Abstract This paper presents an environmentally friendly joining process based on sheet-bulk plastic deformation to connect two polymer (or a polymer and a metal) sheets perpendicular to one another. The methodology draws from material characterization and finite element modelling, using an extension of the flow formulation to pressure-sensitive polymers, to experimentation in a laboratory tool setup and destructive testing of the produced joints. The results allow characterization of the joinability window as a function of the major operating parameters and demonstrate the feasibility of the process to produce polymer and hybrid joints (polymer-metal) at room temperature. A variant to the proposed process is disclosed to handle situations where the elastic recovery of the polymer sheets needs to be better controlled. The overall content of the paper is an extension of a previous work of the authors for fixing longitudinally in position two metal sheets perpendicular to one another, and seems promising for the manufacture of lightweight joints made from polymers or polymers and metals.