Nonlinear Viscoelastic Behavior Research Articles

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.

Non-linear viscoelastic behavior of cooked white, brown, and germinated brown Thai jasmine rice by large deformation relaxation test

ABSTRACTStress relaxation tests at high strain were conducted on scoops of cooked white, brown, and germinated brown Thai jasmine rice using a King Mongkut’s Institute of Technology Ladkrabang test rig. The diameter of the scoop was 35 mm and the height was 10 mm. Non-linear modeling, consisting of four relaxation models, was applied to the data obtained for each type of rice. The modeling methods included Peleg and Normand’s; Yadav, Roopa, and Bhattacharya’s; Jaya and Durance’s; and Myhan, Markowski, and Daszkiewicz’s. The cooked white rice showed greater tenderness compared to the others. The toughness of the three types of cooked rice was not found to be different. The Myhan et al. model was the most accurate in describing the non-linear viscoelastic behavior of all types of cooked rice. The cooked brown rice showed the highest initial decay rate, but the lowest relaxation, lowest elasticity, and greatest viscosity. In contrast, the cooked white rice had opposite characteristics.

Non-linear viscoelastic behavior of polymer melts interpreted by fractional viscoelastic model

Very recently, researchers dealing with constitutive law pertinent viscoelastic materials put forward the successful idea to introduce viscoelastic laws embedded with fractional calculus, relating the stress function to a real order derivative of the strain function. The latter consideration leads to represent both, relaxation and creep functions, through a power law function. In literature there are many papers in which the best fitting of the peculiar viscoelastic functions using a fractional model is performed. However there are not present studies about best fitting of relaxation function and/or creep function of materials that exhibit a non-linear viscoelastic behavior, as polymer melts, using a fractional model. In this paper the authors propose an advanced model for capturing the non-linear trend of the shear viscosity of polymer melts as function of the shear rate. Results obtained with the fractional model are compared with those obtained using a classical model which involves classical Maxwell elements. The comparison between experimental data and the theoretical model shows a good agreement, emphasizing that fractional model is proper for studying viscoelasticity, even if the material exhibits a non-linear behavior.

Periodic response predictions of beams on nonlinear and viscoelastic unilateral foundations using incremental harmonic balance method

Buildings, railway tracks, drill strings and off-shore pipelines are all treated as structures on elastic foundations in order to study their response behavior in many engineering applications. Also, flexible polyurethane foams used for cushioning in furniture, foot-ware, and automotive industries serve as foundations, and exhibit complex nonlinear viscoelastic behavior. It is challenging to develop models of systems that include these foam-like materials and are able to predict the behaviour over a wide range of loading conditions. Even when using the simpler models commonly utilized in the literature, it is computationally expensive to predict the steady-state response of these structures to static and harmonic loads. In this work a pinned-pinned beam interacting with a viscoelastic foundation which can react both in tension and compression, or in compression alone is considered. The model developed here is capable of predicting the response to static as well as dynamic forces, whether they are concentrated or distributed. If the foundation reacts only in compression, the contact region changes with beam motion and the estimation of the unknown contact region is embedded into the iterative solution procedure. The steady-state solution is expressed as the sum of an arbitrary number of modes of an undamped pinned-pinned beam and Galerkin method is used to derive equations for the modal amplitudes. Incremental harmonic balance is used to make the steady-state frequency response predictions more efficient and a pseudo arc-length continuation technique is used to track both stable and unstable solution branches. By using these computationally efficient solution approaches, it is possible to explore a much wider variety of loading conditions and also quickly determine the number of modes required for convergence of the periodic solution. By using this solution method, the influence of various system parameters on the response of the beam is studied.

Evaluation of earthquake ground motion and site effects in the Thessaloniki urban area by 3D finite-fault numerical simulations

In this study earthquake ground motion in the Thessaloniki urban area is evaluated using a 3D spectral element numerical approach. The availability of detailed geotechnical/geophysical data from past microzonation studies together with the seismological information regarding the relevant fault sources allowed for the creation of a large-scale 3D numerical model. The latter is suitable for generating finite-fault physics-based ground shaking scenarios within the city of Thessaloniki up to maximum frequencies of about 1.5 Hz. As a representative case study, the simulation of the historical MW 6.5 June 20th 1978 Volvi earthquake is addressed. The results show that reasonable estimates can be obtained in terms both of ground motion time histories at the only available strong motion station and of spatial distribution of peak ground motion parameters, as compared to the regional map of macroseismic intensity and to the predictions of attenuation laws. The numerical model is, then, used to provide insights into 3D site effects occurring in the city of Thessaloniki, by showing the comparison between synthetic and experimental Standard Spectral Ratios (SSR) as well as the effect of non-linear visco-elastic soil behavior and the spatial variability of amplification factors with respect to outcrop bedrock basement. The results of this study demonstrate the potentialities of 3D physics-based numerical modeling for deterministic-based seismic hazard assessment studies in large urban areas characterized by complex geological configurations, such as the Thessaloniki area.

A non-linear viscoelastic model to describe the mechanical behavior's evolution of biodegradable polymers during hydrolytic degradation

The biodegradable triblock copolymer PLA-b-PEG-b-PLA presents, in its initial state, a non-linear viscoelastic behavior. Its mechanical properties evolves during the in vitro degradation process. Tensile and relaxation tests are performed at 2%, 4% and 6% of load strain for different degradation steps. In order to describe the behavior of the polymer during degradation, an adaptive quasi-linear viscoelastic model is considered. In a first step, the model calibrated on the non-degraded state, perfectly fits the load and relaxation curves for every strain. Then, based on considerations about the preservation of the normalized relaxation curves over degradation time, the adaptive quasi-linear viscoelastic model is adapted to degradation. A degradation parameter that drives the mechanical degradation kinetics is deduced for every tested degradation states. A physically motivated model is finally used to describe the degradation parameter at every degradation step. The whole constitutive model is very accurate to fit the mechanical curves at every strain during degradation.

Linear and non-linear viscoelastic behavior of SBS and LDPE modified bituminous mastics

This article compares bituminous mastics modified by either the tri-block copolymer styrene-butadiene-styrene (SBS) or low density polyethylene (LDPE). Linear and non-linear oscillatory measurements were conducted at 25 and 55°C, taken as representative of the medium and high in-service temperatures, respectively. For 3wt.% polymer, distinct rheological responses were found. The LDPE-mastic showed enhanced linear complex shear modulus and elasticity at 55°C. Conversely, if subjected to deformations beyond the linear viscoelasticity (LVE) limit, the SBS-mastic presented an improved capacity of complex modulus recovery, at 25°C, when it returned to the LVE regime.

Viscoelastic behaviour and modelling of nano and micro TiO2 powder-epoxy resin composites

Epoxy resin composites reinforced with different weight fractions of TiO2 micro-particles 0.2μm in size (1%, 5%, 10%, 15%wt) and of TiO2 nano-particles 21nm in size (0.5%, 1%, 3%wt) were manufactured. The quasi-static mechanical properties of both nano-composites and micro-composites were investigated and compared through tensile testing. The experimental results were predicted and the degree of matrix-particle adhesion and particle dispersion were evaluated, by the Property Prediction Model (PPM) developed by the first author. The composites were also subjected to creep-recovery tests as well as to relaxation tests in order to investigate their viscoelastic behaviour. The experiments were carried out at different filler-weight fractions and loading conditions. Non-linear viscoelastic behaviour was observed in all cases and appropriate models were applied in order to describe, and/or predict the viscoelastic behaviour of all materials tested. A fair agreement between experimental results and theoretical predictions was observed for both viscoelastic and static results.

Rheological characterization of triglyceride shortenings

The rheological properties of shortenings with similar physicochemical characteristics but diverse functionality were investigated under small and large oscillatory shear. Particular attention was drawn to the mechanical behavior of roll-in shortenings, characterized for resisting work softening and forming continuous fat thin films during dough lamination and sheeting. All shortenings displayed low-frequency dependence, reminiscent of viscoelastic solids where the storage modulus is higher than the loss modulus, and displayed a comparable linear envelope, encompassing relatively small shear strains, such as those encountered in other fat systems. Linear elastic moduli and yield stress, previously used to designate roll-in functionality, remained unremarkable. In contrast, nonlinear viscoelastic behavior of roll-in shortenings differed considerably from all-purpose commercial shortenings. Lissajous–Bowditch curves suggested less local intracycle strain stiffening and less average intercycle strain softening for roll-in shortenings than other shortenings. Likewise, their Fourier spectra indicated a gradual evolution of the third harmonic into the nonlinear regime characterized by higher slopes. The third and fifth harmonics grew monotonically, and the third overtone leveled off and showed no stress decays unlike other samples, suggesting a marked ability of roll-in shortenings to withstand deformation at high stresses. Conversely, the dissipative energy scaled in a similar fashion for all shortenings. Moreover, roll-in shortenings displayed enhanced thixotropic behavior supported by lower power law indexes and prompt structural rebuilding after steady shear cessation. Overall, these rheological signatures facilitated the differentiation among the utilization of shortenings and correlated well with the functionality of roll-in shortenings.

Micromechanical investigation of creep-recovery behavior of carbon nanotube-reinforced polymer nanocomposites

Creep-recovery behavior of polymer nanocomposites reinforced by carbon nanotubes (CNTs) is investigated using a 3-dimensional unit cell-based micromechanical model. The representative volume element (RVE) of the model consists of three phases including aligned CNTs, polymer matrix and CNT/polymer interphase formed due to non-bonded van der Waals interaction. The CNTs and polymer are assumed to be as transversely isotropic elastic and isotropic nonlinear viscoelastic materials, respectively. The effects of volume fraction and diameter of the CNTs, loading level and interphase including the materials behavior and size on the creep-recovery strain of the nanocomposite are examined. The predicted elastic and creep-recovery responses for pure polymer and CNT-reinforced polymer nanocomposite are found to be in good agreement with available experiment. Also, the isochronous stress–strain curves during the creep cycle for the nanocomposite under transverse and axial loadings are presented. The results clearly demonstrate that the overall transverse creep strain is dependent on the polymer nonlinear viscoelastic behavior and interphase material, as the applied loading increases. The results also reveal that the overall behavior of the nanocomposite is similar to the elastic response in the axial direction. Moreover, the isochronous stress–strain curves are extracted for biaxial and triaxial loading.

Nonlinear effects in deformation of filled elastomers with nanodimensional fillers

Various nonlinear effects manifesting themselves in the deformation of filled elastomers are analyzed, and the advantages and restrictions in the use of several constitutive relations proposed to describe the nonlinear viscoelastic behavior of the materials under study are discussed. We also note that further development of models of nonlinear deformation of filled elastomers under finite strains, which would permit describing their deformation properties more completely, is highly desirable.

Bio-Based Resin Reinforced with Flax Fiber as Thermorheologically Complex Materials.

With the increase in structural applications of bio-based composites, the study of long-term creep behavior of these materials turns into a significant issue. Because of their bond type and structure, natural fibers and thermoset resins exhibit nonlinear viscoelastic behavior. Time-temperature superposition (TTS) provides a useful tool to overcome the challenge of the long time required to perform the tests. The TTS principle assumes that the effect of temperature and time are equivalent when considering the creep behavior, therefore creep tests performed at elevated temperatures may be converted to tests performed at longer times. In this study, flax fiber composites were processed with a novel liquid molding methacrylated epoxidized sucrose soyate (MESS) resin. Frequency scans of flax/MESS composites were obtained at different temperatures and storage modulus and loss modulus were recorded and the application of horizontal and vertical shift factors to these viscoelastic functions were studied. In addition, short-term strain creep at different temperatures was measured and curves were shifted with solely horizontal, and with both horizontal and vertical shift factors. The resulting master curves were compared with a 24-h creep test and two extrapolated creep models. The findings revealed that use of both horizontal and vertical shift factors will result in a smoother master curves for loss modulus and storage modulus, while use of only horizontal shift factors for creep data provides acceptable creep strain master curves. Based on the findings of this study, flax/MESS composites can be considered as thermorheologically complex materials.

Multi-material 3-D viscoelastic model of a transtibial residuum from in-vivo indentation and MRI data

Although the socket is critical in a prosthetic system for a person with limb amputation, the methods of its design are largely artisanal. A roadblock for a repeatable and quantitative socket design process is the lack of predictive and patient specific biomechanical models of the residuum. This study presents the evaluation of such a model using a combined experimental–numerical approach. The model geometry and tissue boundaries are derived from magnetic resonance imaging (MRI). The soft tissue non-linear elastic and viscoelastic mechanical behavior was evaluated using inverse finite element analysis (FEA) of in-vivo indentation experiments. A custom designed robotic in-vivo indentation system was used to provide a rich experimental data set of force versus time at 18 sites across a limb. During FEA, the tissues were represented by two layers, namely the skin-adipose layer and an underlying muscle-soft tissue complex. The non-linear elastic behavior was modeled using 2nd order Ogden hyperelastic formulations, and viscoelasticity was modeled using the quasi-linear theory of viscoelasticity. To determine the material parameters for each tissue, an inverse FEA based optimization routine was used that minimizes the combined mean of the squared force differences between the numerical and experimental force-time curves for indentations at 4 distinct anatomical regions on the residuum. The optimization provided the following material parameters for the skin-adipose layer: [c=5.22kPam=4.79γ=3.57MPaτ=0.32s] and for the muscle-soft tissue complex [c=5.20kPam=4.78γ=3.47MPaτ=0.34s]. These parameters were evaluated to predict the force–time curves for the remaining 14 anatomical locations. The mean percentage error (mean absolute error/ maximum experimental force) for these predictions was 7±3%. The mean percentage error at the 4 sites used for the optimization was 4%.

Dynamic tensile properties of bovine periodontal ligament: A nonlinear viscoelastic model

As a support to the tooth, the mechanical response of the periodontal ligament (PDL) is complex. Like other connective tissues, the PDL exhibits non-linear and time-dependent behavior. The viscoelasticity of the PDL plays a significant role in low and high loading rates. Little information, however, is available on the short-term viscoelastic behavior of the PDL. Also, due to the highly non-linear stress–strain response, it was hypothesized that the dynamic viscoelastic properties of the PDL would be greatly dependent on the preload. Therefore, the present study was designed to explore the dynamic tensile properties of the bovine PDL as a function of loading frequency and preload. The in vitro dynamic tensile tests were performed over a wide range of frequencies (0.01–100Hz) with dynamic force amplitude of 1N and different preloads of 3, 5 and 10N. The generalized Maxwell model was utilized to describe the non-linear viscoelastic behavior of the PDL. The low loss factor of the bovine PDL, measured between 0.04 and 0.08, indicates low energy dissipation due to the high content of collagen fibers. Moreover, the influence of viscous components in the linear region of the stress–strain curve (10N preload) was lower than those of the toe region (3N preload). The data reported in this study could be used in developing accurate computational models of the PDL.

The peridynamic model of viscoelastic creep and recovery

Purpose – The purpose of this paper is to establish a peridynamic method in predicting viscoelastic creep behaviour with recovery stage and to find the suitable numerical parameters of peridynamic method. Design/methodology/approach – A rheological viscoelastic creep constitutive equation including recovery and an elastic peridynamic equation (with integral basis) are examined and used. The elasticity equation within the peridynamic equation is replaced by the viscoelastic equation. A new peridynamic method with two time parameters, i.e. numerical time and viscoelastic real time is designed. The two parameters of peridynamic method, horizon radius and number of nodes per unit volume are studied to get their optimal values. In validating this peridynamic method, comparisons are made between numerical and analytical result and between numerical and experimental data. Findings – The new peridynamic method for viscoelastic creep behaviour is approved by the good matching in numerical-analytical data comparison with difference of &lt; 0.1 per cent and in numerical-experimental data comparison with difference of 4-6 per cent. It can be used for further creep test which may include non-linear viscoelastic behaviour and creep rupture. From this paper, the variation of constants in Burger’s viscoelastic model is also studied and groups of constants values that can simulate solid, fluid and solid-fluid viscoelastic behaviours were obtained. In addition, the numerical peridynamic parameters were also manipulated and examined to achieve the optimal values of the parameters. Research limitations/implications – The peridynamic model of viscoelastic creep behaviour preferably should have only one time parameter. This can only be done by solving the unstable fluctuation of dynamic results, which is not discussed in this paper. Another limitation is the tertiary region and creep rupture are not included in this paper. Practical implications – The viscoelastic peridynamic model in this paper can serve as an alternative for conventional numerical simulations in viscoelastic area. This model also is the initial step of developing peridynamic model of viscoelastic creep rupture properties (crack initiation, crack propagation, crack branching, etc.), where this future model has high potential in predicting failure behaviours of any components, tools or structures, and hence increase safety and reduce loss. Originality/value – The application of viscoelastic creep constitutive model on peridynamic formulation, effect of peridynamic parameters manipulation on numerical result, and optimization of constants of viscoelastic model in simulating three types of viscoelastic creep behaviours.

Characterisation of filled rubber with a pronounced non‐linear viscoelasticity

AbstractThis contribution presents the characterisation of an incompressible carbon black‐filled elastomer as one characteristical example for highly filled rubber. It shows a strongly pronounced non‐linear viscoelastic behaviour and the most important characteristic is the extremely long relaxation time which has to be taken into account. The material model is developed with respect to uniaxial tension data. The basis in the development of a phenomenological model is given by the basic elasticity. For this evaluation the long term relaxation behaviour results in a complex experimental procedure. Therefore, special attention has to be paid according to an optimised experimental process in order to get the necessary reference data in an adequate and reproduceable way [1].With this model basis further investigations are taken into account concerning the time‐dependent viscoelasticity. Therefore, cyclic deformations from zero up to a maximum of deformation are considered for different strain rates. Furthermore, the relaxation behaviour is investigated for multiple strain levels. The phenomena which are observed in the experimental results yield in a purely viscoelastic model, based on a rheological analogous model consisting of an equilibrium spring and several Maxwell‐elements which contain nonlinear relations for the relaxation times of the dashpot elements [1,2].The material model's numerical realisation is accomplished in two ways. Because of its numerical simplicity especially according to the parameter identification the model is restricted only to the simple case of uniaxial tension. A second, alternative implementation is executed providing the benefit that more complex deformation conditions can also be taken into account. Therefore, the general, three‐dimensional finite model is implemented in an open‐source Finite Element library [3]. (© 2015 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Modelling asphalt concrete viscoelasticity with damage and healing

The behaviour under load of asphalt concrete (AC) was viewed as additively separable into viscoelastic and viscoplastic components, and the study focused on modelling the pre-peak response of the viscoelastic part under constant temperature conditions. Non-linear viscoelastic behaviour was first exposed in several test modes, and a constitutive theory was subsequently offered – potentially capable of capturing and reproducing the observations. The modelling was based on replacing applied stresses in the linear convolution formulation with effective stresses; it included a mechanism for simulating the following effects: (i) short-lasting damage, (ii) long-lasting damage, (iii) stiffening under compressive conditions and (iv) healing during recovery intervals. As an initial validation effort, the model’s reproducibility was assessed by calibration to a uniaxial compression experiment consisting of both small and medium strain levels. Next, the calibrated model was employed to forecast small-strain behaviour in a standard complex modulus test. The simulated results qualitatively agree with recently reported findings that challenge the existence of a linear viscoelastic domain for AC.

Bayesian uncertainty analysis of finite deformation viscoelasticity

The viscoelasticity of the dielectric elastomer, VHB 4910, is experimentally characterized, modeled, and analyzed using Bayesian uncertainty analysis. Whereas these materials are known for their large-field induced deformation and broad applications in smart structures, the rate-dependent viscoelastic effects are not well understood. To address this issue, we quantify both the hyperelastic and viscoelastic constitutive behavior and use Bayesian uncertainty analysis to assess several key modeling attributes. Specifically, we compare an Ogden-based phenomenological model to a nonaffine hyperelastic model and couple hyperelasticity to both linear and nonlinear viscoelasticity. The utilization of Bayesian statistics is shown to provide insight into quantifying nonlinear viscoelasticity behavior as a function of internal state variables. The results are validated experimentally in the finite deformation regime over a range of stretch rates spanning four orders of magnitude (6.7×10-5–0.67Hz). A unique set of hyperelastic parameters are identified, independent of the stretch rate. In addition, comparisons of the linear and nonlinear viscoelastic models demonstrate a reduction in modeling error by approximately a factor of three. Finally, the viscoelastic time constant is shown to produce an inverse stretch rate power law dependence regardless of which hyperelastic model is used.