In this work, we consider dynamic frictionless contact with adhesionbetween a viscoelastic body of the Kelvin-Voigt type and astationary rigid obstacle, based on the Signorini's contact conditions.Including the adhesion processes modeled by the bonding field, a newversion of energy function is defined. We use the energy functionto derive a new form of energy balance which is supported by numericalresults. Employing the time-discretization, we establish a numerical formulation and investigate the convergence of numerical trajectories. The fullydiscrete approximation which satisfies the complementarity conditionsis computed by using the nonsmooth Newton's method with the Kanzow-Kleinmichelfunction. Numerical simulations of a viscoelastic beam clamped attwo ends are presented.
