Mechanics and Physics of Contact Interfaces

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Ideas & very preliminary results

During my academic career, occasionally I had time to touch upon (explore superficially, study and try to understand) various topics in science. Almost all of these attempts were stuck either because of lack of time, enthusiasm or because of technical difficulties which I could not overcome on the spur of the moment. Since I strongly believe that the work is not done if a paper is not written on the topic, almost all of these studies remain rather raw ideas and cannot be considered as scientific production. The only reason to mention these studies here is to leave a trace of these ideas with the hope to interest someone in taking a step forward with or without me. I would be happy to publish one day these raw ideas and first results in a kind of a small open access online book of 💡s, but I am not sure that such a day will ever happen.

During last 10 years I touched upon the following topics and problems:

Below I list some studies for which I’ve some illustrations.

Show animation.
Martensitic transformations using special bi-stable potential [95] with my own molecular dynamics code, which I later used for teaching.
Martensitic transformations using multi-variant Ising-type model with interface energy; first 1D results were published [96]. Later, I obtained some closed form solutions for the probability of sates for the reference Hamiltonian of martensite/austenite including interface energy. I studied coarsening behavior in 2D.
Wave propagation in wave-guides and seismic waves simulations.
Crypto-billiard project: Lorentz gas simulation (elastic rebound of a point particle from a sphere) for various initial conditions could lead to complex chaotic patterns, here I show initial position -- and angle map and the color corresponds to the number of rebounds on a finite size system.
Models for heterogeneous concrete and brittle fracture of resulting microstructures.
Porous media generator based on the self-affine (fractal-like) structure and filtering method for random noise that we use for generation of rough surfaces.
Plastic instabilities, post-buckling behavior with self-contact.
Multi-strand wires simulations.
Contact between soap bubbles: in-house experiments and finite-element modelling.
Characterization of randomness of triangles in a circle and in a square domains.
Shift induced rough surfaces and random surfaces on a sphere.
Constrained-optimization based contact detection and projection algorithms [97].
Collaborative study with Karim Inal and Brice Arrazat on accurate FE simulations reproducing micro-indentation experiments on electroplated gold on silicium substrate.
Coupling DDD (NumoDis) with FEM (Z-set), the topic of my postdoc at Centre des matériaux in the framework of AFGRAP ANR-funded project on the onset of fatigue cracks in steels.
Geometrically induced difference in frictional contact for large penetrations.
One-dimensional slip on a wavy surface, from simple analytical results to root-analysis and statistics of randomly rough profiles.
Topology and morphology of merging and splitting clusters in physics. In Fig. I illustrate surgery cuts that restore manifolds from this topology.
Onset of plastic core and its growth in smooth indentation (in Fig. finite element simulation demonstrating the formation of an elastic layer under the indenter in absence of friction).
Statistics of contact pressure between contacting rough surfaces, the core quantity of Persson's rough contact model.
Molecular dynamics simulations of ultra high speed impacts with my MD code, which I also used for teaching during first few years of teaching Molecular Dynamics, later I switched to LAMMPS.
Simple 2D DDD solver for teaching needs.
Density-caustic formation in early Universe using fractal perturbation of initial velocities inspired by "Catastrophe Theory" by Vladimir Arnold.

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