A note on viscoelastic materials that can age

Materials can stress relax for a variety of reasons, for example stress relaxation in classical viscoelastic bodies and that due to aging or damage. Here, within the context of a specific model we show that the stress relaxation that is characteristic of viscoelasticity is distinctly different from that of aging.     

Finite viscoelasticity and viscoplasticity of semicrystalline polymers

Observations are reported on low-density polyethylene in uniaxial tensile and compressive tests with various strain rates and in tensile and compressive relaxation tests with various strains. A constitutive model is developed for the time-dependent response of a semicrystalline polymer at arbitrary three-dimensional deformations with finite strains. A polymer is treated as an equivalent network of chains bridged by junctions (entanglements between chains in the amorphous phase and physical cross-links at the lamellar surfaces). Its viscoelastic behavior is associated with separation of active strands from temporary junctions and merging of dangling strands with the inhomogeneous network. The viscoplastic response is attributed to sliding of junctions between chains with respect to their reference positions. Constitutive equations are derived by using the laws of thermodynamics. The stress–strain relations involve 6 material constants that are found by matching the observations.      

Hamiltonian and Lagrangian theory of viscoelasticity

The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity.

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Effect of alkali metal ions on the viscoelasticity of concentrated kappa-carrageenan and agarose gels

The effect of the addition of the monovalent cations Li⁺, Na⁺, K⁺, and Cs⁺ on the gelation of agarose and kappa-carrageenan aqueous gels has been studied by the measurement of longitudinal vibration. The dynamic Youngs's modulusE of 2% w/w agarose and 0.4–6% w/w kappa-carrageenan gels containing the alkali metal salt LiCl, NaCl, KCl or CsCl of various concentrations from 0 to 4.5 mol/l has been measured at various temperatures. By the addition of the alkali metal salt, the value ofE for agarose gels is influenced only slightly, while for kappa-carrageenanE is increased substantially. Kappa-carrageenan has many sulphate groups. The addition of the alkali metal ions screens the electrostatic repulsion between these groups. As a result of this, the helical structure of kappa-carrageenan is stabilised and the helices may form densely packed aggregates, so increasingE. In contrast, agarose has a naturally stable molecular structure and therefore, the structure and henceE is not sensitive to added ions. The K⁺ and Cs⁺ ions increaseE more than Li⁺ and Na⁺ for kappa-carrageenan gels. This is interpreted on the basis that these ions are either structure ordering or structure disordering ions for water.     

The influence of pre-loading and thermal recovery on the viscoelastic response of filled elastomers

Experimental data are reported in tensile relaxation tests on carbon black-filled natural rubber at strains up to 200%. Constitutive equations are derived for the time-dependent response of a particle-reinforced elastomer at finite strains. Adjustable parameters in the model are found by fitting observations. The effects on mechanical pre-loading and thermal recovery are analyzed on the material constants.     

A study of viscoelasticity and extrudate distortions of wood polymer composites

Natural fiber composites exhibit a characteristic surface tearing and extrudate distortions upon exiting from extrusion dies. This type of defect is characterized by highly rough, cracked, and distorted extrudate surface. In this study, the extrudate distortions and viscoelastic nature of metallocene-catalyzed polyethylene (mPE)/wood flour composites have been investigated. As the wood flour loading increases the region of linear viscoelasticity shortens. The first normal stress difference decreases, while the storage modulus increases. It was observed that increasing the wood flour loading up to 50 wt% aggravated the surface tearing; however, 60 wt% wood flour in mPE completely eliminated the surface defect. It was also found that increasing the shear rate improved the surface appearance of the filled compounds. This is due to the increased wall slip velocity of the composites at high shear rates and wood filler loadings. Increasing the diameter of the die at the same aspect ratio generally provides more severe surface tearing. This paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

Molecular simulation guided constitutive modeling on finite strain viscoelasticity of elastomers

Viscoelasticity characterizes the most important mechanical behavior of elastomers. Understanding the viscoelasticity, especially finite strain viscoelasticity, of elastomers is the key for continuation of their dedicated use in industrial applications. In this work, we present a mechanistic and physics-based constitutive model to describe and design the finite strain viscoelastic behavior of elastomers. Mathematically, the viscoelasticity of elastomers has been decomposed into hyperelastic and viscous parts, which are attributed to the nonlinear deformation of the cross-linked polymer network and the diffusion of free chains, respectively. The hyperelastic deformation of a cross-linked polymer network is governed by the cross-linking density, the molecular weight of the polymer strands between cross-linkages, and the amount of entanglements between different chains, which we observe through large scale molecular dynamics (MD) simulations. Moreover, a recently developed non-affine network model (Davidson and Goulbourne, 2013) is confirmed in the current work to be able to capture these key physical mechanisms using MD simulation. The energy dissipation during a loading and unloading process of elastomers is governed by the diffusion of free chains, which can be understood through their reptation dynamics. The viscous stress can be formulated using the classical tube model (Doi and Edwards, 1986); however, it cannot be used to capture the energy dissipation during finite deformation. By considering the tube deformation during this process, as observed from the MD simulations, we propose a modified tube model to account for the finite deformation behavior of free chains. Combing the non-affine network model for hyperelasticity and modified tube model for viscosity, both understood by molecular simulations, we develop a mechanism-based constitutive model for finite strain viscoelasticity of elastomers. All the parameters in the proposed constitutive model have physical meanings, which are signatures of polymer chemistry, physics or dynamics. Therefore, parametric materials design concepts can be easily gleaned from the model, which is also demonstrated in this study. The finite strain viscoelasticity obtained from our simulations agrees qualitatively with experimental data on both un-vulcanized and vulcanized rubbers, which captures the effects of cross-linking density, the molecular weight of the polymer chain and the strain rate.     

Finite viscoelasticity of filled rubbers: the effects of pre-loading and thermal recovery

Received October 17, 2001 / Published online February 28, 2002     

Finite viscoelasticity of filled rubber: experiments and numerical simulation

Summary  Constitutive equations are derived for the viscoelastic behavior of particle-re-inforced elastomers at isothermal deformation with finite strain. A filled rubber is thought of as a composite medium where inclusions with high and low concentrations of junctions between chains are randomly distributed in the bulk material. The characteristic length of the inhomogeneities is assumed to be small compared to the size of the specimen and substantially exceed the radius of gyration for macromolecules. Inclusions with high concentration of junctions are associated with regions of suppressed mobility of chains that surround isolated clusters and/or the secondary network of filler. Regions with low concentration of junctions arise during the preparation process due to a heterogeneity in the spatial distribution of the cross-linker and the filler. With reference to the concept of transient networks, the time-dependent response of an elastomer is attribute d to thermally activated rearrangement of strands in the domains with low concentration of junctions. Stress–strain relations for particle-reinforced rubber are developed by using the laws of thermodynamics. Adjustable parameters in the constitutive equations are found by fitting experimental data in tensile relaxation tests for several grades of unfilled and carbon black-filled rubber. It is demonstrated that even at moderate finite deformations (with axial elongations up to 100%), the characteristic rate of relaxation is noticeably affected by strain. Unlike glassy polymers, where the rate of relaxation increases with longitudinal strain, the growth of the elongation ratio results in a decrease in the relaxation rate for natural rubber (unfilled or particle-reinforced). The latter may be explained by (partial) crystallization of chains in the regions with low concentration of junctions. Received 16 October 2001; accepted for publication 25 June 2002 Present address: A. D. Drozdov Department of Production, Aalborg University, Fibigerstraede 16, DK-9220 Aalborg, Denmark We would like to express our gratitude to Dr. K. Fuller (TARRC, UK) for providing us with rubber specimens and to Prof. P. Haupt and Dr. S. Hartmann (University of Kassel, Germany) for sending their experimental data. We are indebted to Mr. G. Seifritz for his assistance in performing mechanical tests. ADD acknowledges stimulating discussions with Prof. N. Aksel (University of Bayreuth, Germany).     

The effects of blood viscoelasticity on the pulse wave in arteries

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The recovery after bending of polycarbonate sheets

Summary The recovery after bending has been extensively studied for metal sheets. The data presented in this work show that in the case of polymeric materials viscoelastic effects play a very important role. In particular the influence of deformation rate, the time the sample is held under load and the recovery time is analysed. A master curve is obtained by proper modification of a recent analysis developed for metal sheets.With 10 figures     

Modeling photo-induced deformation of glassy splay-bend and twist nematic sheets

Azobenzene-containing glassy nematic sheets deform in response to light in a complicated way depending on director distribution. To quantify the large-deflected deformation, a theoretical model is developed for the sheets with typical splay-bend and twist director distributions. A third-order in-plane displacement assumption is adopted to characterize the effect of transverse shear deformation, and the necessity is discussed through two examples for which analytical solutions are obtainable. Though this work is an extension of the third-order shear deformable theory for anisotropic laminates, it involves some new ingredients such as varying spontaneous strains and special material symmetries. The results are expected useful for analysis and design of the glassy nematic sheets in actuation applications.     

Strain recovery of model immiscible blends: effects of added compatibilizer

The effect of added compatibilizer on the strain recovery of model immiscible blends after cessation of shear was studied. Blends were composed of polyisobutylene drops (up to 30% by weight) in a polydimethylsiloxane matrix, with viscosity ratio (viscosity of the drops relative to the matrix viscosity) ranging from 0.3 to 1.7. Up to 1% by weight of a PIB-PDMS diblock copolymer was added as compatibilizer. The ultimate recovery recorded after reaching steady-shear conditions increased significantly due to added compatibilizer. Furthermore, the compatibilizer also slowed down the kinetics of the recovery; however, unlike uncompatibilized blends, the recovery could no longer be captured by a single retardation time. The largest increase in ultimate recovery due to compatibilizer occurred at the lowest viscosity ratio. In contrast, the greatest slowing down of the recovery due to compatibilizer occurred at the highest viscosity ratio. The rheological data by themselves are insufficient to reach a definitive conclusion about the mechanism of compatibilizer action. The results are consistent with the effects of flow-induced gradients in compatibilizer concentration. An alternative constitutive modeling approach that captures compatibilizer effects in terms of an interfacial dilational elasticity can reproduce the recovery curves qualitatively, but some predictions of the model contradict experimental results.     

Specific hardening function definition and characterization of a multimechanism generalized potential-based viscoelastoplasticity model

Given the previous complete-potential structure framework [see Int. J. Plasticity 10(3) (1994) 263], together with the notion of strain- and stress- partitioning in terms of separate contributions of several submechanisms (viscoelastic and viscoplastic) to the thermodynamic functions (stored energy and dissipation), see [Int. J. of Plasticity 17(10) (2001) 1305], a detailed viscoelastoplastic multimechanism characterization of a specific hardening functional form of the model is presented and discussed. TIMETAL 21S is the material of choice as a comprehensive test matrix, including creep, relaxation, constant strain-rate tension tests, etc. are available at various temperatures. Discussion of these correlations tests, together with comparisons to several other experimental results, are given to assess the performance and predictive capabilities of the present model particularly with regard to the notion of hardening saturation as well as the interaction of multiplicity of dissipative (reversible/irreversible) mechanisms.     

Influence of viscoelasticity on drop deformation and orientation in shear flow: Part 1. Stationary states

The influence of matrix and droplet viscoelasticity on the steady deformation and orientation of a single droplet subjected to simple shear is investigated microscopically. Experimental data are obtained in the velocity–vorticity and velocity–velocity gradient plane. A constant viscosity Boger fluid is used, as well as a shear-thinning viscoelastic fluid. These materials are described by means of an Oldroyd-B, Giesekus, Ellis, or multi-mode Giesekus constitutive equation. The drop-to-matrix viscosity ratio is 1.5. The numerical simulations in 3D are performed with a volume-of-fluid algorithm and focus on capillary numbers 0.15 and 0.35. In the case of a viscoelastic matrix, viscoelastic stress fields, computed at varying Deborah numbers, show maxima slightly above the drop tip at the back and below the tip at the front. At both capillary numbers, the simulations with the Oldroyd-B constitutive equation predict the experimentally observed phenomena that matrix viscoelasticity significantly suppresses droplet deformation and promotes droplet orientation. These two effects saturate experimentally at high Deborah numbers. Experimentally, the high Deborah numbers are achieved by decreasing the droplet radius with other parameters unchanged. At the higher capillary and Deborah numbers, the use of the Giesekus model with a small amount of shear-thinning dampens the stationary state deformation slightly and increases the angle of orientation. Droplet viscoelasticity on the other hand hardly affects the steady droplet deformation and orientation, both experimentally and numerically, even at moderate to high capillary and Deborah numbers.     

A viscoelastic constitutive model of rubber under small oscillatory load superimposed on large static deformation considering the Payne effect

The viscoelastic behavior of carbon-black-filled rubber under small oscillatory loads superimposed on large static deformation is dealt with. In this class of problems, as the strain amplitudes of the load increase, the dynamic stiffness decreases, and this phenomenon is known as the Payne effect. Besides the effects of the static deformation and the frequencies of the superimposed dynamic load, the Payne effect is considered in this study. Influence factors are introduced in this model in order to consider the influence of static predeformation, the dynamic-strain-dependent properties, and frequency-dependent properties. For simplicity, separation of the three dominant variables, frequency, prestatic deformation, and dynamic amplitude of strain, is assumed. The Kraus model is used for describing the Payne effect. Dynamic tension tests are executed to obtain the model parameters and also for the verification of the proposed model. The suggested constitutive equation shows reasonable agreement with test data.     

The application of nonlinear gauge mathod to the analysis of local finite deformation in the necking of cylindrical bar

IntroductionNeckingandshearbandaretypicalfailureformationofplasticinstabilityofductilemetals,thephenomenaoflocalizeddeformationthatoftenaPPearinexperiments.W.JohnsonpointedoutthattheinvestigationoflocalizeddeformationcouldbetracedbacktoTresca'sexperimentalsummaryin1878.Fromtheseventies,manyresearcherswerefurthermoreconcernedaboutthisstUdyinthefieldofmaterial,mechanicsandengineering.Localdeformationexistsnotonlyintheprocessofmetalbutalsoingeotechnicssuchastheslideplaneinslopestability.Locali…