rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Brittle Fracture Modeling with a Surface Tension Excess Property
  name:
    name part: Ferguson, Lauren Ann
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Walton, Jay
    role:
      role term: thesis advisor.
  name:
    name part: Texas A & M University
    role:
      role term: degree granting institution.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: txu
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource.
  abstract: The classical theory of linear elastic fracture mechanics for a quasi-static crack in an infinite linear elastic body has two significant mathematical inconsistencies: it predicts unbounded crack-tip stresses and an elliptical crack opening profile. A new theory of fracture developed by Sendova and Walton, based on extending continuum mechanics to the nanoscale, corrects these erroneous effects. The fundamental attribute of this theory is the use of a dividing surface to describe the material interface. The dividing surface is endowed with an excess property, namely surface tension, which accounts for atomistic effects in the interfacial region. When the surface tension is taken to be a constant, Sendova and Walton show that the theory reduces the crack-tip stress from a square root to a logarithmic singularity and yields a finite angle opening profile. In addition, they show that if the surface tension depends on curvature, the theory completely removes the stress singularity at the crack-tip, for all but countably many values of the two surface tension parameters, and yields a cusp-like opening profile. In this work, we develop a numerical model using the finite element method for the Sendova-Walton fracture theory applied to the classical Griffith crack problem in the case of constant surface tension. We show that the numerical model behaves as predicted by the theory, yielding a reduced crack-tip singularity and a finite opening angle for all nonzero values of the constant surface tension. We also lay the groundwork for the numerical implementation of the curvature-dependent model by constructing an algorithm to determine the appropriate threshold values for the surface tension parameters that guarantee bounded crack-tip stresses. These values can then be directly applied to the forthcoming numerical model. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/148359
  note: by Lauren Ann Ferguson.
  note: "Major Subject: Mathematics"
  note: Includes vita.
  note: Doctor of Philosophy Texas A & M University 2012 http://hdl.handle.net/1969.1/148359
  note: Includes bibliographical references.
  note: Text (Dissertation)
  subject:
    topic: Major Mathematics
  subject:
    topic: dividing surface
  subject:
    topic: numerical implementation
  subject:
    topic: modeling
  subject:
    topic: model
  subject:
    topic: surface tension
  subject:
    topic: brittle fracture
  subject:
    topic: fracture
  identifier: http://hdl.handle.net/1969.1/148359
  record info:
    record content source: TXA
    record creation date: 131213
    record change date: 20151206090623.0
    record identifier: in00003381955
    language of cataloging:
      language term: eng