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A new algorithm is developed based on the parametric variational principle for elastic-plastic analysis of Cosserat continuum. The governing equations of the classic elastic-plastic problem are regularized by adding rotational degrees of freedom to the conventional translational degrees of freedom in conventional continuum mechanics. The parametric potential energy principle of the Cosserat theory is developed, from which the finite element formulation of the Cosserat theory and the corresponding parametric quadratic programming model are constructed. Strain localization problems are computed and the mesh independent results are obtained.

The traditional semi-inverse solution method of the Saint Venant problem, which is described in the Euclidian space under the Lagrange system formulation, is updated to be solved in the symplectic space under the conservative Hamiltonian system. It is proved in the present paper that all the Saint Venant solutions can be obtained directly via the zero eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian operator matrix.