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. doi:10.1016/S0022-5096(99)00029-0
Tutorial on states (including examples of Frechet derivatives)
Selected reports and publications
- 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. doi:10.1016/j.cma.2014.01.002
- Variable horizon in a peridynamic medium (with D. Littlewood and P. Seleson) 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)
- Crack nucleation in a peridynamic solid (with O. Weckner, E. Askari, and F. Bobaru), International Journal of Fracture 162 (2010) 219-227. doi:10.1007/s10704-010-9447-z
- Green's functions in non-local three-dimensional linear elasticity (with O. Weckner, G. Brunk, M. A. Epton, and E. Askari). doi: 10.1098/rspa.2009.0234 .
- 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. doi:10:1002/nme.2439
- 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. doi10.1088/1742-6596/125/1/012078
- Convergence of peridynamics to classical elasticity theory (with R. B. Lehoucq), Journal of Elasticity 93 (2008) 13-37. doi:10.1007/s10659-008-9163-3
- Force flux and the peridynamic stress tensor (with R. B. Lehoucq), Journal of the Mechanics and Physics of Solids 56 (2008) 1566-1577. doi:10.1016/j.jmps.2007.08.004
- Peridynamic states and constitutive modeling (with M. Epton, O. Weckner, J. Xu, and E. Askari), Journal of Elasticity 88 (2007) 151-184. doi:10.1007/s10659-007-9125-1
Peridynamics via finite element analysis (with R. W. Macek), Finite Elements in Analysis and Design 43 (2007) 1169-1178. doi:10.1016/j.finel.2007.08.012
Peridynamic modeling of concrete structures (with W. Gerstle and N. Sau), Nuclear Engineering and Design 237 (2007) 1250-1258. doi:10.1016/j.nucengdes.2006.10.002
- 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)
I. A. Kunin's nonlocal theory (predecessor and special case of peridynamics)
Brief survey of nonlocal continuum mechanics theories
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.
MS-1322, P.O. Box 5800, Sandia National Laboratories, Albuquerque, NM 87185-1322 USA
EMU Peridynamic Code
Peridynamics Wikipedia page
LAMMPS Molecular Dynamics Code
Peridigm open source peridynamic code
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(Photo courtesy R. Brannon)
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