Viscoelastic body

Gels are viscoelastic bodies that have intercoimected pores of submicrometric dimensions. A gel typically consists of at least two phases, a soHd network that entraps a Hquid phase. The term gel embraces numerous combinations of substances, which can be classified into the following categories (2) (/) weU-ordered lamellar stmctures (2) covalent polymeric networks that are completely disordered (2) polymer networks formed through physical aggregation that are predominantly disordered and (4) particular disordered stmctures. 

From the results obtained in [344] it follows that the composites with PMF are more likely to develop a secondary network and a considerable deformation is needed to break it. As the authors of [344] note, at low frequencies the Gr(to) relationship for Specimens Nos. 4 and 5 (Table 16) has the form typical of a viscoelastic body. This kind of behavior has been attributed to the formation of the spatial skeleton of filler owing to the overlap of the thin boundary layers of polymer. The authors also note that only plastic deformations occurred in shear flow. 

In which element or model for a viscoelastic body will the elastic response be retarded by viscous resistance (a) Maxwell or (b) Voigt-Kelvin ... 

Gels are viscoelastic bodies, the rheological properties of which can be described by two parameters, the storage modulus (G, which is a measure of its elasticity) and the loss modulus (G", which is a measure of its viscous nature). The combined viscoelastic modulus (G ) is a measure of the overall resistance of a gel to deformation. These moduli are often highly dependent on the time-scale of deformation. Another important parameter of a food gel is its yield stress. 

The creep of a viscoelastic body or the stress relaxation of an elasacoviscous one is employed in the evaluation of T] and G. In such studies, the long-time behavior of a material at low temperatures resembles the short-time response at high temperatures. A means of superimposing data over a wide range of temperatures has resulted which permits the mechanical behavior of viscoelastic materials to be expressed as a master curve over a reduced time scale covering as much as twenty decades (powers of ten). 

Sols arc dispersions of colloidal particles in a liquid. Colloids arc nanoscaled entities dispersed in a fluid. Gels are viscoelastic bodies that have interconnected pores of submicrometric dimensions. A gel typically consists of at Icasl two phases, a solid network that entraps a liquid phase. Sol-gel technology is the preparation of ceramic, glass, or composite materials by the preparation of a sol, gelation of the sol. and removal of the solvent. 

Real polymeric materials are viscoelastic bodies. In a purely elastic material stresses a(t) are proportional to deformations e(t), and the coefficient of proportionality is Young s modulus E, i.e., at any time t... 

A Cole-Cole diagram is shown in Fig. 3.2. The experimental points in the G"- vs - G coordinate system fall lie closely on a half-circle, with the exception of a narrow time interval very close to the transition (gelation) time, t. This curve corresponds to simplest model of a linear viscoelastic body with one relaxation time. In this case, G ( ) is expressed as follows ... 

The model of a viscoelastic body with one relaxation time used above has one principal disadvantage it does not describe the viscous flow of the reactants before the gel-point at t < t. Thus it is important to use a more general model of a viscoelastic medium to interpret the results obtained. The model must allow for flow and may be constructed by combining viscous and viscoelastic elements the former has viscosity rp and the latter has a relaxation modulus of elasticity Gp and viscosity rp,... 

Example 3.3 Small Amplitude Oscillatory Motion of a Linear Viscoelastic Body... 

We wish to derive the steady state response of a linear viscoelastic body to an externally applied sinusoidal shear strain (dynamic testing) using the constitutive Eq. 3.3-8, which for this viscometric flow reduces to... 

Let the linear viscoelastic body be represented by a continuous spectrum of relaxation times,... 

Summary and Conclusions. Simple shear is by far the most important type of deformation in studies of viscoelastic bodies, because [for example] the absence of a volume change facilitates interpretation of the behavior in molecular terms (8). 

Figure 8-12 (A) Stress-Time and (B) Strain-Time Curves of a Viscoelastic Body...

Figure 8-14 (A) Creep Curve for an Ideal Viscoelastic Body and (B) Creep Curve for Butter...

EH Lee. Stress analysis in viscoelastic bodies. Quart Appl Math 13 183, 1955. 

In analogy with Maxwell mode of a viscoelastic body, stress relief at constant... 

The subject matter of this book is the response that polymers exhibit when they are subjected to external forces of various kinds. Almost without exception, polymers belong to a class of substances known as viscoelastic bodies. As the name implies, these materials respond to external forces in a manner intermediate between the behavior of an elastic solid and a viscous liquid. To set the stage for what follows, it is necessary to describe in very general terms the types of force to which the viscoelastic bodies are subjected. 

By considering a sinusoidal stress applied to a viscoelastic body, show that in-phase strain results in conservation of energy (work) whereas out-of-phase strain results in energy dissipation. 

The mechanical response of viscoelastic bodies such as polymers is poorly represented by either the spring or the dashpot. J. C. Maxwell suggested that a better approximation would result from a series combination of the spring and dashpot elements. Such a model, called a Maxwell element, is shown on the right in Figure 3-1. In describing tensile response with the Maxwell element, E, the instantaneous tensile modulus, characterizes the response of the spring while rjE, the viscosity of the liquid in the dashpot, defines the viscous... 

Viscous and Elastic Systems. When both viscosity and elasticity are present in the material, an additive combination of the two responses is needed. In the case of a drying film, the stresses are added, giving the result for a viscoelastic body ... 

Comninou, M. "Contact between Viscoelastic Bodies", Trans. ASME (J. Appl. Mech.) 43 (1976) 630. 

Let us illustrate the Boltzmann principle by considering creep. Suppose the initial creep stress, Oo= on a linear, viscoelastic body is increased sequentially to 0, 02- -On at times tj, t2...t , then according to the Boltzmann principle, the creep at time t due to such a loading history is given by... 

K-BKZ model for non-linear viscoelastic body proposed by Kaye... 

How can we explain such a double life The polymer behaves as a liquid when steadily affected by gravity over a long period of time (Figure C12.2 /). On the other hand, when the action of the force is very short (when hitting the floor. Figure C12.2 c), the reaction is elastic. This is viscoelasticity. In general, viscoelastic bodies tend to show a viscous response to a slowly changing force, and an elastic response to one which varies quickly. 

The hot-stretching was performed at the temperature where the tensile storage modulus at 10 Hz was 10 MPa [212°C]. The stress-strain curve at a strain rate of 0.05 s is shown in Fig. 9.21. The curve is a typical one for a viscoelastic body in a rubbery region. 

Polymers are not ideal energy elastic, but viscoelastic. In such cases, the deformation lags behind the applied stress. With ideal viscoelastic bodies, the resulting phase angle d in the corresponding vector diagram can be assumed constant, such that... 

The skeleton is a deformable elastic or viscoelastic body but sustains infinitesimal strains only. 

The correspondence principle states that for problems of a statically determinate nature involving bodies of viscoelastic materials subjected to boundary forces and moments, which are applied initially and then held constant, the distribution of stresses in the body can be obtained from corresponding linear elastic solutions for the same body subjected to the same sets of boundary forces and moments. This is because the equations of equilibrium and compatibility that are satisfied by the linear elastic solution subject to the same force and moment boundary conditions of the viscoelastic body will also be satisfied by the linear viscoelastic body. Then the displacement field and the strains derivable from the stresses in the linear elastic body would correspond to the velocity field and strain rates in the linear viscoelastic body derivable from the same stresses. The actual displacements and strains in the linear viscoelastic body at any given time after the application of the forces and moments can then be obtained through the use of the shift properties of the relaxation moduli of the viscoelastic body. Below we furnish a simple example. 

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