Elasticity viscous

As a result of simultaneous introduction of elastic, viscous and plastic properties of a material, a description of the actual state functions involves the history of the local configuration expressed as a function of the time and of the path. The restrictions, which impose the second law of thermodynamics and the principle of material objectivity, have been analyzed. Among others, a viscoplastic material of the rate type and a strain-rate sensitive material have been examined. 

The phenomenological approach does not preclude a consideration of the molecular origins of the characteristic timescales within the material. It is these timescales that determine whether the observation you make is one which sees the material as elastic, viscous or viscoelastic. There are great differences between timescales and length scales for atomic, molecular and macromolecular materials. When an instantaneous deformation is applied to a body the particles forming the body are displaced from their normal positions. They diffuse from these positions with time and gradually dissipate the stress. The diffusion coefficient relates the distance diffused to the timescale characteristic of this motion. The form of the diffusion coefficient depends on the extent of ordering within the material. 

Figure H3.2.2 Responses of an ideal elastic, viscous, and viscoelastic material to a sinusoidal deformation. 8, phase angle y, shear strain co, angular frequency o, shear stress.

Bandyopadhyay D, Sharma A, Shankar V (2008) Instabilities and pattern miniaturization in confined and free elastic-viscous bilayers. J Chem Phys 128 154909-154912... 

J. G. Oldroyd, Some Steady Flows of the General Elastic-viscous Liquid, Proc. Roy. Soc., A283, 115 (1965). 

Figure 3.41. Response of a viscoelastic monolayer to a sinusoidal area change (a). Peuiels (b), (c) and (d) represent the elastic, viscous lnd total response of the Interfaclal tension. Schematic.

The following deliberations help matters further. In the description of the flow behavior of viscous and viscoelastic materials, elastic, viscous and inertial forces... 

This is the response of the material to an osdUating stress or strain [1]. When a sample is constrained in, say, a cone and plate or concentric cylinder assembly, an oscillating strain at a given frequency a> (rad s ) (t = 2v r, where v is the frequency in cycles s or Hz) can be appHed to the sample. After an initial start-up period, a stress develops in response of the applied strain that is, it oscillates with the same frequency. The change of the sine waves of the stress and strain with time can be analysed to distinguish between elastic, viscous, and viscoelastic response. An analysis of the resulting sine waves can be used to obtain the various viscoelastic parameters, as discussed below. 

Doraiswamy et al. (1991) developed a non-linear rheological model combining elastic, viscous and yielding phenomena for filled polymers. The model predicts a modified Cox Merz relationship for filled melts ... 

As in other polymers, rubber concretes form three kinds of deformation elastic, viscous, and highly elastic in a stress field (Figure 2.42). 

FIGURE 2.42 Rheological models (a) viscous body, (b) elastic-viscous body, (c) viscous-elastic body. (Reprinted from Yu. Potapov, O. Figovsky, Yu. Borisov, S. Pinaev, and D. Beilin, Creep of Polymer Concrete at Compressive Loading, J. Scientific Israel Technological Advantages 5, nos. 1-2 (2003) 1-10. With permission.)... 

The applied stress results in the shear strain of the cube, i.e. the top face becomes shifted with respect to the bottom one by distance y. This displacement is numerically equal to the tangent of a tilt angle of the side face, i.e. it is equal to the relative shear strain, y, and at small strains tany y. The relationship between shear stress, x, and shear strain, y, and the rates of change in these quantities with time, dx/dt=x, dy/dt=y, represent mechanical behavior, which is the main subject in rheology. One usually begins the description of mechanical behavior with three elementary models, namely elastic, viscous, and plastic behavior. 

It also simulates military exposures to high-speed, nonpenetrating projectiles (Figure 53.6), even though the loading conditions are quite different from the cadaver database used to develop the model. This mechanical system characterizes the elastic, viscous, and inertial components of the torso. 

A smaller channel has a smaller flow characteristic length and time. Thus, Re is smaller and it is difficult to have inertia/viscous flow instability. Conversely, De becomes larger and it is easier to have elastic/viscous instability. The relative dominance of elastic to inertial effects is typified by the Elasticity number, El, i.e., the ratio of fluid elasticity to fluid inertia. El is expressed as... 

Figure 4.15 Representation of elastic, viscous and viscoelastic materials.

An oscillation in pressure, stress, particle displacement, particle velocity, etc., that is propagated in an elastic material, in a medium with internal forces (e.g., elastic, viscous), or the super-position of such propagated oscillations. Sound is also the sensation produced through the organs of hearing, usually by vibrations transmitted in a material medium, commonly air (Table S.3). See also Noise. 

Polymeric materials are all viscoelastic. The face each polymer shows to the observer—elastic, viscous flow, a combination of both—depends on the rate and duration of force application as well as on the nature of the material and external conditions including the temperature T. We discuss the nature of viscoelasticity below and additionally in Section 5. In general, properties of viscoelastics depend on time, in contrast to metals and ceramics. 

During compression within a die, there are a multitude of physical and mechanical processes occurring. These include powder flow, percolation, friction, lubrication, fracture, elastic, viscous, and plastic deformation. As a result of these transformations, a powder is converted into a tablet in a matter of some few hundred milliseconds. 

On the basis of changing values of characteristic viscosity [rj] (which are associated with the rotation and elastic - viscous deformation of macromolecular balls in a stream of solvent) and Hagging s constant one may determine the thermodynamic affinity of solvent to studied polymers or their mixes [2,3]. [rj] is a measure of additional losses of energy during spreading of the solution). Hagging s constant depends on a degree of interaction of polymeric molecules with solvent and is determined by the formula... 

For an isotropic, linearly viscous, incompressible mataial, the constitutive equation is easily obtained from Eq. (11.17) by invoking the elastic-viscous analogy the strain is replaced by the strain rate, E is replaced by the shear viscosity t], and V becomes 1/2 (for an incompressible material), giving (for the x direction)... 

A sinusoidal stress applied to an ideal elastic material produces a sinusoidal strain proportional to the stress amplitude and in phase with it. For ideal viscous materials the stress and strain are out of phase by 90°. Figure 15 gives an example of a stress-strain diagram for a sinusoidal stress applied to a real material. The amplitude of the deformation (strain) in response to the stress is proportional to that of the stress, but lags behind the strain curve by some angle 5 between 0 and 90°, depending on the elastic/viscous characteristic of the material. This behavior is usually analyzed by the use of complex variables to represent stress and strain. These variables, complex stress and complex strain, ie, x and y > respectively, are... 

Plot the strain-time behavior for the following systems Newtonian fluid, Hoo-kean solid, non-Newtonian fluid, a Maxwell fluid (strain is made up of an elastic viscous component), 7 = 7e + 7v... 

In this section, we describe the dynamic features of EOM effects. In particular, we focus on the response times to field-on and field-off these are the rise and decay times, respectively. In the case of the EO effects of nematic liquids, the rise and decay times exhibit the characteristic dependencies on voltage, and these characteristic times reflect the elastic, viscous, and dielectric properties of the materials. They have fully characterized the dynamics of the electric-field responses of LMM-LCs in experiments and established the theoretical background [6]. The dynamic features of the EOM effects in nematic gels are expected to differ from those of the EO effects in LMM-LCs, because the gels possess rubber elasticity and also have a different origin of the memory of the initial director. In addition, the dynamic properties give important information about the applicability of EOM effects in practical applications. 

The response of a viscoelastic material is generally represented as a model containing a combination of elastic, viscous and pure stress-relaxation properties. Then the relaxation function can be written as... 

Viscoelasticity of materials could be expressed in many ways. In this chapter, it will be described as the ability of the material to deform elastically, viscously and/or a combination of those. The interaction between the elastic and viscous behaviours could be explained with the help of the rheology of materials, as discussed in section 3.4. 

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