Utilization of Peridynamic Theory for Modeling at the Nano-Scale

  • E. OterkusEmail author
  • C. Diyaroglu
  • N. Zhu
  • S. Oterkus
  • E. Madenci
Conference paper
Part of the Advances in Atom and Single Molecule Machines book series (AASMM)


Peridynamic theory is a new continuum mechanics formulation that has several advantages over the traditional approaches, such as Classical Continuum Mechanics (CCM) and Molecular Dynamics (MD). Due to its length-scale parameter, horizon, it is capable of capturing phenomena occurring at different length scales, including the nano-scale. Furthermore, van der Waals forces can be represented in a straightforward manner using a buffer-layer approach. In this chapter, various demonstration problems are presented to show the capability of peridynamics at the nano-scale, including nano-indentation and failure analysis of graphene sheets.


Graphene Sheet Graphene Layer Material Point Horizon Size Classical Continuum Mechanic 
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  1. 1.
    Silling, S.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids. 48, 175–209 (2000)CrossRefGoogle Scholar
  2. 2.
    Madenci, E., Oterkus, E.: Peridynamic theory and its applications. Springer, New York (2014)CrossRefGoogle Scholar
  3. 3.
    Macek, R., Silling, S.: Peridynamics via finite element analysis. Finite Elem. Anal. Des. 43, 1169–1178 (2007)CrossRefGoogle Scholar
  4. 4.
    Weckner, O., Brunk, G., Epton, M., Silling, S., Askari, E.: Green’s functions in non-local three-dimensional linear elasticity. Proc Roy Soc A 465, 3463–3487 (2009)CrossRefGoogle Scholar
  5. 5.
    Seleson, P., Parks, M., Gunzburger, M., Lehocq, R.: Peridynamics as an upscaling of molecular dynamics. Multiscale Model Sim. 8, 204–227 (2009)CrossRefGoogle Scholar
  6. 6.
    Mikata, Y.: Analytical solutions of peristatic and peridynamic problems for a 1D infinite rod. Int. J. Solids Struct. 49, 2887–2897 (2012)CrossRefGoogle Scholar
  7. 7.
    Walsh, P., Omeltchenko, A., Kalia, R., Nakano, A., Vashista, P.: Nanoindentation of silicon nitride: a multimillion-atom molecular dynamics study. Appl. Phys. Lett. 82, 118–120 (2003)CrossRefGoogle Scholar
  8. 8.
    Omeltchenko, A., Yu, J., Kalia, R., Vashishta, P.: Crack front propagation and fracture in a graphite sheet: a molecular-dynamics study on parallel computers. Phys. Rev. Lett. 78, 2148–2151 (1997)CrossRefGoogle Scholar
  9. 9.
    Silling, S., Askari, A.: A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83, 1526–1535 (2005)CrossRefGoogle Scholar
  10. 10.
    Yang, B., Rethinam, R., Mall, S.: Modeling and analysis of cylindrical nanoindentation of graphite. J. Appl. Mech. 76, 011010 (2009)CrossRefGoogle Scholar
  11. 11.
    Oterkus, E., Madenci, E.: Peridynamic analysis of fiber reinforced composite materials. J Mech Mater Struct 7, 45–84 (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • E. Oterkus
    • 1
    Email author
  • C. Diyaroglu
    • 1
  • N. Zhu
    • 1
  • S. Oterkus
    • 2
  • E. Madenci
    • 2
  1. 1.Department of Naval Architecture, Ocean and Marine EngineeringUniversity of StrathclydeGlasgowUK
  2. 2.Department of Aerospace and Mechanical EngineeringUniversity of ArizonaTucsonUSA

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