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International Journal for Multiscale Computational Engineering
Impact-faktor: 1.016 5-jähriger Impact-Faktor: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Druckformat: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2020031587
pages 199-240

SECOND-ORDER CONCURRENT COMPUTATIONAL HOMOGENIZATION METHOD AND MULTISCALE HYDROMECHANICAL MODELING FOR SATURATED GRANULAR MATERIALS

Xikui Li
The State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, PR China and International Research Center for Computational Mechanics, Dalian, PR China
Songge Zhang
The State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, PR China and International Research Center for Computational Mechanics, Dalian, PR China
Qinglin Duan
The State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, PR China and International Research Center for Computational Mechanics, Dalian, PR China

ABSTRAKT

A framework of a second-order concurrent computational homogenization method for saturated granular material is established. Saturated granular material is modeled as a porous gradient-enhanced Cosserat continuum at the macroscale and as a compact assembly of saturated discrete particles and its effective saturated porous Cosserat continuum at the representative volume element (RVE) scale. The classical average-strain theorem for the Cauchy continuum is generalized to a gradient-enhanced Cosserat continuum. The generalized Hill's lemma for the second-order concurrent computational homogenization method is derived to specify the downscaling rule from the macroscopic continuum to the mesostructured RVE. The boundary conditions imposed on the RVE boundary are comprised of boundary displacements and pressures specified by downscaled macroscopic strain variables and pore pressures, and constrained hydromechanical periodic boundary conditions. A staggered discrete element method (DEM)/finite element method (FEM) solution scheme is proposed for nonlinear hydromechanical analysis of a saturated discrete particle assembly of the RVE. The effective stress variables with the elastoplastic modular tensor, volume averages of Darcy's velocities with the permeability coefficient tensor, are determined and upscaled to the high scale. A mixed FE is constructed, and the corresponding nonlinear u−p form of FEM formulation is devised for a saturated porous gradient-enhanced Cosserat continuum. A FEM-(DEM/FEM) nested solution scheme is devised for the proposed second-order concurrent computational homogenization method. Numerical examples and results demonstrate the capabilities and performances of the proposed method in multiscale modeling of hydromechanical behaviors, particularly, softening and localization behaviors occurring in saturated granular structures.

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