A generalized Hills lemma and micromechanically based macroscopic constitutive model for heterogeneous granular materials
Based on the Hills lemma for classical Cauchy continuum, a generalized Hills lemma for micromacro homogenization modeling of gradient-enhanced Cosserat continuum is presented in the frame of the average-field theory. In this context not only the strain and stress tensors defined in classical Cosserat continuum but also their gradients are attributed to assigned micro-structural representative volume element (RVE), that leads to a higher-order macroscopic Cosserat continuum modeling and enables to incorporate the micro-structural size effects. The enhanced HillMandel condition for gradient-enhanced Cosserat continuum is extracted as a corollary of the presented generalized Hills lemma. The derived admissible boundary conditions for the modeling are deduced to direct the proper presentation of boundary conditions to be prescribed on the RVE in order to ensure the satisfaction of the HillMandel energy condition. With the link between the discrete particle assembly and its effective Cosserat continuum in an individual RVE, the boundary conditions prescribed on the RVE modeled as Cosserat continuum are transformed into those prescribed to the peripheral particles of the RVE modeled as the discrete particle assembly. The micromechanically based macroscopic constitutive model and corresponding rate forms of the macroscopic stressstrain relations taking into account the local microstructure and its evolution are formulated with neither need of specifying the macroscopic constitutive relation nor need of providing macroscopic material parameters.
generalized hills lemma micromechanically based macroscopic constitutive model heterogeneous granular materials gradient-enhanced cosserat continuum rve boundary conditions