Periodic deformation

Singamaneni S, Bertoldi K, Chang S, Jang JH, Young SL, Thomas EL, Boyce MC, Tsukruk VV (2009) Bifurcated mechanical behavior of deformed periodic porous solids. Adv Funct Mater 19 1426-1436... 

A. B. Metzner, J. L. White, and M. M. Denn, Constitutive Equation for Viscoelastic Fluids for Short Deformation Periods and for Rapidly Changing Flows Significance of the Deborah Number, AIChEJ. (12) 863,1966. 

Figure 18. Surface coverage in units of the complete -s/s monolayer for N2 on graphite near the melting transition from Monte Carlo simulations. Triangles 256 molecules forming an isolated patch subject to free surface boundary conditions. Circles (squares) 16 (64) molecules in the NPTensemble with deformable periodic boundary conditions. Inverted triangles same as circles but obtained from a cooling run starting in the fluid phase. (Adapted from Fig. 1 of Ref. 301.)...

The complete monolayer is modeled by an NVT ensemble with again deformable periodic boundary conditions, where fixed particle number N and fixed area V results in a constant coverage, which was chosen to be unity [102, 301]. This models the situation where either the physical or the grain boundaries prohibit a thermal expansion of the complete monolayer in the graphite plane. Also in this case, a melting transition to a modulated fluid occurs, but the transition is now located at about 87 K see the heat capacity anomaly in Fig. I9b. The transition does not show any noticeable hysteresis nor appreciable size effects, and the modulated fluid persists up... 

Figure 20. Center-of-mass fluctuations of N2 on graphite with respect to the nearest hexagon center (registry point) near the melting transition obtained from Monte Carlo simulations. Left-hand scales root-mean-square fluctuations perpendicular (circles) and parallel (triangles) to the surface plane. Right-hand scales average center-of-mass position above the surface plane (squares). Fluctuations are obtained (a) in the NPT ensemble and (ft) NVT ensemble at coverage unity, both with deformable periodic boundary conditions. (Adapted from Figs. 8 and 14 of Ref. 301.)...

At high strain rates, the deformation period is not less than the time required for stress waves to travel through the material this ensures spatial uniformity of the stress. 

Method Deformation period in s Glass transition temperature in °C... 

Metzner A, White JL, Denn MM (1966) Constitutive equations for viscoelastic fluids for short deformation periods and for rapidly changing flows significance of the Deborah number. AIChE J 12 863-866... 

Method Deformation period, s Glass-transition temperature, "C... 

It is interesting to compare the elasticity of a meniscus with another elasticity involved in wetting processes the CL spring constant. It was shown experimentally that the elasticity energy of a CL is not Hookean. By studying the relaxation of a CL deformed periodically, Ondarfuhu and Veyssie verified that this energy has a nonclassical expression given by ... 

By reference to the outline periodic table shown on p. (i) we see that the metals and non-metals occupy fairly distinct regions of the table. The metals can be further sub-divided into (a) soft metals, which are easily deformed and commonly used in moulding, for example, aluminium, lead, mercury, (b) the engineering metals, for example iron, manganese and chromium, many of which are transition elements, and (c) the light metals which have low densities and are found in Groups lA and IIA. 

The elastic and viscoelastic properties of materials are less familiar in chemistry than many other physical properties hence it is necessary to spend a fair amount of time describing the experiments and the observed response of the polymer. There are a large number of possible modes of deformation that might be considered We shall consider only elongation and shear. For each of these we consider the stress associated with a unit strain and the strain associated with a unit stress the former is called the modulus, the latter the compliance. Experiments can be time independent (equilibrium), time dependent (transient), or periodic (dynamic). Just to define and describe these basic combinations takes us into a fair amount of detail and affords some possibilities for confusion. Pay close attention to the definitions of terms and symbols. 

Figure 12.3A Progressive deformation in aluminum foil exposed to a cavitating fluid for successively longer periods. (A) No exposure (B) 5 s (C) 10 s (D) 20 s. (350x SEM.)...

The relationship between the increase in contact radius due to plastic deformation and the corresponding increase in the force required to detach submicrometer polystyrene latex particles from a silicon substrate was determined by Krishnan et al. [108]. In that study, Krishnan measured the increase in the contact area of the partieles over a period of time (Fig. 7a) and the corresponding decrease in the percentage of particles that could be removed using a force that was sufficient to remove virtually all the particles initially (Fig. 7b). 

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