Deformation of a Peridynamic Bar

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Description

The deformation of an infinite bar subjected to a self-equilibrated load distribution is investigated using the peridynamic formulation of elasticity theory. The peridynamic theory differs from the classical theory and other nonlocal theories in that it does not involve spatial derivatives of the displacement field. The bar problem is formulated as a linear Fredholm integral equation and solved using Fourier transform methods. The solution is shown to exhibit, in general, features that are not found in the classical result. Among these are decaying oscillations in the displacement field and progressively weakening discontinuities that propagate outside of the loading region. These ... continued below

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29 pages

Creation Information

SILLING, STEWART A.; ZIMMERMANN, M. & ABEYARATNE, R. March 1, 2003.

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This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 25 times . More information about this report can be viewed below.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM, and Livermore, CA (United States)
    Place of Publication: Albuquerque, New Mexico

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Description

The deformation of an infinite bar subjected to a self-equilibrated load distribution is investigated using the peridynamic formulation of elasticity theory. The peridynamic theory differs from the classical theory and other nonlocal theories in that it does not involve spatial derivatives of the displacement field. The bar problem is formulated as a linear Fredholm integral equation and solved using Fourier transform methods. The solution is shown to exhibit, in general, features that are not found in the classical result. Among these are decaying oscillations in the displacement field and progressively weakening discontinuities that propagate outside of the loading region. These features, when present, are guaranteed to decay provided that the wave speeds are real. This leads to a one-dimensional version of St. Venant's principle for peridynamic materials that ensures the increasing smoothness of the displacement field remotely from the loading region. The peridynamic result converges to the classical result in the limit of short-range forces. An example gives the solution to the concentrated load problem, and hence provides the Green's function for general loading problems.

Physical Description

29 pages

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  • Other Information: PBD: 1 Mar 2003

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  • Report No.: SAND2003-0757
  • Grant Number: AC04-94AL85000
  • DOI: 10.2172/809105 | External Link
  • Office of Scientific & Technical Information Report Number: 809105
  • Archival Resource Key: ark:/67531/metadc738790

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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Creation Date

  • March 1, 2003

Added to The UNT Digital Library

  • Oct. 18, 2015, 6:40 p.m.

Description Last Updated

  • April 12, 2016, 3:27 p.m.

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SILLING, STEWART A.; ZIMMERMANN, M. & ABEYARATNE, R. Deformation of a Peridynamic Bar, report, March 1, 2003; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc738790/: accessed December 16, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.