Large Deformation Analysis of Elastic Cosserat Continua by FEM

Based on the non linear terms appearing in the strain tensor in classical continuum mechanics, two expressions for large strain in the Cosserat continuum are proposed. The generalized form of principal of virtual work together with the constitutive equations for an isotropic elastic Cosserat continuum are used to derive the finite element formulations for elastic large deformation analysis based on the Cosserat theory. The finite element formulations are then applied to a four-node quadrilateral element with three degrees of freedom at each node including two translational and one rotational degrees of freedom. The tension of a semi-infinite plate with a circular whole in the center is solved using the Cosserat finite element formulation and the results are compared with those obtained by the classical theory. Also, pure bending and shear of a cantilever beam are done and the differences of the results obtained based on the two proposed formulations of large strains are investigated.