Halo approach to evaluate the stress distribution in 3D discrete element method simulation: validation and application to flax/bio based epoxy composite

Abstract

Discrete element method (DEM) is an interesting alternative to classical approaches as the finite element method (FEM) to simulate homogeneous and heterogeneous materials. Indeed, although DEM was initially developed to simulate granular systems in motion, it also enables to model a continuous medium with the help of a dense granular packing in which the cohesion is introduced between each pair of particles in contact using beam or spring elements. However, among other issues, the local stress field obtained using DEM is heterogeneous, even in the case where it is theoretically homogeneous. In the present contribution, we investigate the stress field distribution in 3D DEM mechanical simulation, and propose an approach we named Halo, to evaluate the level of stress distribution. The idea of the method is to evaluate the stress at the scale of every discrete element (DE) taking into account the contribution of its neighbors, inside the Halo of the DE. The effect of the number of DEs per Halo on the stress distribution is discussed in homogeneous and heterogeneous media. The approach results for homogeneous media are compared to FEM calculations and to the theoretical Hertz solution via a Brazilian test. For the homogeneous media, we use the unidirectional flax/bio based epoxy composite, for which macroscopic longitudinal Young’s modulus is experimentally quantified. Furthermore, comparisons with FEM are performed in this context. Results highlight a good agreement between both approaches in terms of stress fields including extremal values.

DECM: A Discrete Element for Multiscale Modeling of Composite Materials Using the Cell Method

“…This leads to an overestimation of the local stress, triggering an early crack initiation and accelerating crack propagation. A successful technique to reduce the heterogeneity of the stress field is to evaluate the stress of each discrete element (DE) taking into account the contributions of the DEs contained in an appropriate meso-scale neighborhood-called the Halo [49]-of the DE. However, since this technique requires a number of DEs per Halo of the order of 10 3 to achieve convergence in the stress values, the Halo approach is not suitable for use with macroscopic rigid blocks.…”

“…It is worth noting that the long-range interaction [18] and the Halo approach [49]-both used to model the macroscopic behavior of composite continua-characterizes the DEM as a nonlocal model [97][98][99][100][101][102][103], in a broad sense. In fact, in nonlocal continua the stress at a certain point is a function of the strain distribution over a certain representative volume of the material centered at that point and not a function of the strain at the same point [104].…”

DECM: A Discrete Element for Multiscale Modeling of Composite Materials Using the Cell Method

“…It is worth noting that the long-range interaction [13] and the Halo approach [44]-both used to model the macroscopic behavior of composite continua characterizes the DEM as a nonlocal model [97][98][99][100][101][102][103], in a broad sense. In fact, in nonlocal continua the stress at a certain point is a function of the strain distribution over a certain representative volume of the material centered at that point and not a function of the strain at the same point [104].…”

“…In fact, non-standard analysis extends the real line,  , to the hyperreal line, * ,where each real number has a collection of numbers (hyperreals) infinitely close to it. The name given to a collection of hyperreals is "monad", or "halo" (not to be confused with the Halo of the Halo approach [44]). Since the standard part function associates to a finite hyperreal, x , the unique standard real number 0…”

“…This leads to an overestimation of the local stress, triggering an early crack initiation and accelerating crack propagation. A successful technique to reduce the heterogeneity of the stress field is to evaluate the stress of each discrete element (DE) taking into account the contributions of the DEs contained in an appropriate meso-scale neighborhood-called the Halo [44]-of the DE. However, since this technique requires a number of DEs per Halo of the order of 10 3 to achieve convergence in the stress values, the Halo approach is not suitable for use with the macroscopic rigid blocks.…”