The Optimal Transportation Method in Solid Mechanics

Citation

Li, Bo (2009) The Optimal Transportation Method in Solid Mechanics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/FAT3-0247. https://resolver.caltech.edu/CaltechETD:etd-05212009-173044

Abstract

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.

Thesis Files