  The contact between a rigid Hertzian indenter and an adhesive broad-band
viscoelastic substrate is considered. The material behaviour is described by a
modified power law model, which is characterized by only four parameters, the
glassy and rubbery elastic moduli, a characteristic exponent n and a timescale
${\tau}_0$. The maximum adherence force that can be reached while unloading the
rigid indenter from a relaxed viscoelastic half-space is studied by means of a
numerical implementation based on the boundary element method, as a function of
the unloading velocity, preload and by varying the broadness of the
viscoelastic material spectrum. Through a comprehensive numerical analysis we
have determined the minimum contact radius that is needed to achieve the
maximum amplification of the pull-off force at a specified unloading rate and
for different material exponents n. The numerical results are then compared
with the prediction of Persson and Brener viscoelastic crack propagation
theory, providing excellent agreement. However, comparison against experimental
tests for a glass lens indenting a PDMS substrate show data can be fitted with
the linear theory only up to an unloading rate of about $100 \textrm{
$\mu$}$m/s showing the fracture process zone rate-dependent contribution to the
energy enhancement is of the same order of the bulk dissipation contribution.
Hence, the limitations of the current numerical and theoretical models for
viscoelastic adhesion are discussed in light of the most recent literature
results.
