Abstract
The paper presents a multi-scale modeling of Boundary Value Problem (BVP) approach involving cohesive-frictional granular materials in the FEM × DEM multi-scale framework. On the DEM side, a 3D model is defined based on the interactions of spherical particles. This DEM model is built through a numerical homogenization process applied to a Volume Element (VE). It is then paired with a Finite Element code. Using this numerical tool that combines two scales within the same framework, we conducted simulations of biaxial and pressuremeter tests on a cohesive-frictional granular medium. In these cases, it is known that strain localization does occur at the macroscopic level, but since FEMs suffer from severe mesh dependency as soon as shear band starts to develop, the second gradient regularization technique has been used. As a consequence, the objectivity of the computation with respect to mesh dependency is restored.
Highlights
Since its appearance in the late 70s, the Discrete Element Method (DEM) has become well known as an effective method for modeling granular material at the grain scale
We present a × (3D-DEM) model of boundary value problems (BVP) with cohesive-frictional granular materials and an emphasis on strain localization
The implementation consists in pairing the DEM code as another "constitutive law", and solving some specific difficulties linked to convergence issues
Summary
Since its appearance in the late 70s, the Discrete Element Method (DEM) has become well known as an effective method for modeling granular material at the grain scale. Seeking for a constitutive model that can account for all the relevant properties of granular materials, or a significant part of them, is difficult - and even not possible Such mathematical (often very sophisticated) models are necessarily phenomenological, and involve a number of parameters for which the physical meaning can be tricky. To avoid FEM mesh dependencies for shear bands, an internal length is introduced by means of the 2nd gradient regularization technique Thanks to this technique, associated with a high performance computing ability of the code (MPI parallelization), the tool is able to address some real-size geotechnical structures by accounting grain-scale features and strain localization.
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