Larsen, Christopher J.
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.
Worcester Polytechnic Institute
Major Qualifying Project
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