A micromechanical approach of nonlocal modeling for media with periodic microstructures

This work endeavors to identify the microscopic and macroscopic behaviors of an elastic medium with periodic microstructure in case a polynomial displacement field is imposed on its representative unit cell. A micromechanical method is developed to solve this microstructural boundary value problem and the spatial averaging theorem is adopted to derive macroscopic equivalent descriptions of the medium. The higher-order macroscopic constitutive responses derived in this work is found identical with that obtained by asymptotic homogenization method and a novel Cosserat-type macroscopic constitutive relation is also delivered.