Mixed FEM–Crushable DEM Nested Scheme in Second-Order Computational Homogenization for Granular Materials

Abstract

A mixed FEM–crushable discrete-element method (DEM) nested scheme in the frame of second-order computational homogenization for granular materials was proposed. The particle breakage followed by the discontinuity and dissipative relative movements between each of two immediate neighboring particles were modeled at the mesoscale to perform both the downscaling and upscaling between the mixed FEM at the macroscopic continuum scale and the crushable DEM at the mesoscopic discrete particle assembly scale. To develop the crushable DEM for modeling the mesostructural evolution within representative volume elements (RVEs) assigned to integrating points of the macroscopic Cosserat continuum in the homogenization, two grain breakage models consisting of crushing criteria and the fracture mode for an individual crushable particle were developed. Not only the contact forces, but also contact moments exerted on each individual grain via the contacting points on the grain surface, were taken into account to set up the proposed crushing criteria. The stress measures, responsible for the particle breakage, involved both the average Cauchy stress tensor and the average couple stress tensor exerted on a crushable particle modeled as the Cosserat continuum. A fracture mode to specify how a crushable parent particle is replaced with a specific arrangement of postcrushing fragments was proposed and implemented. The mass conservation in the postcrushing replacement of fragments was ensured, whereas neither overlaps among the fragments nor overlaps with the fragments of the immediate neighboring particles of the crushable parent particle were introduced. The numerical results demonstrate the performance of the proposed mixed FEM–crushable DEM nested scheme in the frame of second-order computational homogenization for granular materials and the effects of the particle breakage on the failure behavior of the overall geostructure.