A new strategy for discrete element numerical models: 1. Theory

Abstract

[1] A new derivative of the particle-based discrete element method (DEM) for computationally modeling the mechanics of granular materials is suggested. In contrast to the conventional DEM, the new stress-based discrete element method (SDEM) presented here is formulated using a macroscopic parameterization, lending itself well for structural geomodeling for which the Mohr-Coulomb constitutive relation is the underlying model assumption. In SDEM, consistency exists between the macroscopic properties of a particle assembly and the microscopic parameters specified for each particle, unlike for the standard DEM for which microscopic and macroscopic properties can at best be calibrated through troublesome testing experiments. Importantly, this consistency allows for modeling realistically unforced formation and growth of faults and shear zones, with orientations as predicted by Mohr-Coulomb theory and in agreement with general observations. By measuring the virtual deformation of spherical elastic particles rather than just virtual particle overlaps, this new formulation introduces strain rate and stress tensors at the particle level. Strain rates are obtained by adopting interpolation techniques from the methodology of meshless continuum methods like smoothed particle hydrodynamics, while the appealing discrete kinematic of DEM, including inherent dilatation effects and stick-slip instabilities, is preserved as particles interact by finite contact forces. The SDEM theory, the computational strategy, and test examples are presented here. In the companion paper, SDEM computational ''sandboxtype'' models illustrate the method's potential for contributing insight into the dynamics and kinematics of more advanced geomechanical processes.

Crack nucleation in solid materials under external load - simulations with the Discrete Element Method

“…The method consists on representation of the medium by an ensemble of finite size particles (real atoms in the case of molecular dynamic simulation), which interact according to a specified interaction forces. [15,16] The evolution of the system is achieved by sequential evaluating (Figure 1), for each time step, the positions, momenta and circular momenta of all particles, using Newton dynamical equation with prescribed interaction forces and assumed initial and boundary condition. [17,18] Although the approach is computationally time consuming and requires advanced HPC computational techniques, it provides the most direct insight into fully 3D dynamics of rupturing process.…”

Reduction of discrete element models by Karhunen–Loève transform: a hybrid model approach

“…As a result of this approach, forces act between discrete elements and are evaluated individually for each element. This results in a system of (formally) decoupled, more or less stiff equations of motion (5) and (6). There are two major branches of DEM that differ in the formulation of particle-particle forces: (1) Models that assign attracting and repulsing potential fields to each particle, merely used to model dynamics on atomistic scale 1 and (2) Models that apply elasto-plastic contact laws, employing more complex neighborhood/contact detection algorithms, mainly used at macro-scale level.…”

“…[2,3], stability of assemblies [4][5][6][7] or granular/structure interactions in material handling processes [8][9][10]. In recent publications the DEM is expanded to analyses of solid structures, ref.…”

“…This approach allows for very simple formulations of the equations of motion (5) and (6) and thus for flexible models. However, the evaluation of the right-hand sides of Eqs.…”

“…However, the evaluation of the right-hand sides of Eqs. (5) and (6) can become very numerical expensive, depending on the range and choice of governing potentials U . Up to date, the numerical costs limit size and time interval of numerical analyses by DEM, Ref.…”