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.

• 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

• Smith, Michael Benjamin

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-032215-182913

Advisor

• Larsen, Christopher J.

Year

• 2015

Date created

• 2015-03-22

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright