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Discrete Modeling of Granular Media: A NURBS-based Approach

Citation

Lim, Keng-Wit (2015) Discrete Modeling of Granular Media: A NURBS-based Approach. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9W093V4. http://resolver.caltech.edu/CaltechTHESIS:12042014-104112714

Abstract

This dissertation is concerned with the development of a new discrete element method (DEM) based on Non-Uniform Rational Basis Splines (NURBS). With NURBS, the new DEM is able to capture sphericity and angularity, the two particle morphological measures used in characterizing real grain geometries. By taking advantage of the parametric nature of NURBS, the Lipschitzian dividing rectangle (DIRECT) global optimization procedure is employed as a solution procedure to the closest-point projection problem, which enables the contact treatment of non-convex particles. A contact dynamics (CD) approach to the NURBS-based discrete method is also formulated. By combining particle shape flexibility, properties of implicit time-integration, and non-penetrating constraints, we target applications in which the classical DEM either performs poorly or simply fails, i.e., in granular systems composed of rigid or highly stiff angular particles and subjected to quasistatic or dynamic flow conditions. The CD implementation is made simple by adopting a variational framework, which enables the resulting discrete problem to be readily solved using off-the-shelf mathematical programming solvers. The capabilities of the NURBS-based DEM are demonstrated through 2D numerical examples that highlight the effects of particle morphology on the macroscopic response of granular assemblies under quasistatic and dynamic flow conditions, and a 3D characterization of material response in the shear band of a real triaxial specimen.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Discrete element method, contact dynamics, NURBS, granular media
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Awards:Centennial Prize For The Best Thesis In Mechanical And Civil Engineering, 2015
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Andrade, Jose E.
Thesis Committee:
  • Ortiz, Michael (chair)
  • Ampuero, Jean-Paul
  • Ravichandran, Guruswami
  • Andrade, Jose E.
Defense Date:25 November 2014
Non-Caltech Author Email:kengwit (AT) gmail.com
Funders:
Funding AgencyGrant Number
National Science FoundationCMMI 1060087
Air Force Office of Scientific ResearchFA9550-11-1-0052
Record Number:CaltechTHESIS:12042014-104112714
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:12042014-104112714
DOI:10.7907/Z9W093V4
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8734
Collection:CaltechTHESIS
Deposited By: Keng Wit Lim
Deposited On:10 Dec 2014 23:47
Last Modified:12 Apr 2016 22:27

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