Project Details
Projekt
Modeling and Analysis of Adhesion Hysteresis Between Rough Surfaces
Subject Area
Mathematics
Mechanics
Mechanics
Term
since 2023
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 523956128
Surfaces are adhesive or "sticky" if breaking contact requires a finite force. At atomic scales, all surface interact via ubiquitous van-der-Waals interactions, that produce forces per unit area that are orders of magnitude larger than atmospheric pressure. This leads to strong adhesion of small objects, such as Gecko setae and engineered mimics. The strength of these interactions is commonly described by the intrinsic work of adhesion, i.e., the energy that is gained by microscopic interactions per surface area of intimate contact. While for hard substrates roughness limits this area to the highest protrusions, soft solids are sticky because they can deform to come into contact over a large portion of the rough topography. In this thermodynamic view of conforming contact, breaking adhesive contact becomes a fracture-mechanical problem. A common observation from soft contact is that the force needed to break the contact is typically much higher than the force measured during indentation. This observation contradicts expectations from theories that assume the contact follows thermodynamic equilibrium. Indeed, the surface roughness puts the adhesion problem in the "wiggly class" instead of the "Serfaty class" - in short, taking the energetic homogenization limit does not commute with solving the associated gradient flow evolution problem. This leads to a rate-independent contact-line hysteresis emerging from the interplay between a rapidly oscillating potential energy landscape and a viscous evolution. The main objectives in this project are as follows. We will study crack-front pinning and depinning effects on rough surfaces, starting with first-order approximate models, which include a fractional-order Laplacian to describe the elastic interaction in the material. This makes those models amenable to both analytic as well as efficient numerical treatment. The next step is then to extend these models to higher order. Here, comparison principles need to be proved, both to make these higher-order expansions amenable to rigorous mathematical study of pinning and depinning effects, but also to justify efficient numerical methods. Finally, we will examine the fully nonlinear models numerically by means of boundary-element methods. The pinning results obtained will be again compared to constructed sub- and super-solutions which give deterministic estimates on the emerging contact line hysteresis.
DFG Programme
Priority Programmes
