Contact Mechanics and Adhesion between Elastic Bodies with Randomly Rough surfaces

Bo Persson
Forschungszentrum Jülich

Adhesion, friction and wear are major problems in many modern high-tech applications. In particular they limit both the fabrication yield and operation lifetime of many microelectromechanical (MEMS) devices. Thus, a good understanding of
microscale contact mechanics and adhesion in MEMS is fundamental for the design of such systems.

The van der Waals interaction is the weakest attractive force between solids on
the macroscopic level. But even this force that is so strong that under ideal conditions
the force _ 10000 N (the weight of a car) would be necessary to separate two bodies if the contact area between them would be of order 1 cm2. Thus the fundamental question related to adhesion is not why it is sometimes observed but rather why it is usually not observed. In this talk I will address this adhesion paradox.

I have developed a theory of contact mechanics and adhesion between an elastic solid and a hard randomly rough substrate. The theory takes into account that partial contact may occur between the solids on all length scales. I present numer-
ical results for the case where the substrate surface is self a ne fractal. When the
fractal dimension is close to 2, complete contact typically occur in the macro asperity contact areas, while when the fractal dimension is larger than 2.5, the area of (apparent) contact decreases continuously when the magnification is increased. An important result is that even when the surface roughness is so high that no adhesion
can be detected in a pull-o_ experiment, the area of real contact (when adhesion is included) may still be several times larger than when the adhesion is neglected. Since it is the area of real contact which determines the sliding friction force, the adhesion interaction may strongly a_ect the friction force even when no adhesion can be detected in a pull-o_ experiment.

I also briefly consider adhesion relevant to biological systems, e.g., flies, crickets and lizards, where the adhesive microstructures consist of arrays of thin fibers. The e_ective elastic modulus of the fiber arrays can be very small which is of fundamental importance for adhesion on smooth and rough substrates. I show how the adhesion depend on the substrate roughness amplitude and apply the theoretical results to lizards.

Back to Workshop II: Multiscale Modeling in Condensed Matter and Materials Sciences, including Mini-Workshop: Time Acceleration Methods in Atomistic Simulations