Doctoral Thesis
DOI
10.11606/T.3.2017.tde-17042017-092647
Document
Author
Full name
Marco Antonio Brasiel Sampaio
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2016
Supervisor
Committee
Pimenta, Paulo de Mattos (President)
Pereira, André Maués Brabo
Alves, José Luis Drummond
Campello, Eduardo de Morais Barreto
Gay Neto, Alfredo
Title in Portuguese
O método dos elementos discretos com superelipsoides usando a parametrização das rotações de Rodrigues.
Keywords in Portuguese
Geomecânica
Método dos elementos discretos
Parametrização de Rodrigues
Rotações vetoriais
Superelipsóide
Abstract in Portuguese
Title in English
Discrete element method with superellipsoid using Rodrigues parameterization for rotations.
Keywords in English
Discrete element method
Rodrigues parameterization
Superel-liptical
Vector rotations
Abstract in English
This work presents a formulation for Discrete Element Method (DEM) adopting a vector ap-proach to solve rotations. Herein, rotations are solved using Rodrigues parameterization. The main contributions of this work are: tangential displacements using the incremental rotation vector from Rodrigues parameterization, and integration of the rotation movement using leap-frog method and Rodrigues rotation tensor. The formulations are presented to spheres and superelliptical particles. Tangential displacements, which are used to get friction forces, are calculated through angular velocity. In most of DEM implementations, tangential displacements are calculated through the instantaneous linear velocity of the contact point. Instead, here the displacement of the contact point is given through the rotation of the particle. It is showed that the vector of in-cremental rotations can be calculated through the angular velocity. Particle movement is described using an updated Lagrangian approach. Leapfrog method is formulated in such a way to use the Rodrigues expression for successive rotations. Contact detection between superellipsoids is solved using a technic called "common normal approach", and it is solved as a minimization problem. The results show that the Rodrigues parameterization can be applied to discrete element method to both execute rotations and to evaluate physical quantities that are related to this kind of movement as tangential displacement.