Simulation of elastic wave propagation using cellular automata and peridynamics, and comparison with experiments
Abstract
Peridynamics is a non-local continuum mechanics formulation that can handle spatial discontinuities as the governing equations are integro-differential equations which do not involve gradients such as strains and deformation rates. This paper employs bond-based peridynamics. Cellular Automata is a local computational method which, in its rectangular variant on interior domains, is mathematically equivalent to the central difference finite difference method. However, cellular automata does not require the derivation of the governing partial differential equations and provides for common boundary conditions based on physical reasoning. Both methodologies are used to solve a half-space subjected to a normal load, known as Lamb’s Problem. The results are compared with theoretical solution from classical elasticity and experimental results. Furthermore, this paper is used to validate our implementation of these methods.
- Authors:
-
[1];
- Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States)
- Georgia Institute of Technology, Atlanta, GA (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1263595
- Report Number(s):
- SAND-2015-8693J
Journal ID: ISSN 0165-2125; PII: S0165212515001195
- Grant/Contract Number:
- AC04-94AL85000
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Wave Motion
- Additional Journal Information:
- Journal Volume: 60; Journal Issue: C; Journal ID: ISSN 0165-2125
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; peridynamics; Cellular Automata; Lamb’s problem; wave propagation; surface waves; validation
Citation Formats
Nishawala, Vinesh V., Ostoja-Starzewski, Martin, Leamy, Michael J., and Demmie, Paul N. Simulation of elastic wave propagation using cellular automata and peridynamics, and comparison with experiments. United States: N. p., 2015.
Web. doi:10.1016/j.wavemoti.2015.08.005.
Nishawala, Vinesh V., Ostoja-Starzewski, Martin, Leamy, Michael J., & Demmie, Paul N. Simulation of elastic wave propagation using cellular automata and peridynamics, and comparison with experiments. United States. https://doi.org/10.1016/j.wavemoti.2015.08.005
Nishawala, Vinesh V., Ostoja-Starzewski, Martin, Leamy, Michael J., and Demmie, Paul N. Thu .
"Simulation of elastic wave propagation using cellular automata and peridynamics, and comparison with experiments". United States. https://doi.org/10.1016/j.wavemoti.2015.08.005. https://www.osti.gov/servlets/purl/1263595.
@article{osti_1263595,
title = {Simulation of elastic wave propagation using cellular automata and peridynamics, and comparison with experiments},
author = {Nishawala, Vinesh V. and Ostoja-Starzewski, Martin and Leamy, Michael J. and Demmie, Paul N.},
abstractNote = {Peridynamics is a non-local continuum mechanics formulation that can handle spatial discontinuities as the governing equations are integro-differential equations which do not involve gradients such as strains and deformation rates. This paper employs bond-based peridynamics. Cellular Automata is a local computational method which, in its rectangular variant on interior domains, is mathematically equivalent to the central difference finite difference method. However, cellular automata does not require the derivation of the governing partial differential equations and provides for common boundary conditions based on physical reasoning. Both methodologies are used to solve a half-space subjected to a normal load, known as Lamb’s Problem. The results are compared with theoretical solution from classical elasticity and experimental results. Furthermore, this paper is used to validate our implementation of these methods.},
doi = {10.1016/j.wavemoti.2015.08.005},
journal = {Wave Motion},
number = C,
volume = 60,
place = {United States},
year = {Thu Sep 10 00:00:00 EDT 2015},
month = {Thu Sep 10 00:00:00 EDT 2015}
}
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Works referencing / citing this record:
Solving partial differential equations in computational mechanics via nonlocal numerical approaches
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