Finite Element Method for Elastic Cosserat Continuum and Its Application to Deformation Behavior of Materials with Microstructure.

Abstract

To clarify the influence of microstructures on the apparent mechanical properties and the influence of the macroscopic mechanical condition on the microstructural stress and strain, a finite element method for the elastic Cosserat continuum has been developed. For materials obeying micropolar theory and couple stress theory, the validity of the proposed method has been verified through comparison with the exact solution for the case of a circular hole in a uniform tension field. For materials with microstructures which are modeled as a lattice continuum that consists of rigidly interconnected elastic beams, it has been clarified that the characteristic parameters that represent microstructural dimensions and properties are reflected in the apparent mechanical properties as a Cosserat continuum. Furthermore, it has been confirmed that the proposed methods enable us to evaluate the relationship between microscopic and macroscopic deformation behavior.