Geometrically nonlinear Cosserat elasticity with chiral effects based upon granular micromechanics

In this short discussion, we exemplify how the Cosserat kinematics, intro duced into classical continuum mechanics at the turn of the 𝑋 𝑋𝑡 ℎ century, ariseswhen we consider the granular microstructure inherent in all matter. The discusseddiscrete-continuum identification, that follows Piola’s ansatz, is utilized to developkinematic measures in the framework of finite deformations. These kinematic mea sures are then utilized to express the internal deformation (strain) energy in terms ofboth grain-scale and continuum kinematic measures. As a result, we have identifiedthe macroscopic elastic constants of geometrically nonlinear Cosserat continuummodel in terms of the grain scale parameters