This work is an intermediate step towards the extension of a recently proposed block-based model for masonry structures, which was based on a hemivariational approach and inspired from granular micromechanics. Here, contrarily to the previous model, plastic effects will also be taken into account along with damage and elastic behaviours, and the full hemivariational derivation of the strong-form (in)equations will be detailed for the case of a lone vertex spring. The resulting model and methods shall then be used in future works to enrich the behaviours modelled by the previously mentioned masonry model.