Abstract
Peridynamics is a formulation of continuum mechanics based on integral equations. It is a nonlocal model, accounting for the effects of long-range forces. Correspondingly, classical molecular dynamics is also a nonlocal model. Peridynamics and molecular dynamics have similar discrete computational structures, as peridynamics computes the force on a particle by summing the forces from surrounding particles, similarly to molecular dynamics. We demonstrate that the peridynamics model can be cast as an upscaling of molecular dynamics. Specifically, we address the extent to which the solutions of molecular dynamics simulations can be recovered by peridynamics. An analytical comparison of equations of motion and dispersion relations for molecular dynamics and peridynamics is presented along with supporting computational results.
| Original language | English |
|---|---|
| Pages (from-to) | 204-227 |
| Number of pages | 24 |
| Journal | Multiscale Modeling and Simulation |
| Volume | 8 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2009 |
| Externally published | Yes |
Funding
‡Department of Applied Mathematics and Applications, Sandia National Laboratories, P.O. Box 5800, MS 1320, Albuquerque, NM 87185-1320 ([email protected], [email protected]). The work of these authors was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94-AL85000. ∗Received by the editors January 28, 2009; accepted for publication (in revised form) July 10, 2009; published electronically November 25, 2009. The U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. Copyright is owned by SIAM to the extent not limited by these rights. http://www.siam.org/journals/mms/8-1/74807.html †Department of Scientific Computing, Florida State University, 400 Dirac Science Library, Tallahassee, FL 32306-4120 ([email protected], [email protected]). The research of these authors was supported by the DOE/OASCR under grant DE-FG02-05ER25698. The research of these authors was supported by the DOE/OASCR under grant DE-FG02-05ER25698. The work of these authors was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94-AL85000.
| Funders | Funder number |
|---|---|
| DOE/OASCR | DE-FG02-05ER25698 |
| OASCR | |
| U.S. Department of Energy | DE-AC04-94-AL85000 |
| Sandia National Laboratories | |
| Laboratory Directed Research and Development |
Keywords
- Higher-order gradient
- Molecular dynamics
- Peridynamics
- Upscaling