My main research interest:

Development of peridynamics and its applications.

What is peridynamics?

Peridynamics is a new approach to continuum mechanics based on integral equations. It extends the classical theory of continuum mechanics to allow:

• 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 from 16th US National Congress on Theoretical and Applied Mechanics (USNCTAM), State College, Pennsylvania, July 2010: Energy Balance for a Moving Defect in a Peridynamic Solid

• Presentation slides from SIAM Conference on Mathematical Aspects of Materials Science, Philadelphia, May 2010: Length scales and time scales in peridynamics

• Presentation slides from seminar at Purdue University School of Aeronautics and Astronautics, August 2009: Unifying the mechanics of continua, cracks, and particles

• Presentation slides from keynote lecture at the 15th International Symposium on Plasticity, St. Thomas, 2009: Peridynamic modeling of the dynamic response of heterogeneous media

• Paper from the Joint US-Russian Conference on Advances in Materials Science, Prague, 2009: Accurate prediction of dynamic fracture with peridynamics. Presentation slides: Peridynamics and dynamic fracture

Selected publications

• A coarsening method for linear peridynamics, to appear in International Journal for Multiscale Computational Engineering. SAND2010-3303

• Crack nucleation in a peridynamic solid (with O. Weckner, E. Askari, and F. Bobaru), to appear in International Journal of Fracture. doi:10.1007/s10704-010-9447-z

• Linearized theory of peridynamic states, Journal of Elasticity 99 (2010) 85-111. doi:10.1007/s10659-009-9234-0, 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). 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)

• A meshfree method based on the peridynamic model of solid mechanics (with E. Askari), Computers and Structures 83 (2005) 1526-1535. doi:10.1016/j.compstruc.2004.11.026 

• Peridynamic modeling of membranes and fibers (with F. Bobaru), International Journal of Non-Linear Mechanics 40 (2005) 395-409. doi:10.1016/j.ijnonlinmec.2004.08.004 

• Deformation of a peridynamic bar (with M. Zimmermann and R. Abeyaratne), Journal of Elasticity 73 (2003) 173-190. 10.1023/B:ELAS.0000029931.03844.4f

• 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  

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 Dynamic Multiscale Material Modeling Department.

Some people who have contributed to peridynamics

Prof. Rohan Abeyaratne, Massachusetts Institute of Technology

Ms. Abigail Agwal, University of Arizona

Dr. Bacim Alali, Lousiana State University

Mr. Leonardo F. Alves, University of Nebraska, Lincoln

Dr. Abe Askari, The Boeing Company

Prof. Kaushik Bhattacharya, California Institute of Technology

Mr. Justin Birkey, Kansas State University

Dr. Joseph Bishop, Sandia National Laboratories

Prof. Florin Bobaru, University of Nebraska, Lincoln

Prof. Kaushik Dayal, Carnegie-Mellon University

Dr. Paul Demmie, Sandia National Laboratories

Prof. Etienne Emmrich, Technical University of Berlin

Mr. John Foster, Sandia National Laboratories

Prof. Walter Gerstle, University of New Mexico

Mr. Bahattin Kilic, University of Arizona

Prof. Kevin Lease, Kansas State University

Dr. Richard Lehoucq, Sandia National Laboratories

Prof. Robert Lipton, Louisiana State University

Dr. Richard W. Macek, Los Alamos National Laboratories

Prof. Erdogan Madenci, University of Arizona

Mr. Erkan Oterkus, University of Arizona

Dr. Michael Parks, Sandia National Laboratories

Dr. Steven Plimpton, Sandia National Laboratories

Dr. Nicolas Sau, University of New Mexico

Prof. David Steigmann, University of California, Berkeley

Prof. Dan Swenson, Kansas State University

Mr. Michael Taylor, Univeristy of California, Berkeley

Dr. Paul Taylor, Sandia National Laboratories

Dr. Thomas L. Warren, Consultant

Dr. Olaf Weckner, The Boeing Company

Ms. Wei Xie, University of Nebraska, Lincoln

Dr. Jifeng Xu, The Boeing Company

Prof. Mijia Yang, University of Texas at El Paso

Mr. Kebing Yu, Kansas State University