Anisotropic power law strain correlations in sheared amorphous 2D solids.

The local deformation of steadily sheared two-dimensional Lennard-Jones glasses is studied via computer simulations at zero temperature. In the quasistatic limit, spatial correlations in the incremental strain field are highly anisotropic. The data show power law behavior with a strong angular dependence of the scaling exponent, and the strongest correlations along the directions of maximal shear stress. These results support the notion that the jamming transition at the onset of flow is critical, but suggest unusual critical behavior. The predicted behavior is testable through experiments on sheared amorphous materials such as bubble rafts, foams, emulsions, granular packings, and other systems where particle displacements can be tracked.

Finite-element analysis of contact between elastic self-affine surfaces.

Finite-element methods are used to study nonadhesive, frictionless contact between elastic solids with self-affine surfaces. We find that the total contact area rises linearly with the load at small loads. The mean pressure in the contact regions is independent of load and proportional to the root-mean-square slope of the surface. The constant of proportionality is nearly independent of the Poisson ratio and roughness exponent and lies between previous analytic predictions. The contact morphology is also analyzed. Connected contact regions have a fractal area and perimeter. The probability of finding a cluster of area a(c) drops as a(-tau )(c ) where tau increases with a decrease in roughness exponent. The distribution of pressures shows an exponential tail that is also found in many jammed systems. These results are contrasted to simpler models and experiments.

Yield conditions for deformation of amorphous polymer glasses.

Shear yielding of glassy polymers is usually described in terms of the pressure-dependent Tresca or von Mises yield criteria. We test these criteria against molecular dynamics simulations of deformation in amorphous polymer glasses under triaxial loading conditions that are difficult to realize in experiments. Difficulties and ambiguities in extending several standard definitions of the yield point to triaxial loads are described. Two definitions, the maximum and offset octahedral stresses, are then used to evaluate the yield stress for a wide range of model parameters. In all cases, the onset of shear is consistent with the pressure-modified von Mises criterion, and the pressure coefficient is nearly independent of many parameters. Under triaxial tensile loading, the mode of failure changes to cavitation, and the von Mises criterion no longer applies.

Molecular and continuum boundary conditions for a miscible binary fluid.

We show that molecular-dynamics simulations can furnish useful boundary conditions at a solid surface bounding a two-component fluid. In contrast to some previous reports, convective-diffusive flow is consistent with continuum equations down to atomic scales. However, concentration gradients can produce flow without viscous dissipation that is inconsistent with the commonly used Navier slip condition. Also, differential wetting of the two components coupled to a concentration gradient can drive convective flows that could be used to make nanopumps or motors.

Molecular dynamics study of slip at the interface between immiscible polymers.

Nonequilibrium molecular dynamics simulations were used to study the structural properties and viscous response of interfaces in binary blends of symmetric polymers. The polymers were made immiscible by increasing the repulsion between unlike species. As the repulsion increased, the interface narrowed, and the fraction of chain ends in the interfacial region increased. The viscosity in the interfacial region eta(I) was lower than the bulk viscosity, leading to an effective slip boundary condition at the interface. As the degree of immiscibility increased, the interfacial viscosity decreased, and the slip length increased. When the radius of gyration of the chains was much larger than the interfacial width, eta(I) was independent of chain length. As predicted by de Gennes and co-workers, eta(I) corresponds to the bulk viscosity of chains whose radius of gyration is proportional to the width of the interfacial region.

Simple microscopic theory of Amontons's laws for static friction.

A microscopic theory for the ubiquitous phenomenon of static friction is presented. Interactions between two surfaces are modeled by an energy penalty that increases exponentially with the degree of surface overlap. The resulting static friction is proportional to load, in accordance with Amontons's laws. However, the friction coefficient between bare surfaces vanishes as the area of individual contacts grows, except in the rare case of commensurate surfaces. An area independent friction coefficient is obtained for any surface geometry when an adsorbed layer of mobile atoms is introduced between the surfaces. The predictions from our simple analytic model are confirmed by detailed molecular dynamics simulations.

Molecular origins of friction: the force on adsorbed layers.

Simulations and perturbation theory are used to study the molecular origins of friction in an ideal model system, a layer of adsorbed molecules sliding over a substrate. These calculations reproduce several surprising features of experimental results. In most cases, the frictional force on a solid monolayer has a different form from that observed between macroscopic solids. No threshold force or static friction is needed to initiate sliding; instead, the velocity is proportional to the force. As in experiments, incommensurate solid layers actually slide more readily than fluid layers. A comparison of experiment, simulation, and analytic results shows that dissipation arises from anharmonic coupling between phonon modes and substrate-induced deformations in the adsorbate.

Origin of stick-slip motion in boundary lubrication.

Molecular dynamics simulations of atomically thin, fluid films confined between two solid plates are described. For a broad range of parameters, a generic stick-slip motion is observed, consistent with the results of recent boundary lubrication experiments. Static plates induce crystalline order in the film. Stick-slip motion involves periodic shear-melting transitions and recrystllization of the film. Uniform motion occurs at high velocities where the film no longer has time to order. These results indicate that the origin of stick-slip motion is thermodynamic instability of the sliding state, rather than a dynamic instability as usually assumed.