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.

Creator

• Richardson, Casey Lyndale

Contributeurs

• Lurie, Konstantin
• Larsen, Christopher J.
• Francfort, Gilles A.
• Sarkis-Martins, Marcus
• Ortiz, Michael

Degree

• PhD

Unit

• Mathematical Sciences

Publisher

• Worcester Polytechnic Institute

Language

• English

Identifier

• etd-042508-150419

Mot-clé

• variational fracture crack fronts level set

Advisor

• Larsen, Christopher J.

Committee

• Francfort, Gilles A.
• Ortiz, Michael
• Lurie, Konstantin A.
• Sarkis-Martins, Marcus

Defense date

• 2008-04-21

Year

• 2008

Date created

• 2008-04-25

Resource type

• Dissertation

Rights statement

• In Copyright

Dernière modification

• 2023-09-27