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Frontiers of Structural and Civil Engineering

Front Struc Civil Eng    2013, Vol. 7 Issue (3) : 304-315     https://doi.org/10.1007/s11709-013-0213-y
RESEARCH ARTICLE |
Two-scale modeling of granular materials: A FEM-FEM approach
Yun-Zhu CAI, Yu-Ching WU()
Building Engineering Department, College of Civil Engineering, Tongji University, Shanghai 200092, China
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Abstract

In the present paper, a homogenization-based two-scale FEM-FEM model is developed to simulate compactions of visco-plastic granular assemblies. The granular structure consisting of two-dimensional grains is modeled by the microscopic finite element method at the small-scale level, and the homogenized viscous assembly is analyzed by the macroscopic finite element method at large-scale level. The link between scales is made using a computational homogenization method. The two-scale FEM-FEM model is developed in which each particle is treated individually with the appropriate constitutive relations obtained from a representative volume element, kinematic conditions, contact constraints, and elimination of overlap satisfied for every particle. The method could be used in a variety of problems that can be represented using granular media.

Keywords homogenization      two-scale      representative volume element      compaction      granular assembly      finite element method     
Corresponding Authors: WU Yu-Ching,Email:ycwu@tongji.edu.cn   
Issue Date: 05 September 2013
 Cite this article:   
Yun-Zhu CAI,Yu-Ching WU. Two-scale modeling of granular materials: A FEM-FEM approach[J]. Front Struc Civil Eng, 2013, 7(3): 304-315.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-013-0213-y
http://journal.hep.com.cn/fsce/EN/Y2013/V7/I3/304
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Yun-Zhu CAI
Yu-Ching WU
Fig.1  The experimental study for granular polyethylene glycol made by Cuitino et al. [] and a schematic representation of the compaction process
Fig.2  Distribution of particles in microstructure unit (RVE) and the geometrical model for RVE used to finite element simulation
Fig.3  On the basis of the homogenization theory, the macroscopic level is locally formed by the spatial repetition of very small microstructures
Fig.4  In the process of finite element simulation, the macroscopic level is considered as continuous. Each point in the macrostructure is characterized by the representative volume element
Fig.5  The flow chart of the whole compaction simulation for granular assemblies using RVEM
Fig.6  Particles in the RVE is covered with quadrilateral elements used for finite element simulation to the microstructure. The whole region of RVE is covered with automatic adaptive triangular grids used for tracing the process of condensation [-]
Fig.7  The loading condition and boundary condition of vertical compactions to both of RVE and macroscopic level
Fig.8  The vertical compaction simulation for RVE
Fig.9  Compaction curves for RVE. (a) Density ratio vs. compaction pressure for RVE; (b) density ratio vs. log (compaction pressure) for RVE
Fig.10  The variation of elements of matrix during compaction. The datum comes from the vertical condensation, lateral condensation and shearing tests on RVE step by step. (a) Vertical condensation tests for REV; (b) lateral condensation tests for REV; (c) shearing tests for REV
Fig.11  The state of effective stresses for macroscopic level during compaction
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