In this paper, the "crack derivatives", which de ned to be the limits of the blow-up sequences,are formulated and studied. Both quasi-static fracture evolution and dynamic fracture evolution are included. For quasi-static fracture evolution, the crack derivatives are proven to exist and globally minimize the energy functional on domain with arbitrary growing cracks. For dynamic fracture evolution, the crack derivatives are proven to be solutions of the wave equations on domain with arbitrary growing locally connected cracks.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Zhu, Meng

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-042513-152217

Advisor

• Ram-Mohan, L. Ramdas
• Larsen, Christopher J.

Year

• 2013

Date created

• 2013-04-25

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences
• Physics

Rights statement

• In Copyright