  Is the maximum force required to detach a rigid sphere from a viscoelastic
substrate dependent on the initial value of the contact radius? Experimental
and theoretical investigations reported in the literature have given opposite
responses. Here, we try to answer the above question by exploiting a fully
deterministic model in which adhesive interactions are described by
Lennard-Jones potential and the viscoelastic behaviour with the standard linear
solid model. When the approach and retraction phases are performed under
quasi-static conditions, the substrate behaves as an elastic medium and, as
expected, the pull-off force Fpo (i.e., the maximum tensile force) is found to
be independent of the maximum contact radius amax reached at the end of
loading. Size-dependent effects are instead observed (i.e., pull-off force Fpo
changes with amax) when transient effects occur as the larger the contact area,
the greater the size of the bulk volume involved in the dissipation. Results
are also discussed in the light of viscoelastic crack Persson's theory, which
is modified to capture size effects related to amax.
