Homogenization shear

The behavior of constitutive equations may be investigated by prescribing particular deformations. Consider tbe simple homogeneous shear deformation... 

Fig. 9. Illustrating the "homogeneous shear model". In (a) the unit cell built on (a], a2, a3) is sheared and becomes (af, a2, azimuth a. In (b) the corresponding...

Molecular dynamics, in contrast to MC simulations, is a typical model in which hydrodynamic effects are incorporated in the behavior of polymer solutions and may be properly accounted for. In the so-called nonequilibrium molecular dynamics method [54], Newton s equations of a (classical) many-particle problem are iteratively solved whereby quantities of both macroscopic and microscopic interest are expressed in terms of the configurational quantities such as the space coordinates or velocities of all particles. In addition, shear flow may be imposed by the homogeneous shear flow algorithm of Evans [56]. 

The effect of driving shear stresses on the dislocations are studied by superimposing a corresponding homogeneous shear strain on the whole model before relaxation. By repeating these calculations with increasing shear strains, the Peierls barrier is determined from the superimposed strain at which the dislocation starts moving. 

Crystal dislocations were invented (circa. 1930) by Orowan, Prandtl, and Taylor to explain why pure metal crystals are soft compared with homogeneous shear strengths calculated from atomic theory. They do this very well. However, roughly 15 years later (circa 1945) it was found that pure semiconductor crystals (e.g., Ge and Si) have hardnesses at room temperature comparable with calculated homogeneous shear strengths. Furthermore, it was known... 

Flows with shear do not exhibit simple gradient transport. See, for example, the homogeneous shear flow results reported by Rogers et al. (1986). 

Nomura, K. K. and S. E. Elgobashi (1992). Mixing characteristics of an inhomogeneous scalar in isotropic homogeneous sheared turbulence. Physics of Fluids A Fluid Dynamics 4, 606-625. 

The monodisperse materials described hereafter were obtained with the Couette type cell designed by Bibette et al. [ 150,159]. It consists of two concentric cylinders (rotor and stator) separated by a very narrow gap (100 pm), allowing application of spatially homogeneous shear rates over a very wide range (from 0 to 14280 s ), with shearing durations of the order of 10 s. 

Mashayek, F. 1998. Droplet-tnrbnlence interactions in low-Mach-number homogeneous shear two-phase flows. J. Fluid Mechanics 376 163-203. 

Mashayek, F. 2000. Numerical investigation of reacting droplets in homogeneous shear turbulence. J. Fluid Mechanics 405 1-36. 

Mashayek, F. 2001. Velocity and temperature statistics in reacting droplet-laden homogeneous shear turbulence. J. Propulsion Power 77(1). 

Finally, close to Ta, an homogeneous shear of the BPA-PC film is observed. 

A single droplet of liquid deformed into a spheroid in a homogeneous shear flow field. 

Consider a single, freely suspended axisymmetric particle in a homogeneous shear flow held of an incompressible Newtonian liquid. The free suspension condition implies that the net instantaneous force and torque on the particle vanish. There is, however, a finite net force along the axis that one half of the particle exerts on the other, as shown schematically in Fig. 7.25. 

Consider an unbounded, incompressible, Newtonian fluid undergoing a homogeneous shear flow characterized by the position-independent velocity gradient dyadic G, which can be decomposed into symmetric and antisymmetric contributions S and A, respectively, as... 

As is well known, Einstein (1906, 1911) calculated the additional rate of mechanical energy dissipation engendered by the introduction of a single sphere into a homogeneous shear flow and ultimately obtained... 

Lumley has solved the equation system for homogeneous shear, and compared the results with homogeneous strain and homogeneous shear experiments. Lumley s model predicts that the time scale T grows without bound, so that homogeneous flows can never attain an equilibrium structure. Champagne et al. (C4) experiments are consistent with Lumley s notion, but Lumley s model does not predict the observed structure very well. Some improvements on Lumley s model based on Eq. (63) are suggested in Section V. 

Formation of large cavities, homogeneous shear of intervening ligaments... 

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