A variational discrete element method for the computation of Cosserat elasticity

The variational discrete element method developed in [Marazzato et al, 2020] for dynamic elasto-plastic computations is adapted to compute the dynamic evolution of elastic Cosserat materials. In addition to cellwise displacement degrees of freedom (dofs), cellwise rotational dofs are added. A reconstruction is devised to obtain P1 non-conforming polynomials in each cell and thus constant strains and stresses in each cell. The method requires only the usual macroscopic parameters of a Cosserat material and no microscopic parameter. The mass matrix is naturally diagonal and thus allows fast dynamic computations. Numerical examples show the robustness of the method and that it converges at order one in energy norm similarly to the usual Lagrange P2-P1 mixed element. Also, the robustness of the method with respect to the incompressible limit {\nu} \to 0.5 is proved numerically.