​

A parametrized six-field variational principle for micropolar compressible linear elasticity is presented. The primary variables are symmetric and skew stresses, symmetric and skew strains, micropolar rotations and displacements. The governing functional is characterized by six free parameters. The connection between this formulation and the functionals with relaxed stress symmetry and independent rotations fields proposed by Reissner and Hughes-Brezzi for classical (non-polar) linear elasticity is examined. It is shown that the Hughes-Brezzi functionals are special cases of the parametrized functional but that the Reissner functionals are not. The former may be interpreted as a regularization (consistent stabilization) of the Reissner functionals that places them within the framework of micropolar elasticity. An eight-field parametrized principle that accounts for couple stresses is briefly described in the Appendix.

​