Finite-size scaling in the interfacial stiffness of rough elastic contacts

The total elastic stiffness of two contacting bodies with a microscopically rough interface has an interfacial contribution K that is entirely attributable to surface roughness. A quantitative understanding of K is important because it can dominate the total mechanical response and because it is proportional to the interfacial contributions to electrical and thermal conductivity in continuum theory. Numerical simulations of the dependence of K on the applied squeezing pressure p are presented for nominally flat elastic solids with a range of surface roughnesses. Over a wide range of p, K rises linearly with p. Sublinear power-law scaling is observed at small p, but the simulations reveal that this is a finite-size effect. We derive accurate, analytical expressions for the exponents and prefactors of this low-pressure scaling of K by extending the contact mechanics theory of Persson to systems of finite size. In agreement with our simulations, these expressions show that the onset of the low-pressure scaling regime moves to lower pressure as the system size increases.Comment: Supplementary material is available at arXiv:1210.4255, 5 pages, 3 figure

Elastic contact between self-affine surfaces: Comparison of numerical stress and contact correlation functions with analytic predictions

Contact between an elastic manifold and a rigid substrate with a self-affine fractal surface is reinvestigated with Green's function molecular dynamics. Stress and contact autocorrelation functions (ACFs) are found to decrease algebraically. A rationale is provided for the observed similarity in the exponents for stress and contact ACFs. Both exponents differ substantially from analytic predictions over the range of Hurst roughness exponents studied. The effect of increasing the range of interactions from a hard sphere repulsion to exponential decay is analyzed. Results for exponential interactions are accurately described by recent systematic corrections to Persson's contact mechanics theory. The relation between the area of simply connected contact patches and the normal force is also studied. Below a threshold size the contact area and force are consistent with Hertzian contact mechanics, while area and force are linearly related in larger contact patches.Comment: 12 pages, 9 figure

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.Comment: 9 pages, 8 figures, revte

Simulations of the Static Friction Due to Adsorbed Molecules

The static friction between crystalline surfaces separated by a molecularly thin layer of adsorbed molecules is calculated using molecular dynamics simulations. These molecules naturally lead to a finite static friction that is consistent with macroscopic friction laws. Crystalline alignment, sliding direction, and the number of adsorbed molecules are not controlled in most experiments and are shown to have little effect on the friction. Temperature, molecular geometry and interaction potentials can have larger effects on friction. The observed trends in friction can be understood in terms of a simple hard sphere model.Comment: 13 pages, 13 figure

The autocorrelation function for island areas on self-affine surfaces

The spatial distribution of regions that lie above contours of constant height through a self-affine surface is studied as a function of the Hurst exponent H. If the surface represents a landscape, these regions correspond to islands. When the surface represents the height difference for contacting surfaces, the regions correspond to mechanical contacts in the common bearing area model. The autocorrelation function C(Delta r) is defined as the probability that points separated by Delta r are both within islands. The scaling of C has important implications for the stiffness and conductance of mechanical contacts. We find that its Fourier transform (C) over tilde (q) scales as a power of the wavevector magnitude q: (C) over tilde (q) alpha q(-mu) with mu = 2 + H rather than the value mu = 2 + 2H reported previously. An analytic argument for mu = 2 + H is presented using the distribution of areas contained in disconnected islands