We study the frictionless and non-adhesive contact between elastic and elasto-plastic solids with randomly rough surfaces.
Because of this roughness (inevitably present in most natural and engineering surfaces), when these solids are brought in contact,
the <real contact area> - islands on which two solids touch each other - presents only a small portion of the nominal contact area.
In the first part, we study (1) how this real contact area evolves with increasing pressure applied on the solids and (2) how this evolution and the morphology of contact
can be linked with material and surface properties. In this context, we will discuss some details of generation of synthetic fractal surfaces, their characterization and
the interplay of parameters: root mean squared height and slope, Nayak's parameter, Gaussianity, cutoff wavelengths and fractal dimension .
We will also briefly expose the numerical methods, that we use to carry out simulations of a mechanical boundary value problem with contact constraints:
a finite element method  and an FFT boundary element method . The numerical results will be compared with analytical models:
asperity based models [4,5] and Persson's contact theory .
In the second part, we will present new results on simulation of transport phenomena weakly coupled with mechanical contact resolution:
First, we will consider (3) leakage and percolation of a viscous fluid through the interface between rough surfaces.
Some generalization on the leakage regimes and the percolation limit will be suggested.
Afterwards, the problem of (4) the electric (thermal) transfer across the contact interface will be addressed by numerical and experimental study.
 Yastrebov, V.A., Anciaux, G., Molinari, J.F., From infinitesimal to full contact between rough surfaces: evolution of the contact area, Int. J. Solids Struct., 52:83-102 (2015).
 Yastrebov, V.A., Numerical Methods in Contact Mechanics, WILEY-ISTE (2013).
 Stanley, H.M., Kato, T., An FFT-based method for rough surface contact. J.Tribol. Trans. ASME 119, 481-485 (1997).
 Bush, A.W., Gibson, R.D., Thomas, T.R., The elastic contact of a rough surface. Wear 35 (1), 87-111 (1975).
 Carbone, G., Bottiglione, F., Asperity contact theories: do they predict linearity between contact area and load? J. Mech. Phys. Solids 56, 2555-2572 (2008).
 Persson, B.N.J., Theory of rubber friction and contact mechanics. J. Chem. Phys. 115, 3840-3861 (2001).