Faculty Advisor

Larsen, Christopher J.

Abstract

Certain energy functionals used in the study of cohesive fracture impose a finite stress threshold and prevent the use of standard minimization techniques based on a compactness property of SBV, the natural space of functions for the investigation of fracture. The issue is that in the limit, crack sets can become diffuse and a limiting function may not be in SBV. An alternative formulation is developed in Larsen (2013) which places a constraint on the crack set and seeks an "admissible" crack, defined as those cracks for which the restricted minimizers satisfy a threshold condition. We show the existence of such cracks in 2 dimensions for a subclass of energy functionals and in the case of affine boundary conditions by explicitly constructing the minimizing functions.

Publisher

Worcester Polytechnic Institute

Date Accepted

March 2015

Major

Mathematical Sciences

Project Type

Major Qualifying Project

Accessibility

Unrestricted

Advisor Department

Mathematical Sciences

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