  Mechanical responses of soft particle packings to quasi-static deformations
are determined by the microscopic restructuring of force-chain networks, where
complex non-affine displacements of constituent particles cause the
irreversible macroscopic behavior. Recently, we have proposed a master equation
for the probability distribution functions of contact forces and interparticle
gaps [K. Saitoh et al., Soft Matter 11, 1253 (2015)], where mutual exchanges of
contacts and interparticle gaps, i.e. opening and closing contacts, are also
involved in the stochastic description with the aid of Delaunay triangulations.
We describe full details of the master equation and numerically investigate
irreversible mechanical responses of soft particle packings to cyclic loading.
The irreversibility observed in molecular dynamics simulations is well
reproduced by the master equation if the system undergoes quasi-static
deformations. We also confirm that the degree of irreversible responses is a
decreasing function of the area fraction and the number of cycles.
