Computer simulations yield stresses

Eq. (22) is a key expression because it links the quantity F h)/R that can be determined directly in SFA experiments to the local stress available from computer simulations (see Sec. IV A1). It is also interesting that differentiating Eq. (22) yields... 

The yield stress can in principle be predicted from the polarization model. Rigorous calculation of the movement of one sphere in a flowing ER fluid under an electric field requires computation of the dielectric and hydrodynamic forces on that sphere. But these forces depend on the location and movement of all surrounding spheres, which are themselves responding to similar forces. Thus, one must solve a many-body problem, and this requires computer simulation. 

Fig. 7.18 Computer-simulation results on the stress-strain behavior of amorphous silicon showing yield phenomena, strain softening, steady-state flow, annealing and re-straining (from Argon and Demkowicz (2008) courtesy of TMS).

Usually, experiments and numerical simulations are rather complementary and it may be difficult to make meaningful comparisons. Nevertheless, there are two cases where this can be done. The first one is related to the mobility of non-dissociated dislocations. The computed Peierls stress for the non-dissociated shuffle screw dislocation is 4 GPa, in good agreement with the order of magnitude of the extrapolation at OK of flow stress measurements below 300°C (Section 2.3.2). In addition, the extrapolation at OK of yield stress measurements performed in the medium temperature range fits quite well the computed values of the Peierls stress for glide dislocations. Numerical simulations revealed that the thermally activated motion of non-dissociated screw dislocations was possible at 300 °C under an applied stress of 1.5 GPa, as reported from yield stress measurements (Section 2.3.2). The second case concerns the nucleation of dislocations. Molecular dynamics simulations of the dislocation nucleation from surface steps... 

Computer simulations of bijds, published by Stratford and co-workers, explore the fundamental interactions of the two liquids in the presence of the nanopartides and probe domain formation as a function of interaction parameters. The chosen experimental fluid parameters correspond to a mixture of short chain hydrocarbons with water, or alcohols with water, with viscosity >/ = 10 Pas, volume densityp = 103 kgm", and stress cr= 6 X lO Nm at T=27 C. The combined picture of these simulations and subsequent experiments define three characteristic features of bijds (1) an amorphous stmcture (2) the presence of bicontinuous fluid phases and (3) the onset of physical properties, such as yield stress, not present in droplet emulsions. 

A new model [109] for the deformation of glassy thermoplastics captures the behavior as a function of strain rate and temperature up to the yield point, based on a physical picture of a polymeric glass as a mosaic of nanoscale clusters of differing viscoelastic characteristics. It does not require computationally demanding simulations. It does, however, require a limited set of experimental stress-strain data to obtain values for its fitting parameters for a given material and to then allow both interpolations and extrapolations to be made to other testing conditions. 

Earlier we mentioned that Voth and co-workers conducted equilibrium MD simulations on [C2mim][N03] at 400 K and computed the self-diffusivity and shear viscosity using both a fixed charge and polarizable force field. They computed the viscosity not from integrating the stress-stress autocorrelation function as is normally done, but rather from integrating the so-called transverse current correlation function, details of which are foimd in a work by Hess. ° They used the standard Einstein formula (Eq. [15]) for the self-diffusivity and were careful to ensure that diffusive behavior was achieved when computing the self-diffusivity. Their calculated values of ca. 1 x 10 m /s for the polarizable model and ca. 5 x 10 m /s are reasonable. The finding that the polarizable model yielded faster dynamics than with the nonpolarizable model... 

At the air/liquid interface, viscous stress and surface tension are acting. In order to estimate the ratio of surface tension to stress contribution, the curvature is computed using height functions, cf. [5]. The accuracy, estimated by comparison with the known curvature of a sphere, is better than 1 %. At the air/high viscous liquid interface, a pressure jump of 449 Pa can be observed in the simulations, while the estimate yields 106 Pa contributed by viscous stress and 369 Pa contributed by surface tension. The sum of the estimated stresses is 456 Pa 1.5% less than predicted by the simulation. At the low viscous liquid/air interface, the stress contribution is only 1.2 Pa due to the low viscosity of the liquid. The surface tension contribution is estimated to be 350 Pa the simulated pressure jump is 100 Pa higher. 

The methods so far described for the estimation of elastic properties illustrate some principles, but are inaccurate due to the numerous geometric approximations and to the use of finite differences rather than true derivatives of the potential. A more ingenious method [11] introduces an external force and computes the energy expended by this force in deforming the system under investigation minimization of the total energy, internal plus external, directly yields the equilibrium structure under external stress, from which all the resulting strains can be extracted. For example, hydrostatic pressure is simulated by a barostat whose pressure work is FA V, where AT is the volume... 

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