From the stand point of continuum mechanics, there are two distinct approaches to fracture, namely the global or classical approach and the local approach. In the former, a crack is viewed as a line or surface of discontinuity for the displacement and stress fields, which, by their turn, are singular at the crack tip. On the other hand, the local approach views a crack as a small region in which damage accumulates and the displacement and stress fields are continuous but have high gradients. This work aims at investigating possible relationships between two fracture theories: a global one and a local one. Specifically, under certain constitutive assumptions, the present work establishes necessary conditions for the local theory be a regularization of the global theory, or, equivalently, the global theory be obtained as an asymptotic limit of the local theory. The development of this work relies on the use of matching asymptotic technique and the balance of configurational forces.

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Graduate Courses:

1. ​introduction to elasticity

2. introduction to continuum mechanics

3. introduction to continuous thermodynamics

4. Hausdorff measure and Sobolev spaces

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