An accurate nonlocal bonded discrete element method for nonlinear analysis of solids: application to concrete fracture tests

Abstract

We present a numerical procedure for elastic and non linear analysis (including fracture situations) of solid materials and structures using the Discrete Element Method (DEM). It can be applied to strongly cohesive frictional materials such as concrete and rocks. The method consists on defining non-local constitutive equations at the contact interfaces between discrete particles using the information provided by the stress tensor over the neighbour particles. The method can be used with different yield surfaces and in the paper it is applied to the analysis of fracture of concrete samples. Good comparison with experimental results is obtained.

A fully Lagrangian formulation for fluid-structure interaction problems with free-surface flows and fracturing solids

“…The FSI problem is here solved with a novel hybrid strategy that combines three different Lagrangian numerical methods. The free-surface flow problem is solved with the stabilized PFEM formulation presented in [7], while the solid deformation, fracture and frictional contact effect are modeled by combining a Finite Element Method (FEM) with smoothed isotropic damage model [3,16] and a Discrete Element Method (DEM) [13][14][15], in the spirit of the so-called FEM-DEM procedure [1][2][3].…”

A bonded discrete element method for modeling ship–ice interactions in broken and unbroken sea ice fields

“…The DEM was initially developed by Cundall et al [4] in the 1970's. It is based in the interaction of discrete elements (also called particles) typically cylinders (in 2D) and spheres (in 3D) to simulate the behavior of continuum and discontinuum domains [3,7,8,10,20,21,31,34,35,42]. This interaction is governed by a set of dynamic equilibrium equations involving the displacements, the velocities and the accelerations of the particles induced by the forces acting on the discrete element.…”

“…In the following sections a brief description of this model is presented. An enhanced non-local version of the bonded constitutive model is presented in [3].…”

Improved numerical integration for locking treatment in the Peridynamic Timoshenko beam model

“…The nonlocal continuum theory, offered a link between the classic continuum mechanics theory and MD, is accordingly stated to account for the long-range effects using displacement field rather than the derivatives of the displacement (Oñate and MA, 2020; Patnaik et al ., 2020; Patnaik et al ., 2021). When the radius shrinks to infinitely small, nonlocal theory converts into a typical continuum mechanics case (Voyiadjis, 2019).…”