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The optimal transportation method in solid mechanics


Li, Bo (2009) The optimal transportation method in solid mechanics. Dissertation (Ph.D.), California Institute of Technology.


This dissertation is concerned with the development of a robust and efficient meshless method, the Optimal Transportation Method (OTM), for general solid flows involving extremely large deformation, fast, transient loading and hydrodynamic phenomena. This method is a Lagrangian particle method through an integration of optimal transportation theory with meshless interpolation and material point integrations. The theoretical framework developed in this thesis generalized the Benamou-Brenier differential formulation of optimal transportation problems and leads to a multi-field variational characterization of solid flows, including elasticity, inelasticity, equation of state, and general geometries and boundary conditions. To this end, the accuracy, robustness and versatility of OTM is assessed and demonstrated with convergence and stability test, Taylor anvil test and a series of full three-dimensional simulations of high/hyper-velocity impact examples with the aid of a novel meshless dynamic contact algorithm presented in this thesis.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:extremely large deformation; hypervelocity impact; local maximum-entropy approximation; material point integration; meshless contact algorithm; meshless methods; optimal transportation theory
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Ortiz, Michael
Thesis Committee:
  • Ortiz, Michael (chair)
  • Daraio, Chiara
  • Ravichandran, Guruswami
  • Lapusta, Nadia
Defense Date:6 May 2009
Author Email:libo (AT)
Record Number:CaltechETD:etd-05212009-173044
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5193
Deposited By: Imported from ETD-db
Deposited On:29 May 2009
Last Modified:26 Dec 2012 03:15

Thesis Files

PDF (Thesis_Bo_Li.pdf) - Final Version
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