  The interaction between visco-elasto-plastic and adhesive particles is the
subject of this study, where "meso-particles" are introduced, i.e., simplified
particles, whose contact mechanics is not taken into account in all details. A
few examples of meso-particles include agglomerates or groups of primary
particles, or inhomogeneous particles with micro-structures of the scale of the
contact deformation, such as core-shell materials. A simple, flexible contact
model for meso-particles is proposed, which allows to model the bulk behavior
of assemblies of many particles in both rapid and slow, quasi-static flow
situations. An attempt is made to categorize existing contact models for the
normal force, discuss all the essential mechanical ingredients that must enter
the model (qualitatively) and finally solve it analytically. The model combines
a short-ranged, non-contact part (resembling either dry or wet materials) with
an elaborate, visco-elasto-plastic and adhesive contact law. Using energy
conservation arguments, an analytical expression for the coefficient of
restitution is derived in terms of the impact velocity (for pair interactions
or, equivalently, without loss of generality, for quasi-static situations in
terms of the maximum overlap or confining stress). Adhesive particles (or
meso-particles) stick to each other at very low impact velocity, while they
rebound less dissipatively with increasing velocity, in agreement with previous
studies. For even higher impact velocities an interesting second sticking and
rebound regime is reported. The low velocity sticking is due to non-contact
adhesive forces, the first rebound regime is due to stronger elastic and
kinetic energies with little dissipation, while the high velocity sticking is
generated by the non-linearly increasing, history dependent plastic dissipation
and adhesive contact force.
