  This work presents a general finite element formulation based on a six--field
variational principle that incorporates the consistent couple stress theory. A
simple, efficient and local iteration free solving procedure that covers both
elastic and inelastic materials is derived to minimise computation cost. With
proper interpolations, membrane elements of various nodes are proposed as the
examples. The implemented finite elements are used to conduct numerical
experiments to investigate the performance of the in-plane drilling degrees of
freedom introduced by the consistent couple stress theory. The mesh dependency
issue is also studied with both elastic and inelastic materials. It is shown
that the consistent couple stress theory provides an objective definition of
rotation compared with the Cauchy theory but additional regularisation (or
other techniques) is required to overcome mesh/size dependency in softening or
fracture related problems. In the case of hardening continuum problems and/or
large characteristic lengths, the proposed formulation and elements offer a
more reliable approach to model structures with both translational and
rotational degrees of freedom.
