Rate of stretching

If V v = 0, e,s(l/2)m in two-dimensional (2D) flows and (2/3)1/2 in three-dimensional (3D) flows, where i = A,r/. The efficiency can be thought of as the specific rate of stretching of material elements normalized by a factor proportional to the square root of the energy dissipated locally. 

The first term on the right side of Equation 5 corresponds to the rate of stretching/squeezing and is sensitive to pore geometry. The sharper the constriction (i.e., high R /R ), the... 

Paul Is it length or is it stretch Does rate of stretch matter ... 

We conclude this section by pointing out an important relationship between the decay rate 7, the Lyapunov exponent A and the fractal dimension d of a one-dimensional self-similar fractal. In the context of fractals, the Lyapunov exponent is the rate of stretching given by... 

The behavior of LLDPE blends at constant rate of stretching, e, was examined at 150°C. The results are shown In Fig. 13 for Series I and II as well as in Fig. 14 for Series III. The solid lines In Fig. 13 represent 3n calc values computed from the frequency relaxation spectrtmi by means of Equation (36), while triangles Indicate the measured in steady state 3n values at y = 10 2 (s ), I.e. the solid lines and the points represent the predicted and measured linear viscoelastic behavior respectively. The agreement Is satisfactory. The broken lines In Fig. 13 represent the experimental values of the stress growth function In uniaxial extension, nE 3he distance between the solid and broken lines Is a measure of nonlinearity of the system caused by strain hardening, SH. 

Since, as mentioned, the behavior of the sample is affected by the rate of stretching, stress-strain curves are typically obtained at low strain rates. 

The last term is closely related to the rate of stretching of the springs in the molecular model beyond their thermal equilibnum lengths (DPL, Eq. (13.4-11)). It is thus an elastic contribution , in addition to that implicit in ll that does not appear in the equation for Newtonian fluids. Such a term has been included in the equation of change for temperature by Wiest [35]. If this last term is omitted, then the usual equation of change for temperature for Newtonian fluid mixtures is obtained ([11], Table 18.3-1). 

Consider a uniaxial tensile test, parallel to axis 1, say, in which at any instant the stretch is and the rate of stretching is X hence cr = cr, a-n = 0. It follows from equation (4.15) that the applied true stress cr may be expressed unambiguously as the sum of two distinct terms ... 

Chaotic motion generated by periodic flow represents an important dass of chaotic flows in general. Chaotic mixing is characterized by an exponential rate of stretching (as opposed to linear stretching in a non-diaotic flow) of fluid elements. As a fluid... 

Cold drawing has been observed at rates of stretch such that everywhere in the specimen the deformation is slow enough to be nearly isothermal, even in the transition zones at the ends of the neck. 

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