The Model of Reflective Surface based on The Scattering Layer with Diffuse Substrate and Randomly Rough Fresnel Boundary

In this article, we describe the mathematical model of the reflective surface as a scattering layer with the diffuse substrate and randomly rough Fresnel boundary. This model opens the way for a physically correct description of the light reflection processes with polarization account and hence enables engineers and designers to obtain much more precise results in their work. The algorithm of Fresnel boundary modeling based on the method of mathematical expectations reduces calculation time by constructing the randomly rough surface only at the ray trajectory nodes instead of constructing realizations of a random field. As a part of the complete reflective surface model, the algorithm made it able for us to model the effect of the average lens emergence.

The effect of finite roughness size and bulk thickness on the prediction of rubber friction and contact mechanics

We present the numerical results for the viscoelastic and adhesive contribution to rubber friction for a tread rubber sliding on a hard solid with a randomly rough surface. In particular, the effect of the high- and low-frequency roughness power spectrum cut-off is investigated. The numerical results are then compared to the predictions of an analytical theory of rubber friction. We show that the friction coefficient for large load is given exactly by the theory while some difference between theory and simulations occur for small loads, due to a finite sample-size effects, whereas the contact area is almost unaffected by the low frequency cut-off. Finally, the role of a finite rubber thickness on viscoelastic friction and contact area is introduced and critically discussed. Interestingly, we show that classical rough contact mechanics scaling rules do not apply for this case.