A Biot-Cosserat two-dimensional elastic nonlinear model for a micromorphic medium

A possible strain energy density, incorporating Cosserat's micro-rotations and Biot's change in porosity conferred by the microstructure geometry, is proposed in an elastic, two-dimensional, nonlinear context. The nonlinearities are taken into account both extracting the exact macro-rotations by the polar decomposition of the standard deformation gradient F and evaluating the change in the area at the macroscopic level of observation as J - 1. Moreover, the bulk behavior of the material is assumed to be described by a compressible neo-Hookean model. Based on a variational formulation, finite element numerical simulations of static tests in some representative examples have been performed to illustrate the main features of the proposed model and the effect of the boundary conditions.