Faculty Advisor or Committee Member

Christopher Larsen, Advisor

Faculty Advisor or Committee Member

Marcus Sarkis, Committee Member

Faculty Advisor or Committee Member

Konstantin Lurie, Committee Member

Faculty Advisor or Committee Member

Michael Ortiz, Committee Member

Faculty Advisor or Committee Member

Gilles Francfort, Committee Member

Identifier

etd-042508-150419

Abstract

This dissertation presents results for two separate problems, both in the context of variational fracture models. The first problem involved developing and analyzing models of fracture in which we modeled the energy dissipated by crack growth as concentrated on the front of the crack. While many engineering models of fracture are based on a notion of crack front, there had not been a rigorous definition. We present the first work in this area, which includes a natural weak definition of crack front and front speed, a model of fracture whose evolution is described at the crack front, and a relaxation result that shows that these front based dissipations are all effectively equivalent to a Griffith-type dissipation. The second problem involved the computation of stationary points for Mumford-Shah and fracture using a level set method. Our method improves on existing techniques in that it can handle tips in the singular set and can find minimizers that previous techniques are unable to resolve.

Publisher

Worcester Polytechnic Institute

Degree Name

PhD

Department

Mathematical Sciences

Project Type

Dissertation

Date Accepted

2008-04-25

Accessibility

Unrestricted

Subjects

variational fracture crack fronts level set

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