  The collision of convex bodies is considered for small impact velocity, when
plastic deformation and fragmentation may be disregarded. In this regime the
contact is governed by forces according to viscoelastic deformation and by
adhesion. The viscoelastic interaction is described by a modified Hertz law,
while for the adhesive interactions, the model by Johnson, Kendall and Roberts
(JKR) is adopted. We solve the general contact problem of convex viscoelastic
bodies in quasi-static approximation, which implies that the impact velocity is
much smaller than the speed of sound in the material and that the viscosity
relaxation time is much smaller than the duration of a collision. We estimate
the threshold impact velocity which discriminates restitutive and sticking
collisions. If the impact velocity is not large as compared with the threshold
velocity, adhesive interaction becomes important, thus limiting the validity of
the pure viscoelastic collision model.
