From micro scale to boundary value problem: using a micromechanically based model

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.