The deformation and adhesion of soft elastic particles interacting with a L
ennard-Jones potential is obtained by solving self-consistently the elastic
ity equations. Hysteresis is demonstrated between loading and unloading. Al
so, the pull-off force or maximum adhesion is shown to increase and eventua
lly to saturate as the maximum applied load is increased. The origin of bot
h of these phenomena, which have been observed experimentally, is traced to
limited equilibration and dynamic hysteresis of the shape and contract ang
le between the advancing and receding deformed solids.