Grain Days 2023

Particle-based simulation methods are widely used across disciplines. They have the ability to accurately describe material behaviour at a macroscopic scale while retaining local information. This gives access to information which would be extremely challenging to obtain experimentally, such as local density field, stress field etc. In addition, compared to other simulation methods such as finite element, they usually allow large deformations and material separation and merging with little to no additional implementation work required.  

This session aims to give a general overview of the specificities of particle-based methods in the broader field of numerical simulations, and to serve as an introduction to the more detailed sessions on discrete element methods by Klaus Thoeni and smooth particle hydrodynamics by Ha Bui.

We will start by reviewing the physical grounds on which numerical simulation methods are built. In particular we will focus our attention on the distinction between discrete and continuum descriptions on one hand, and Lagrangian and Eulerian description on the other hand, and the consequences on those in particle-based numerical simulations. In a second part, we will discuss in detail the up-scaling processes we can use to go from individual particle information to continuum field information. This process is crucial as particle level information is generally not very useful by itself, and spatial or temporal averaging are often required to obtain more relevant information on the material. This method, usually called coarse-graining in the context of discrete element simulations, carries its own subtlety, assumptions and limitations, which we will discuss in details.

The Discrete element Method (DEM) has become a reliable tool for the dynamic simulation of bonded and unbonded granular materials. The material is represented by an assembly of particles. Interactions between particles are considered explicitly and relatively simple models are used to calculate the contact forces. Although the particles can have any shape, spherical particles are most widely used. This results in efficient contact detection. In addition, arbitrary shapes can generally be approximated by an assembly of spherical particles. 

Many commercial and open-source DEM codes are now available, each coming with its own benefits. This lecture will focus on the open-source framework YADE, an efficient and flexible tool for the dynamic simulations of granular materials. The framework has been around for more than 10 years and is very popular within the geomechanics community. It is relatively user-friendly and supported by a big community. Firstly, the fundamental concepts of the classical DEM as implemented in YADE will be discussed. Secondly, an overview of the basic functionalities of YADE is provided. This will include how to set up and run simulations within a Python environment. Advanced features such as post-processing, parameter calibration, deformable structures, non-spherical particles and coupling with other methods will also be covered.

Robust numerical methods for solving complex problems involving multi-phase multi-physical processes are crucial and also an increasing trend in recent years in the field of computational geomechanics. The key reason is because most popular existing computational tools for field scale-application are still heavily relied on the traditional finite element method (FEM), which is a continuum mesh-based method and is well-known for suffering from mesh-distortion issues associated with large deformation of geomaterials. 

Alternative to FEM is continuum particle-based methods, which offer great capacity for solving field-scale applications involving large-deformation and post-failure of geomaterials. Among several existing point-based methods, SPH is the only numerical method that is completely mesh-free and requires no background mesh. The method was originally developed for astrophysics applications, but soon becoming a popular method for various engineering applications including geomechanics. The fundamental difference between SPH and other particle-based FEM methods is that SPH solve the governing PDE equations in strong form. Since there is no need to go through the weak forms, it is more straightforward to incorporate SPH approximation of a new PDE describing a new physical phenomenon in an existing SPH framework. In this lecture, we will present the fundamental concepts of SPH and its applications in modelling granular flows. In the first part of the lecture, we will focus on establishing fundamental SPH equations and discussing how they are applied in solving governing differential equations for continuum systems. In the second part of lecture, we will provide some hand-on experience working with a new SPH-based computing software, namely GeoXPM (https://geoxpm.com) recently developed for solving complex geomechanics and geotechnical engineering applications involving fracture and large deformations and made free to public. To maximize the learning outcome from this short course, we will focus on the application of GeoXPM to model granular flows using standard constitutive models.

A Hands-on session will be organised after the lectures where the participants will be given the opportunity to apply their learnings. Some examples with specific tasks will be prepared and participants will have the opportunity to solve the same problem with different methods/codes. This interactive session is designed to be a practical dialogue between discrete (DEM) and continuum (SPH) methods and to provide a deeper understanding of the powerful capabilities of the two methods presented in the lectures.

Participants are encouraged to bring their own laptop. GeoXPM will run under MS Windows whereas YADE requires Linux. Note that a virtual machine will be provided to participants that do not have access to a Linux machine. The virtual machine should be installed prior to the session. More details will be provided on the ANAGRAM website.