Particulate Discrete Element Modelling: A Geomechanics by Catherine O'Sullivan

By Catherine O'Sullivan

Particulate discrete point research is changing into more and more renowned for examine in geomechanics in addition to geology, chemical engineering, powder know-how, petroleum engineering and in learning the physics of granular fabrics. With elevated computing energy, working towards engineers also are changing into extra attracted to utilizing this expertise for research in commercial purposes. this can be the 1st unmarried paintings on Discrete point Modelling (DEM) delivering the data to start with this robust numerical modelling technique. Written through an self reliant writer with event either in constructing DEM codes and utilizing advertisement codes, this ebook offers the elemental information of the numerical procedure and the techniques used to interpret the result of DEM simulations. delivering a easy review of the numerical technique, Particulate Discrete aspect Modelling discusses concerns on the topic of time integration and numerical balance, particle forms, touch modelling and boundary stipulations. It summarizes methods to interpret DEM information in order that clients can maximize their perception into the fabric reaction utilizing DEM. the purpose of this e-book is to supply either clients and potential clients of DEM with a concise reference booklet that incorporates the way to optimize their utilization. Particulate Discrete aspect Modelling is appropriate either for first time DEM analysts in addition to more matured clients. it will likely be of use to execs, researchers and better point scholars, because it offers a theoretical assessment of DEM in addition to sensible counsel on working DEM simulations and analyzing DEM simulation facts.

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The creation of triangulations of the system is useful for applications including construction of the initial specimen geometry (Chapter 7), application of boundary stresses (Chapter 5), calculation of strain (Chapter 9), and analysis of the material fabric (Chapter 10). An overview of triangulation is therefore included at this point. More detailed considerations of the application of Delaunay triangulation in granular mechanics are given by Li and Li (2009), Goddard (2001), Ferrez (2001) and Bagi (1999a).

Rapaport (2004) describes the implementation of a subroutine to construct a Voronoi polygon to analyse the structure of particulate systems in a molecular dynamics code, while Ferrez (2001) discusses the use of triangulation for contact detection. It may also be possible to use triangulation to couple DEM particle codes with continuum mechanics to represent a fluid phase. e. with no gaps). These tessellations can exist in two- and three-dimensional space. Amongst the most commonly used tessellations are the Delaunay triangulation and the Voronoi diagram; these geometrical constructs are closely related and each is said to be the “dual” of the other.

If predictions are made using a time calculated as T = 2π m k increment that exceeds this critical value the results quickly become physically unreasonable and the analysis is said to be unstable. These restrictions on the choice of time increment that occur when using the central-difference approach to this simple, single degree of freedom system also apply in the multi degree of freedom simulations in DEM. The critical time increment for stable analysis can be calculated using linear stability analysis by considering the amplification matrix, Zienkiewicz and Taylor (2000a).

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