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My main research interest:

Development of peridynamics and its applications.

What is peridynamics?

Peridynamics is a mathematical theory of mechanics that extends classical continuum mechanics to include discrete particles and growing cracks. Its applications include:

  • Unguided modeling of fracture in metals and composites.
  • Transition from continuous damage to fracture.
  • Modeling of long-range forces within a continuous body.
  • Atomistic to continuum coupling in a consistent mathematical framework.

Some background material (presentation slides)

Review article on peridynamics

  • Peridynamic theory of solid mechanics (with R. B. Lehoucq) Advances in Applied Mechanics 44 (2010) 73-166. Google books page here. Preprint available here.

First article on peridynamics

  • Reformulation of elasticity theory for discontinuities and long-range forces, Journal of the Mechanics and Physics of Solids 48 (2000) 175-209. Paper.  

Tutorial on states (including examples of Frechet derivatives)

Selected reports and publications

  • Attenuation of waves in a viscoelastic peridynamic medium, Mathematics and Mechanics of Solids 24 (2019) 3597-3613. Paper. Also see SAND2018-13198.
  • Non-ordinary state-based peridynamic analysis of stationary crack problems (by M.S. Breitenfeld, P.H. Geubelle, O. Weckner, and S.A. Silling) Computer Methods in Applied Mechanics and Engineering 272 (2014) 233-250.Paper.
  • Origin and effects of nonlocality in a composite, Journal of Mechanics of Materials and Structures 9 (2014) 245-258. Paper. Also see SAND2013-8140.
  • Non-ordinary state-based peridynamic analysis of stationary crack problems (by M.S. Breitenfeld, P.H. Geubelle, O. Weckner, and S.A. Silling) Computer Methods in Applied Mechanics and Engineering 272 (2014) 233-250.Paper.
  • Variable horizon in a peridynamic medium (with D. Littlewood and P. Seleson) Journal of Mechanics of Materials and Structures 10 (2015) 591-612. Paper. Also see SAND2014-19088 (2014)
  • Hierarchical multiscale method development for peridynamics (with J. V. Cox) SAND2014-18565 (2014)
  • Peridynamic model for fatigue cracking (with A. Askari) SAND2014-18590 (2014)
  • A coarsening method for linear peridynamics, International Journal for Multiscale Computational Engineering 9 (2011) 609-622. doi:Paper. Also see SAND2010-3303 .
  • Crack nucleation in a peridynamic solid (with O. Weckner, E. Askari, and F. Bobaru), International Journal of Fracture 162 (2010) 219-227. Paper.
  • Linearized theory of peridynamic states, Journal of Elasticity 99 (2010) 85-111. Paper. Also see SAND2009-2458
  • Green's functions in non-local three-dimensional linear elasticity (with O. Weckner, G. Brunk, M. A. Epton, and E. Askari). Paper.
  • Convergence, adaptive refinement, and scaling in 1D peridynamics (with F. Bobaru, M. Yang, L. F. Alves, E. Askari, and J. Xu), International Journal for Numerical Methods in Engineering 77 (2009) 852-877. Paper.
  • Peridynamics for multiscale materials modeling (with E. Askari, F. Bobaru, R. B. Lehoucq, M. L. Parks, and O. Weckner), Journal of Physics Conference Series 125 (2008) 012078. Paper.
  • Convergence of peridynamics to classical elasticity theory (with R. B. Lehoucq), Journal of Elasticity 93 (2008) 13-37. Paper.
  • Force flux and the peridynamic stress tensor (with R. B. Lehoucq), Journal of the Mechanics and Physics of Solids 56 (2008) 1566-1577. Paper. 
  • Peridynamic states and constitutive modeling (with M. Epton, O. Weckner, J. Xu, and E. Askari), Journal of Elasticity 88 (2007) 151-184. Paper.
  • Peridynamics via finite element analysis (with R. W. Macek), Finite Elements in Analysis and Design 43 (2007) 1169-1178. Paper. 

  • Peridynamic modeling of concrete structures (with W. Gerstle and N. Sau), Nuclear Engineering and Design 237 (2007) 1250-1258. Paper. 

  • Statistical coarse-graining of molecular dynamics into peridynamics (with R. B. Lehoucq) SAND2007-6410 (2007)
  • Peridynamic analysis of damage and failure in composites (with E. Askari and J. Xu) 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA-2006-88 (2006)
  • A meshfree method based on the peridynamic model of solid mechanics (with E. Askari), Computers and Structures 83 (2005) 1526-1535. Paper. 
  • Peridynamic modeling of membranes and fibers (with F. Bobaru), International Journal of Non-Linear Mechanics 40 (2005) 395-409. Paper. 

  • Deformation of a peridynamic bar (with M. Zimmermann and R. Abeyaratne), Journal of Elasticity 73 (2003) 173-190. Paper.


  • My CV
  • My background

    S.B., 1977, Massachusetts Institute of Technology, Physics and Nuclear Engineering

    M.Eng., 1980, University of California, Berkeley, Nuclear Engineering

    Ph.D. 1986, California Institute of Technology, Applied Mechanics

    I have been a faculty member at Brown University, a visiting faculty member at the California Institute of Technology, and a Visiting Scholar at the Boeing Company.

    I am currently a Distinguished Member of the Technical Staff at Sandia National Laboratories in Albuquerque, New Mexico, USA, in the Multiscale Science Department, Computing Research Center.





    Stewart Silling

    Mailing address:

    MS-1322, P.O. Box 5800, Sandia National Laboratories, Albuquerque, NM 87185-1322 USA


    Related Links

    Peridynamics Wikipedia page

    LAMMPS Molecular Dynamics Code

    Peridigm open source peridynamic code



    "Please repeat the question?"

    (Photo courtesy R. Brannon)