In this work, we consider dynamic frictionless contact with adhesion
between a viscoelastic body of the Kelvin-Voigt type and a
stationary rigid obstacle, based on the Signorini's contact conditions.
Including the adhesion processes modeled by the bonding field, a new
version of energy function is defined. We use the energy function
to derive a new form of energy balance which is supported by numerical
results. Employing the time-discretization,
we establish a numerical formulation and investigate the convergence of numerical trajectories. The fully
discrete approximation which satisfies the complementarity conditions
is computed by using the nonsmooth Newton's method with the Kanzow-Kleinmichel
function. Numerical simulations of a viscoelastic beam clamped at
two ends are presented.