  A collision of viscoelastic bodies is analysed within a mathematically
rigorous approach. We develop a perturbation scheme to solve continuum
mechanics equation, which deals simultaneously with strain and strain rate in
the bulk of the bodies' material. We derive dissipative force that acts between
particles and express it in terms of particles' deformation, deformation rate
and material parameters. It differs noticeably from the currently used
dissipative force, found within the quasi-static approximation and does not
suffer from inconsistencies of this approximation. The proposed approach may be
used for other continuum mechanics problems where the bulk dissipation is
addressed.

Statistical Mechanics;Soft Condensed Matter