**Ongoing**

**Thin films:** Coatings are omnipresent. Surface coatings modify interaction with the surface they coat. Also, often to know the properties of materials experimentalists prepare a small amount of the stuff, not a half-space of it, and press probes into a layer of that stuff. The load-displacement characteristics are noted and the thin-film’s material may be analyzed by comparing the experimental results with some indentation theory. More complexity may be introduced by incorporating the effects of adhesion. Thin-film contact problems are significantly harder than corresponding ones for a half-space. I am interested in modeling thin-film contact to address problems such as (a) tunable adhesion by preparing micro-mechanical structures, and (b) adhesion of wavy thin films.

**Structural adhesives:** Coatings

**Bio-contact:** Coatings

**Dormant**

**Visco-elastic contact:** Another set of contact problems that I am involved with relate to contact of indenters with visco-elastic half spaces. Two types of contact interest me at present: bonding followed by debonding, and rolling contact.

Theoretical contact problems typically develop backgrounds in elasto- / visco-elasto- statics, integral equations and finite element calculations.

**AFM tip contact :** The Atomic Force Microscope (AFM) is an instrument that is often employed in various ways to gauge the surface force characteristic of materials. These surface forces are due to many sources: van Der Waals forces, Hydrogen bonds, who-knows, etc. Whatever the underlying reason may be, the idea is to know how the force field drops off as we move away from the surface. For this, both static and dynamic AFM modes are employed. In the former the AFM tip, which is almost of atomic dimensions, is brought close to the surface and the deflection is measured. Doing this at various distances produces the force-displacement property of the surface. In the dynamic mode, the resonant frequency at various mean distances are found. These, along with an appropriate mechanical model then produces a force-displacement curve. Most mechanical models employ a lumped-mass approach, neglecting the continuum nature of the AFM cantilever. There is also much confusion about how to patch together long-range microscopic forces and in-contact macroscopic contact models. We hope to have provided some answers to these. The next step is to also include the fact due to force interaction between the AFM tip and the surface, the surface, if soft, may deform. This will change the force-displacement curve significantly. Extensions to visco-elastic materials is also a future goal.

This project employs rudiments of beam theory, numerical solution of partial differential equations, and non-linear vibrations.

**Related publications **

Dalmeya, R. I. Sharma, C. Upadhyay and A. Anand 2012. Contact of a Rigid Cylindrical Punch with an Adhesive Elastic Layer. *J. Adhesion*. **88**, 311-. pre-print

Punati, V. S., I. Sharma, P. Wahi 2017. Contact mechanics of adhesive beams. Part I: Moderate indentation. *Proc. R. Soc. A.* **Under review**.

Punati, V. S., I. Sharma, P. Wahi 2017. Contact mechanics of adhesive beams. Part II: Deep indentation. **To be submitted**.

Punati, V. S., Bhuvana T., I. Sharma 2017. Contact mechanics of adhesive beams. Part III: Experiments. **Under preparation**.