From micro scale to boundary value problem: using a micromechanically based model
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A 3D multi-scale approach is presented to investigate the mechanical behavior of a macroscopic specimen consisting of a granular assembly, as a boundary value problem. The core of this approach is a multi-scale coupling, wherein the finite element method is used to solve a boundary value problem and a micromechanically based model is employed as constitutive relationship used at a representative volume element scale. This approach provides a convenient way to link the macroscopic observations with intrinsic microscopic mechanisms. The plane strain triaxial loading condition is selected to simulate the occurrence of strain localization. A series of tests are performed, wherein distinct failure patterns are observed and analyzed. A system of shear band naturally appears in a homogeneous setting specimen. By defining the shear band area, microstructural mechanisms are separately investigated inside and outside the shear band. The normalized second-order work introduced as an indicator of instability occurrence is analyzed not only on the macroscale but also on the micro scale.
KeywordsFEM Granular materials Mesoscopic scale Micromechanics Multi-scale approach Second-order work Shear band Strain localization
The authors would like to express their sincere thanks to the scholarship from China Scholarship Council (CSC) under the Grant CSC Number 201406250016, the National Natural Science Foundation of China (Grant No. 51579179), the Region Pays de la Loire of France (Project RI-ADAPTCLIM) and the French Research Network GeoMech (Multi-physics and Multi-scale Couplings in Geo-environmental Mechanics, GDRI CNRS, 2016–2019).
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