Geometrically Nonlinear Cosserat Elasticity with Chiral Effects Based upon Granular Micromechanics

In this short contribution, we exemplify how the Cosserat kinematics, introduced into classical continuum mechanics at the turn of the XXth century, arises when we consider the granular microstructure inherent in all matter. The discussed discrete-continuum identification, that follows Piola’s ansatz, is utilized to develop kinematic measures in the framework of finite deformations. These kinematic measures are then utilized to express the internal deformation (strain) energy in terms of both grain-scale and continuum kinematic measures. As a result, we have identified the macroscopic elastic constants of geometrically nonlinear Cosserat continuum model in terms of the grain scale parameters.