In this paper, an alternative formulation of the NS-FEM based on an assumed stress field is presented to include drilling rotations. Within each triangular element the displacement field is described by a revised Allman triangle interpolation, while the stress field is assumed as linear or linear reduced on the conflict domain of the background grid. The elastic solution is constructed through the stationarity condition of a constrained mixed Hellinger–Reissner principle. The numerical experiments show that the proposed model performs well in elastic problems, in particular in the case of incompressibility, and takes advantage of the enrichment of the interpolation functions from quadratic contributions to the displacement field. The paper also shows a way to improve the description of the stress field
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