Some remarks about a simple history dependent nonlinear viscoelastic model

A simple model for history dependent nonlinear viscoelasticity is considered. The determining equation governing shear motions is derived and investigated in the quasistatic approximation and under the traveling waves ansatz. Traveling waves are possible only if an inequality involving the constitutive parameters is satisfied. This fact is in contrast to what happens in viscoelasticity of the Kelvin–Voigt type. On the other hand, in the quasi-static approximation (classical creep and recovery experiments) the behavior of the history dependent model is similar to analogous rate dependent models.     

Spatial energy decay estimate in dynamical problems for a micropolar viscoelastic solid

We consider a linear micropolar viscoelastic solid occupying a domainB in dynamical conditions. First, on assuming thatB is of the kindB={∈R:x’ =(x ₁,x ₂)∈D(x ₃);x ₃∈R⁺⁺}, and that the body is subjected to boundary data different from zero only onD(0), we estimate for any fixedt>0, in terms of the initial and boundary data, the «energy» of the portions of the solid at distance greater thanz fromD(0)(g _t(z)) and its norm inL ¹(0,t) (G_t(z)). Moreover we show that, if there exists somez ₀≥0, such that past histories vanish onD(z) withz≥z ₀, then for any fixedt>0 the points (x’’, z) withz?z ₀≥Vt are at rest, while forz?z ₀≤Vt, G_t(z) decays withz?z ₀, the decay rate being described by the factor $1 - \frac{{z - z_0 }}{{Vt}}$ .V is a computable positive constant depending on the relaxation functions, the mass density and the microinertial tensor. Finally these last results are extended to more general domains under the hypothesis that the initial and boundary data have a bounded support. In our analysis we make use of a Maximal Free Energy which allows us to impose very mild restrictions on the relaxation functions.     

A mathematical model for impulse resistance welding

We present a mathematical model of impulse resistance welding. It accounts for electrical, thermal and mechanical effects, which are non‐linearly coupled by the balance laws, constitutive equations and boundary conditions. The electrical effects of the weld machine are incorporated by a discrete oscillator circuit which is coupled to the field equations by a boundary condition. We prove the existence of weak solutions for a slightly simplified model which however still covers most of its essential features, e.g. the quadratic Joule heat term and a quadratic term due to non‐elastic energy dissipation. We discuss the numerical implementation in a 2D setting, present some numerical results and conclude with some remarks on future research. Copyright © 2003 John Wiley & Sons, Ltd.     

Some connections between viscoelastic properties of PVC and plasticized PVC and molecular kinetics

A coupling model that has been shown in the past to be capable of relating macroscopically measured relaxation parameters to molecular ones has been presented. In this article the coupling model is applied to the analysis of stress relaxation data collected by Cama and Sternstein on PVC and plasticized PVC. The Kohlrausch-Williams-Watts form, exp — (t/τ*)^1?n, using n = 0.77 is found to be capable of describing the stress relaxation master curve at temperatures below the glass transition, T_g. From the temperature-independent apparent activation energy found by Cama and Sternstein, the primitive activation energy of the α-relaxation was calculated to be 7.5 kcal/mol, which is a reasonable value for the energy barrier to internal rotational isomerism in PVC. Support for this value is found from the data on two plasticized PVCs with different T_gs and apparent activation energies. By applying the coupling model in a similar manner, the primitive activation energies were found to be 8.5 kcal/mol for PVC plasticized with 6 pph dioctylphthalate and 7.7 kcal/mol for PVC plasticized with 6 pph tricresyl phosphate. Within experimental uncertainties, the three primitive activation energies can be considered to be the same. This finding is consistent with the physical basis for primitive activation energy and its identification with the internal rotation barrier, which should be independent of the type and amount of plasticizer in the system. Analysis of Cama and Sternstein's data on the effect of repeated stress aging on stress relaxation of quenched samples of PVC and plasticized PVC show that the coupling constant n increases systematically with each successive stress-aging cycle until it approaches the value for slow-cooled samples. These results are consistent with the notion that stress-aging changes the structural state of the glass in ways similar to physical aging.     

Viscoelasticity and birefringence of polyisobutylene

The complex Young's modulus, E*(ω), and the complex strain-optical coefficient, O*(ω), were measured for polyisobutylene (PIB) over a wide temperature range near and above its glass transition temperature. The master curves could be constructed well for each function with the method of reduced variables. The shift factor, a_T, for E*(ω) is the same as that for O*(ω). The ratio of the imaginary parts of O*(ω) and E*(ω), O″(ω)/E″(ω), takes an extremum, which has never been observed for other polymers. The relation between O*(ω) and E*(ω) cannot be described by a modified stress-optical rule (MSOR) which has been found valid for various polymers. The basic concept of the MSOR. i.e., the chain orientation and the orientation of flat monomer units in the stretch direction, is not sufficient to describe the behavior of PIB and another origin of stress, presumably due to the fluctuation of local stress, should be included. This term does not contribute to the birefringence. The main maximum of tan δ is ascribed to the relaxation of the chain orientation in contrast with many other polymers, such as polyisoprene and polycarbonate, for which the maximum of tan δ is ascribed to the rotational relaxation of monomer units. © 1995 John Wiley & Sons, Inc.     

On the simulation of the transient temperature field or some viscoelasticity problems by structural analysis program

An idea is presented to solve the parabolic differential equation by the hyperbolic differential equation. We can simulate and compute the transient temperature field problems by a structural analysis program. Using only a single structural analysis program, the users can compute both temperature and thermal stress distributions on the same finite element mesh. The method thus extends the application of the structural analysis programs which have been implemented widely. As an example, the transient temperature field problem of a square plate is computed. The result is consistent with the theoretical result. A similar method for simulating some viscoelasticity problems of Kelvin model is also presented.     

Rheological and electron microscopic characterization of aqueous carboxymethyl cellulose gels Part I: Rheological aging of aqueous gels of carboxymethyl cellulose in the free acid form (HCMC)

Aqueous gels of carboxymethylcellulose in the free acid form (HCMC) are obtained when dialyzed sodium carboxymethylcellulose (NaCMC)-gels are treated with a strongly acidic ion exchanger. These gels age rheologically. During the aging process (maximum 60 days), thixotropy and increased viscoelasticity occur. The rheological changes are measured by shear viscosity, coefficient of thixotropy H, complex dynamic shear modulus G^*, shear storage modulusG, shear loss modulusG, and tangent of the phase angle. The aging process is caused by the formation of quasi-crystalline microaggregates of HCMC which can be detected by electron microscopy (Part II).     

Influence of temperature on sage seed gum (Salvia macrosiphon) rheology in dilute and concentrated regimes

Herein, the influence of temperature (10°C, 30°C, 50°C, 70°C, and 90°C) on the dynamic (using amplitude sweep, frequency sweep, and temperature sweep tests), steady-shear, thixotropy (using hysteresis loop, single shear decay, and in-shear structural recovery tests), yield stress (static and dynamic yield stresses), and dilute solution (intrinsic viscosity ([η]), voluminosity (v_s), shape factor (v), Berry number (C[η]), and chain flexibility) properties of sage seed gum (SSG) have been studied. In this way, the effect of type of thermal procedure (iso-thermal and non-isothermal), temperature program (temperature gradient and temperature profile sweeps), and the rate of thermal program (1, 5, and 10°C/min) on the structural changes during heating and cooling stages were also investigated. Furthermore, the time–temperature superposition and Cox–Merz rules were tested on dynamic and steady shear rheological data.     

Theoretical analysis of microscopic oil displacement mechanism by viscoelastic polymer solution

The microscopic oil displacement mechanism in viscoelastic polymer flooding is theoretically analyzed with mechanical method. The effects of viscoelasticity of polymer solution on such three kinds of residual oil as in pore throat, in sudden expansion pore path, and in dead end are analyzed. Results show that the critical radius of mobile residual oil for viscoelastic polymer solution is larger than that for viscous polymer solution, which makes the oil that is immobile in viscous polymer flooding displaced under the condition of viscoelastic polymer solution. The viscous polymer solution hardly displaces the oil in dead ends. However, when the effect of viscoelasticity is considered, the residual oil in sudden expansion pore paths and dead ends can be partly displaced. A dimensionless parameter is suggested to denote the relative dominance of gravity and capillary pressure. The larger the dimensionless parameter, the more accurate the increment expressions.