Micro–macro homogenization of granular materials based on the average-field theory of Cosserat continuum

Abstract

Effective couple stress tensor Micromechanically based constitutive models a b s t r a c t This paper performs further study on the micro-macro homogenization approach of granular materials (Li et al., 2010) based on the advancement of Hill's lemma for Cosserat continuum (Liu, 2013). Firstly, the average couple stress tensor, expressed as the volume integration of quantities over the representative volume element (RVE) in the average-field theory of Cosserat continuum, is further deduced and expressed in terms of discrete quantities on the discrete particle assembly RVE of granular materials. The expression is also discussed and compared with other typical definitions of the effective couple stress tensor for granular materials in the literature. Then, rate forms of micromechanically based constitutive models consistent with different types of RVE boundary conditions are derived and discussed. Since the presented micro-macro homogenization approach is used, not only the micro-macro energy equivalence is satisfied, but also the microstructure and its evolution can be taken into account in the constitutive formulation with no need of specifying macroscopic phenomenological constitutive model.

Systematic study of homogenization and the utility of circular simplified representative volume element

“…Central to computational homogenization is the separation of the length scales between the micro-and the macroscale. The key idea of computational homogenization is to identify the effective properties at the macroscale through averaging of the microproblem [92][93][94][95][96][97][98]. At the microscale, it is Figure 1.…”