Title page for ETD etd-042508-150419

Document Type	dissertation
Author Name	Richardson, Casey Lyndale
URN	etd-042508-150419
Title	Some Problems in the Mathematics of Fracture: Paths From Front Kinetics and a Level Set Method
Degree	PhD
Department	Mathematical Sciences
Advisors	Christopher Larsen, Advisor Gilles Francfort, Committee Member Michael Ortiz, Committee Member Konstantin Lurie, Committee Member Marcus Sarkis, Committee Member
Keywords	variational fracture crack fronts level set
Date of Presentation/Defense	2008-04-21
Availability	unrestricted
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.
Files	Casey_Richardson_Dissertation.pdf Casey_Richardson_Dissertation_Signatures.pdf

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