus peak asymmetry, exhibited by the materials, has been encountered by the five‐parameter version of the fractional Zener model. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 43505.

Dissipation of Stress in the Cytoskeleton VIA Alpha-Actinin Dynamic Crosslinking

The actin cytoskeleton is known to be a main structural and mechanical component of many eukaryotic cells. Dynamic crosslinking of actin filaments by proteins such as alpha-actinin, can change these mechanics, however, the effect of dynamic crosslinking on cell mechanics has not been previously reported. Here we quantify the viscoelastic moduli of cells with alpha-actinin isoforms that have varied binding affinity.We apply several techniques, including passive and active micro-rheology and AFM measurements to measure cellular moduli with alpha-actinin isoforms. The experiments are also performed after myosin inhibition and ATP depletion to study the contribution of active contractility to the viscoelastic properties of these cells. AFM-based stress relaxation and dynamic indentation tests are used to calculate the mechanical properties of the cellular cortex, while active micro-rheology using optical tweezers allows us to calculate the storage and loss moduli of the cytoplasm.Furthermore, the overall energy dissipation is estimated at cellular level, and these results are compared with cell work on the elastic substrates, using traction force microscopy data. Energy dissipation via dynamic crosslinkers in the cytoskeleton can regulate cellular viscoelasticity and basic biological functions such as spreading, force-generation, and migration.

Viscoelasticity of periodontal ligament: an analytical model.

BackgroundUnderstanding of viscoelastic behaviour of a periodontal membrane under physiological conditions is important for many orthodontic problems. A new analytic model of a nearly incompressible viscoelastic periodontal ligament is suggested, employing symmetrical paraboloids to describe its internal and external surfaces.MethodsIn the model, a tooth root is assumed to be a rigid body, with perfect bonding between its external surface and an internal surface of the ligament. An assumption of almost incompressible material is used to formulate kinematic relationships for a periodontal ligament; a viscoelastic constitutive equation with a fractional exponential kernel is suggested for its description.ResultsTranslational and rotational equations of motion are derived for ligament’s points and special cases of translational displacements of the tooth root are analysed. Material parameters of the fractional viscoelastic function are assessed on the basis of experimental data for response of the periodontal ligament to tooth translation. A character of distribution of hydrostatic stresses in the ligament caused by vertical and horizontal translations of the tooth root is defined.ConclusionsThe proposed model allows generalization of the known analytical models of the viscoelastic periodontal ligament by introduction of instantaneous and relaxed elastic moduli, as well as the fractional parameter. The latter makes it possible to take into account different behaviours of the periodontal tissue under short- and long-term loads. The obtained results can be used to determine loads required for orthodontic tooth movements corresponding to optimal stresses, as well as to simulate bone remodelling on the basis of changes in stresses and strains in the periodontal ligament caused by such movements.

Viscoelastic constitutive modeling of solid propellant with damage

• A new type of softening function is suggested to represent the softening phenomena which are affected by growth of void, stress state and adhesion energy in the interface. • The viscoelastic dewetting function is derived from the viscoelastic dewetting criteri on to obtain the volumetric strain at the onset of the dewetting. • The model is implemented into the commercial finite element code ABAQUS via the user subroutine UMAT to validate the constitutive model. An isotropic nonlinear viscoelastic constitutive model for solid propellant is proposed. The damage due to cyclic loading and dewetting is modeled. Dewetting is a particle-binder interfacial debonding which induces softening under severe deformation. The cyclic loading effects include rapid a decrease of stress during the unloading and large amount of hysteresis known as Mullins’ effect. These effects are modeled by introducing damage functions in the free energy function. The softening due to dewetting is caused by the formation and growth of voids between the matrix and the particles, and a new damage function is proposed to represent the softening behavior. It is represented as a function of the ratio of the volumetric strains before and after dewetting. The volumetric strain at the onset of dewetting is predicted by using viscoelastic dewetting function, which is derived from the viscoelastic dewetting criterion. Cyclic loading effects are accounted for by employing another damage function which is the function of the octahedral shear strain. In addition to the material nonlinearities caused by the damage, geometrical nonlinearity is also considered. The constitutive model is implemented into the commercial finite element code ABAQUS via the user material subroutine UMAT for stress analysis. Laboratory tests of uniaxial and biaxial specimens for the stress response are performed under several different loading conditions. The material parameters and damage functions are calibrated using uniaxial tests only. The effects of strain rate, temperature and loading conditions on the stress are discussed. The computational results are compared with the experiments.

A statistical approach to characterize the viscoelastic creep compliances of a vinyl ester polymer

The objective of this study was to develop a model to predict the viscoelastic material functions of a vinyl ester (VE) polymer with variations in its experimentally obtained material properties under combined isothermal and mechanical loading. Short-term tensile creep experiments were conducted at three temperatures below the glass transition temperature of the VE polymer, with 10 replicates for each test configuration. The measured creep strain versus time responses were used to determine the creep compliances using the generalized viscoelastic constitutive equation with a Prony series representation. The variation in the creep compliances of a VE polymer was described by formulating the probability density functions (PDFs) and the corresponding cumulative distribution functions (CDFs) of the creep compliances using a two-parameter Weibull distribution. Both Weibull scale and shape parameters of the creep compliance distributions were shown to be time and temperature dependent. Two-dimensional quadratic Lagrange interpolation functions were used to characterize the Weibull parameters to obtain the PDFs and, subsequently, the CDFs of the creep compliances for the complete design temperature range during steady state creep. At each test temperature, creep compliance curves were obtained for constant CDF values and compared with the experimental data. The predicted creep compliances of the selected VE polymer in the design space are in good agreement with the experimental data for all three test temperatures.

A method for the determination of the viscoelastic relaxation function of reactive materials

Modern insensitive high explosives HE are heterogeneous materials consisting of a mixture of explosive grains within a polymeric binder matrix [1]. The mechanical material behaviour is strongly determined by this heterogeneous structure. The stiffness and strength comes mainly from the explosive grains whereas the softer polymeric binder is responsible for the viscoelastic behaviour. Depending on the mechanical loading regime different mechanisms are present and must be taken into account for the material modelling.

Thermo-rheological behavior and compatibility of modified asphalt with various styrene–butadiene structures in SBS copolymers

The knowledge of the morphological structure or effect of polymer structure on the performance of polymer-modified asphalt (PMA) is not systematic and completed yet. In this paper, SBS-modified asphalts were prepared by asphalts with different compositions and styrene–butadiene–styrene (SBS) copolymers with various styrene–butadiene structures, which in turn were subjected to frequency sweep tests, viscous measurements and fluorescence microscopy. The results revealed that the SBS-modified asphalt containing 30wt.% styrene had the optimal viscoelastic functions and the highest viscosity, indicating enhanced viscoelastic characteristics and less sensitivity to temperature changes. Furthermore, it is less susceptible to shear forces for asphalts as the increase of styrene content because larger and stronger aggregated polystyrene domains can render deformation and movement more difficult. For system studied, the compatibility becomes poorer as the increase of styrene contents and polymer phase sizes decrease with the enhancement of styrene contents as well as their volume proportions. The scope of distribution curves becomes narrower and the swelling degree is lower as the increase of styrene contents by image analysis. As a conclusion, there is a moderate styrene content for SBS to acquire equilibrium between the compatibility and viscoelastic characteristics.

Viscoelastic Properties of Dental Pulp Tissue and Ramifications on Biomaterial Development for Pulp Regeneration

IntroductionA critical step in biomaterial selection effort is the determination of material as well as the biological properties of the target tissue. Previously, the selection of biomaterials and carriers for dental pulp regeneration has been solely based on empirical experience. MethodsIn this study, first, the linear viscoelastic material functions and compressive properties of miniature pig dental pulp were characterized using small-amplitude oscillatory shear and uniaxial compression at a constant rate. They were then compared with the properties of hydrogels (ie, agarose, alginate, and collagen) that are widely used in tissue regeneration. ResultsThe comparisons of the linear viscoelastic material functions of the native pulp tissue with those of the 3 hydrogels revealed the gel-like behavior of the pulp tissue over a relatively large range of time scales (ie, over the frequency range of 0.1–100 rps). At the constant gelation agent concentration of 2%, the dynamic properties (ie, storage and loss moduli and the tanδ) of the collagen-based gel approached those of the native tissue. Under uniaxial compression, the peak normal stresses and compressive moduli of the agarose gel were similar to those of the native tissue, whereas alginate and collagen exhibited significantly lower compressive properties. ConclusionsThe linear viscoelastic and uniaxial compressive properties of the dental pulp tissue reported here should enable the more appropriate selection of biogels for dental pulp regeneration via the better tailoring of gelation agents and their concentrations to better mimic the dynamic and compressive properties of native pulp tissue.

Logarithmic method for continuous relaxation spectrum and comparison with previous methods

Various algorithms for determining relaxation time spectrum have been to the fore, because relaxation spectrum plays an important role in interconversion between various viscoelastic functions. In this study, a new algorithm is developed by means of double-logarithmic power series approximation and the Levenberg–Marquardt method. Compared with most previous algorithms, new algorithm is applicable not only to dynamic data but also to the Laplace transform of relaxation modulus, which is available for optical data from the generalized Stokes–Einstein equation or creep data with ringing. It is worth noticing that the new algorithm determines continuous relaxation spectrum without any additional parameters and precedent procedures. This paper suggests such framework of newly developed algorithm and its applications to various kinds of viscoelastic data.

Ionic and viscoelastic mechanisms of a bucky-gel actuator

Ionic electromechanically active polymers (IEAPs) are considered attractive candidates for soft, miniature, and lightweight actuators. The bucky-gel actuator is a carbonaceous subtype of IEAP that due to its structure (i.e. two highly porous electrodes sandwiching a thin ion-permeable electrolyte layer) and composition (i.e. being composed of soft porous polymer, carbon nanotubes, and ionic liquid) is very similar to an electric double-layer capacitor. In response to the voltage applied between the electrodes of a bucky-gel actuator, the laminar structure bends. The time domain behavior exhibits, however, a phenomenon called the back-relaxation, i.e., after some time the direction of bending is reversed even though voltage remains constant. In spite of the working mechanism of IEAP actuators being generally attributed to the transport of ions within the soft multilayer system, the specific details remain unclear. A so-called two-carrier model proposes that the bending and subsequent back-relaxation are caused by the relocation of two ionic species having different mobilities as they enter and exit the electrode layers. By adopting the two-carrier model for bucky-gel actuators, we see very good agreement between the mathematical representation and the experimental data of the electromechanical behavior. Furthermore, since the bucky-gel actuator is viscoelastic, we propose to use the time domain response of a blocking force as the key parameter related to the inner ionic mechanism. We also introduce a method to estimate the viscoelastic creep compliance function from the time domain responses for curvature and blocking force. This analysis includes four types of bucky-gel actuators of varying composition and structure.

Rheological and TGA study of acylated chitosan gel-like dispersions in castor oil: Influence of acyl substituent and acylation protocol

Summary This work deals with the development and characterization of new formulations based on different types of acylated chitosan, obtained using different acylation protocols and acyl chlorides, which are able to generate stable gel-like dispersions in castor oil. These dispersions can be proposed as promising candidates to replace current non-biodegradable lubricating grease formulations. The biopolymers and gel-like dispersions were characterized through Fourier transform infrared (FTIR) spectroscopy and thermogravimetric analysis (TGA). In addition to this, small-amplitude oscillatory shear (SAOS) measurements were performed on gel-like dispersions. The resulting oleogels demonstrated suitable thermal resistance although the inclusion of acyl segments into the polymer structure reduces thermal stabilities. The values of the linear viscoelastic functions and their evolution with frequency for gel-like dispersions of chitosans N -acylated with decanoyl chloride or N - and O -acylated with palmitoyl chloride were very similar to those exhibited for non-biodegradable commercial greases. A significant decrease in the storage and loss moduli was detected as the carbon chain length in the acyl group decreases in both N -acylated and N - and O -acylated chitosans. Moreover, both moduli decrease when the acylation reaction time increases, as a result of a major chitosan acylation degree, which provides weaker gels.

Influence of polymer reprocessing cycles on the microstructure and rheological behavior of polypropylene/mineral oil oleogels

The overall objective of this work was to study the effect of reprocessing cycles of isotactic polypropylene (PP) on the rheological behavior and microstructure of gel-like dispersions in mineral oil. PP was subjected to 10 reprocessing cycles and oleogel samples were further prepared by using the mixing rheometry technique and characterized from a rheological point of view and polarized light optical microscopy (PLOM). Recycled polymer samples were also characterized by means of rheological measurements, differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) to evaluate the property changes induced by reprocessing. The values of different linear viscoelastic functions (elastic modulus and complex viscosity) of recycled PP decrease with the number of reprocessing cycles, which influences oleogel rheological response. An empirical exponential correlation between the storage modulus (G′) of PP samples and the plateau modulus (GNo) of oleogels has been proposed to predict the rheological behavior of oleogels. Results were explained considering the scission of PP chains induced by the thermomechanical reprocessing treatment applied.

Tribological, rheological, and microstructural characterization of oleogels based on EVA copolymer and vegetables oils for lubricant applications

This work deals with the development of oleogels based on conventional (SO) and high-oleic sunflower (HOSO) vegetable oils and ethylene–vinyl acetate copolymer (EVA) for lubricant applications. Particularly, the influence of EVA concentration on the tribological, rheological properties and microstructure of these oleogels was analyzed. The results showed that the evolution of linear viscoelasticity functions was similar to that found for lithium greases. The different fatty acid profile in vegetable oils tested exerted an important influence on friction and wear in the ball-on-plates contact. The friction coefficient values became lower when EVA content was decreased. The wear marks obtained after the frictional tests for EVA–SO oleogels significantly reduced the wear scars versus EVA–HOSO oleogels and it was similar to commercial grease.

Fractional dynamics in silk: From molecular picosecond subdiffusion to macroscopic long-time relaxation.

Structural relaxations in humid silk fibers exposed to tensile stress have been reported to take place on a very wide range of time scales from a few milliseconds to several hours. The time-dependence of the measured tensile force following a quasi-instantaneously applied external strain on the fibers can be understood in terms of a fractional viscoelastic relaxation function introducing memory effects by which the mechanical state of a fiber depends on its tensile history. An analog fractional relaxation also gives rise to the subdiffusion observed on picosecond time scales, which governs the mobility of the amorphous polymer chains and adsorbed water on the molecular level. The reduction of the subdiffusive memory effect in stretched fibers compared to native fibers is consistent with the higher order of the polymers in the stretched state.

Characterization, stability and rheology of highly concentrated monodisperse emulsions containing lutein

Highly concentrated oil-in-water (O/W) emulsions, also called high internal (or dispersed) phase emulsions (HIPEs), containing lutein, were prepared using a two-stage process: membrane emulsification (ME) and further vacuum evaporation. Monodisperse HIPEs with controlled droplet size, a water volume fraction (fw) of 0.25, and encapsulation efficiency (EE) up to 97% were obtained. Membranes such as Shirasu porous glass (SPG), ceramic, and metallic were used in the first stage, yielding emulsions with fw of 0.84 and controlled droplet size. Final concentrated emulsions (fw = 0.25) were obtained by vacuum evaporation.Emulsions were formulated with two different food-grade oils (soybean oil and miglyol) and a non-ionic surfactant Tween 20, 2% (w/w). Sodium carboximethylcellulose (CMCNa) in the range of 0.1–0.5 % (w/w) was used as hydrocolloid stabilizer.Emulsions were characterized in terms of rheology, stability, droplet mean diameter, and efficiency of lutein encapsulation. Rheological properties of HIPEs and dilute emulsions resulting from ME stage were also compared.Results showed that emulsion viscosity, as well as their rheological properties, depended greatly on oil droplet diameter and dispersed phase concentration. However, the effect of oil droplet diameter on viscoelastic behavior was considerably larger for HIPEs than for dilute emulsions. CMCNa increased emulsion viscosity and also improved stability of oil droplets. The highest viscosity value and dynamic viscoelastic functions were obtained for HIPEs with the smallest droplet mean diameter. HIPEs exhibited high stability and large creaming resistance making them suitable for their use in functional foods or cosmetic products.

Influence of pH on mechanical relaxations in high solids LM-pectin preparations

The influence of pH on the mechanical relaxation of LM-pectin in the presence of co-solute has been investigated by means of differential scanning calorimetry, ζ-potential measurements and small deformation dynamic oscillation in shear. pH was found to affect the conformational properties of the polyelectrolyte altering its structural behavior. Cooling scans in the vicinity of the glass transition region revealed a remarkable change in the viscoelastic functions as the polyelectrolyte rearranges from extended (neutral pH) to compact conformations (acidic pH). This conformational rearrangement was experimentally observed to result in early vitrification at neutral pH values where dissociation of galacturonic acid residues takes place. Time–temperature superposition of the mechanical shift factors and theoretical modeling utilizing WLF kinetics confirmed the accelerated kinetics of glass transition in the extended pectin conformation at neutral pH. Determination of the relaxation spectra of the samples using spectral analysis of the master curves revealed that the relaxation of macromolecules occurs within ∼0.1s regardless of the solvent pH.

Natural fiber composite: Challenges simulating inelastic response in strain-controlled tensile tests

Problems occurring, when nonlinear time-dependent material model with parameters identified in creep tests is applied to simulate high-strain response in strain-controlled tests, are described and analyzed. Reasons for discrepancies with experimental loading curves are revealed. Presented numerical/experimental examples deal with three bio-based composites showing highly nonlinear behavior due to damage, nonlinear viscoelasticity and viscoplasticity. Schapery's approach for viscoelasticity and Zapas' model for viscoplasticity are used. The model is generalized to include microdamage effect. It is shown that the main problem in simulations at high stresses is the reliability of data from creep test for model identification in this region because creep rupture limits the available data region and extrapolation to higher stresses is rather uncertain. Alternative solution is to employ relaxation tests at high strains to obtain the missing information. However, it would work only in absence of viscoplastic strains: viscoelastic relaxation functions cannot be determined by maintaining constant total strain if viscoplastic-strain is developing. Based on sensitivity analysis of composite response to variations of the elastic modulus, damage, viscoelastic and viscoplastic parameters, suggestions are made for improving (further “tuning”) the model in high stress region by using tensile stress–strain curves in quasi-static loading.

A comparison of nanoindentation creep deformation characteristics of hydrothermal vent shrimp (Rimicaris exoculata) and shallow water shrimp (Pandalus platyceros) exoskeletons

Abstract

The role of the reference temperature in the construction of generalized viscoelastic functions for predicting damping properties of epoxy polymer

The role of the reference temperature in the construction of generalized viscoelastic functions for predicting damping properties of epoxy polymer