Equilibrium Correction for viscoplasticity

In general for incremental plasticity problems it is well known that one has to use an iteration scheme (Newton-Raphson, modified Newton-Raphson or Quassi Newton etc.) in order to achieve a converged solution for finite element equations. Is it also neccessary to have an iteration scheme for an incremental viscoplastic problems ? I am also attaching a paper where the authors have implemented an equilibrium correction scheme in the principle of virtual work, which is supposed to ensure convergence. I am not able to comprehend how it takes care of the convergence without any iterations. Any help would be highly appreciated.

Thanks

Suman