Date of Award

Spring 1-1-2014

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Franck J. Vernerey

Second Advisor

John Pellegrino

Third Advisor

David Bortz

Fourth Advisor

Richard Regueiro

Fifth Advisor

Ronald Pak

Abstract

The mechanics of the interaction between a fluid and a soft interface (such as an elastic membrane or shell) undergoing large deformations appears in many places, such as in biological systems or industrial processes. We present here an Eulerian approach that describes the mechanics of an interface and its interactions with a surrounding fluid via the so-called Navier boundary condition. The interface is modeled as a curvilinear surface with arbitrary mechanical properties across which discontinuities in pressure and tangential fluid velocity can naturally be enforced using a modified version of the extended finite element method. The tracking and evolution of the membrane is then handled with the Grid Based Particle method, and the handling of complex singular boundary conditions around sharp corner is accounted for with the use of an asymptotic/numerical matching method. We show that this method is ideal to describe large membrane deformations, enforce volume constraints, and Navier boundary conditions on the interface with velocity/pressure discontinuities. The method is applied to the study of the filtration of deformable particles through a fibrous network, and an the equivalent permeabilities with respect to the fluid and particles are estimated. The method is then adapted to the study of an elastic material in an Eulerian framework and is shown to be capable of handling arbitrarily large deformations, which is ideal for the study of biological problems.

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