Project sponsored by National Natural Science Foundation of China, No. 11372066, 2014.1-2016.12.
A second-order computational homogenization method of granular materials with unsaturated discrete particle assembly – porous gradient Cosserat continuum modeling for the two scale analysis of coupled hydro-mechanical process is presented. The mathematical model and corresponding numerical method GCFD to determine the flow fields of pore fluids and the fluid drags on particles are developed with consideration of the liquid bridge effect and different flow modes depending on the saturation degree distribution within the representative volume element (RVE) of discrete particle assembly. In combination with the discrete element method (DEM) applied to the RVE taking into account the effect of liquid bridges and flowing pore fluids, the numerical method DEM-GCFD for coupled hydro-mechanical process is constructed.The Voronoi cell model is developed in the meso-scale to define locally averaged hydro-mechanical measures in unsaturated porous Cosserat continuum in terms of the microscopically based information. The generalized Hill’s lemma for coupled hydro-mechanical process is presented. The microscopically informed macroscopic hydro-mechanical constitutive relations for unsaturated porous gradient Cosserat continuum are formulated. The global-local FEM-(DEM-GCFD) nested algorithm is developed and implemented. That is the finite element method for unsaturated porous gradient Cosserat continuum model with the nested DEM-GCFD for unsaturated RVE of discrete particle assembly model. The performance of the proposed second-order computational homogenization method along with the developed algorithm and its capability in detecting the microscopic mechanisms of macroscopic response are demonstrated.
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