Variable horizon in a peridynamic medium
Abstract
Here, a notion of material homogeneity is proposed for peridynamic bodies with variable horizon but constant bulk properties. A relation is derived that scales the force state according to the position-dependent horizon while keeping the bulk properties unchanged. Using this scaling relation, if the horizon depends on position, artifacts called ghost forces may arise in a body under a homogeneous deformation. These artifacts depend on the second derivative of the horizon and can be reduced by employing a modified equilibrium equation using a new quantity called the partial stress. Bodies with piecewise constant horizon can be modeled without ghost forces by using a simpler technique called a splice. As a limiting case of zero horizon, both the partial stress and splice techniques can be used to achieve local-nonlocal coupling. Computational examples, including dynamic fracture in a one-dimensional model with local-nonlocal coupling, illustrate the methods.
- Authors:
-
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC)
- OSTI Identifier:
- 1311296
- Grant/Contract Number:
- AC05-00OR22725
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Mechanics of Materials and Structures
- Additional Journal Information:
- Journal Volume: 10; Journal Issue: 5; Journal ID: ISSN 1559-3959
- Publisher:
- Mathematical Science Publishers
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; elasticity; nonlocality; localānonlocal coupling; peridynamics
Citation Formats
Silling, Stewart A., Littlewood, David J., and Seleson, Pablo. Variable horizon in a peridynamic medium. United States: N. p., 2015.
Web. doi:10.2140/jomms.2015.10.591.
Silling, Stewart A., Littlewood, David J., & Seleson, Pablo. Variable horizon in a peridynamic medium. United States. https://doi.org/10.2140/jomms.2015.10.591
Silling, Stewart A., Littlewood, David J., and Seleson, Pablo. Thu .
"Variable horizon in a peridynamic medium". United States. https://doi.org/10.2140/jomms.2015.10.591. https://www.osti.gov/servlets/purl/1311296.
@article{osti_1311296,
title = {Variable horizon in a peridynamic medium},
author = {Silling, Stewart A. and Littlewood, David J. and Seleson, Pablo},
abstractNote = {Here, a notion of material homogeneity is proposed for peridynamic bodies with variable horizon but constant bulk properties. A relation is derived that scales the force state according to the position-dependent horizon while keeping the bulk properties unchanged. Using this scaling relation, if the horizon depends on position, artifacts called ghost forces may arise in a body under a homogeneous deformation. These artifacts depend on the second derivative of the horizon and can be reduced by employing a modified equilibrium equation using a new quantity called the partial stress. Bodies with piecewise constant horizon can be modeled without ghost forces by using a simpler technique called a splice. As a limiting case of zero horizon, both the partial stress and splice techniques can be used to achieve local-nonlocal coupling. Computational examples, including dynamic fracture in a one-dimensional model with local-nonlocal coupling, illustrate the methods.},
doi = {10.2140/jomms.2015.10.591},
journal = {Journal of Mechanics of Materials and Structures},
number = 5,
volume = 10,
place = {United States},
year = {Thu Dec 10 00:00:00 EST 2015},
month = {Thu Dec 10 00:00:00 EST 2015}
}
Web of Science
Works referenced in this record:
A Morphing framework to couple non-local and local anisotropic continua
journal, May 2013
- Azdoud, Yan; Han, Fei; Lubineau, Gilles
- International Journal of Solids and Structures, Vol. 50, Issue 9
The morphing method as a flexible tool for adaptive local/non-local simulation of static fracture
journal, April 2014
- Azdoud, Yan; Han, Fei; Lubineau, Gilles
- Computational Mechanics, Vol. 54, Issue 3
Adaptive Refinement and Multiscale Modeling in 2d Peridynamics
journal, January 2011
- Bobaru, Florin; Ha, Youn Doh
- International Journal for Multiscale Computational Engineering, Vol. 9, Issue 6
Convergence, adaptive refinement, and scaling in 1D peridynamics
journal, February 2009
- Bobaru, Florin; Yang, Mijia; Alves, Leonardo Frota
- International Journal for Numerical Methods in Engineering, Vol. 77, Issue 6
Non-ordinary state-based peridynamic analysis of stationary crack problems
journal, April 2014
- Breitenfeld, M. S.; Geubelle, P. H.; Weckner, O.
- Computer Methods in Applied Mechanics and Engineering, Vol. 272
Review of experimental techniques for high rate deformation and shock studies
journal, August 2004
- Field, J. E.; Walley, S. M.; Proud, W. G.
- International Journal of Impact Engineering, Vol. 30, Issue 7
Coupling of nonlocal and local continuum models by the Arlequināapproach: COUPLING OF NONLOCAL/LOCAL CONTINUUM MODELS BY THE ARLEQUIN APPROACH
journal, August 2011
- Han, Fei; Lubineau, Gilles
- International Journal for Numerical Methods in Engineering, Vol. 89, Issue 6
Force flux and the peridynamic stress tensor
journal, April 2008
- Lehoucq, R.; Silling, S.
- Journal of the Mechanics and Physics of Solids, Vol. 56, Issue 4
A Nonlocal Approach to Modeling Crack Nucleation in AA 7075-T651
conference, August 2012
- Littlewood, David J.
- ASME 2011 International Mechanical Engineering Congress and Exposition, Volume 8: Mechanics of Solids, Structures and Fluids; Vibration, Acoustics and Wave Propagation
A coupling approach of discretized peridynamics with finite element method
journal, October 2012
- Liu, Wenyang; Hong, Jung-Wuk
- Computer Methods in Applied Mechanics and Engineering, Vol. 245-246
A morphing strategy to couple non-local to local continuum mechanics
journal, June 2012
- Lubineau, Gilles; Azdoud, Yan; Han, Fei
- Journal of the Mechanics and Physics of Solids, Vol. 60, Issue 6
Peridynamics via finite element analysis
journal, November 2007
- Macek, Richard W.; Silling, Stewart A.
- Finite Elements in Analysis and Design, Vol. 43, Issue 15
Combined finite element and peridynamic analyses for predicting failure in a stiffened composite curved panel with a central slot
journal, February 2012
- Oterkus, Erkan; Madenci, Erdogan; Weckner, Olaf
- Composite Structures, Vol. 94, Issue 3
Fully coupled peridynamic thermomechanics
journal, March 2014
- Oterkus, Selda; Madenci, Erdogan; Agwai, Abigail
- Journal of the Mechanics and Physics of Solids, Vol. 64
Peridynamic thermal diffusion
journal, May 2014
- Oterkus, Selda; Madenci, Erdogan; Agwai, Abigail
- Journal of Computational Physics, Vol. 265
On the role of the Influence Function in the Peridynamic Theory
journal, January 2011
- Seleson, Pablo; Parks, Michael
- International Journal for Multiscale Computational Engineering, Vol. 9, Issue 6
A force-based coupling scheme for peridynamics and classical elasticity
journal, January 2013
- Seleson, Pablo; Beneddine, Samir; Prudhomme, Serge
- Computational Materials Science, Vol. 66
Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains
journal, November 2013
- Seleson, Pablo; Gunzburger, Max; Parks, Michael L.
- Computer Methods in Applied Mechanics and Engineering, Vol. 266
Concurrent Coupling of Bond-Based Peridynamics and the Navier Equation of Classical Elasticity by Blending
journal, January 2015
- Seleson, Pablo; Ha, Youn Doh; Beneddine, Samir
- International Journal for Multiscale Computational Engineering, Vol. 13, Issue 2
Reformulation of elasticity theory for discontinuities and long-range forces
journal, January 2000
- Silling, S. A.
- Journal of the Mechanics and Physics of Solids, Vol. 48, Issue 1
Linearized Theory of Peridynamic States
journal, January 2010
- Silling, S. A.
- Journal of Elasticity, Vol. 99, Issue 1
A meshfree method based on the peridynamic model of solid mechanics
journal, June 2005
- Silling, S. A.; Askari, E.
- Computers & Structures, Vol. 83, Issue 17-18
Convergence of Peridynamics to Classical Elasticity Theory
journal, April 2008
- Silling, S. A.; Lehoucq, R. B.
- Journal of Elasticity, Vol. 93, Issue 1
Peridynamic Theory of Solid Mechanics
book, September 2010
- Silling, S. A.; Lehoucq, R. B.
- Advances in Applied Mechanics
Peridynamic States and Constitutive Modeling
journal, July 2007
- Silling, S. A.; Epton, M.; Weckner, O.
- Journal of Elasticity, Vol. 88, Issue 2
A finite difference-augmented peridynamics method for reducing wave dispersion
journal, October 2014
- Wildman, Raymond A.; Gazonas, George A.
- International Journal of Fracture, Vol. 190, Issue 1-2
Kinematic constraints in the state-based peridynamics with mixed local/nonlocal gradient approximations
journal, September 2014
- Wu, C. T.
- Computational Mechanics, Vol. 54, Issue 5
Works referencing / citing this record:
An implicit dualābased approach to couple peridynamics with classical continuum mechanics
journal, August 2019
- Bie, Yehui; Li, She; Hu, Xin
- International Journal for Numerical Methods in Engineering, Vol. 120, Issue 12
Dual-horizon peridynamics: Dual-horizon peridynamics
journal, July 2016
- Ren, Huilong; Zhuang, Xiaoying; Cai, Yongchang
- International Journal for Numerical Methods in Engineering, Vol. 108, Issue 12
Superposition-based coupling of peridynamics and finite element method
journal, February 2019
- Sun, Wei; Fish, Jacob
- Computational Mechanics, Vol. 64, Issue 1
Voronoi-based peridynamics and cracking analysis with adaptive refinement: Voronoi-based peridynamics and cracking analysis with adaptive refinement
journal, August 2017
- Gu, Xin; Zhang, Qing; Xia, Xiaozhou
- International Journal for Numerical Methods in Engineering, Vol. 112, Issue 13
Peridynamics review
journal, October 2018
- Javili, Ali; Morasata, Rico; Oterkus, Erkan
- Mathematics and Mechanics of Solids, Vol. 24, Issue 11
A new peridynamic formulation with shear deformation for elastic solid
journal, July 2016
- Ren, Huilong; Zhuang, Xiaoying; Rabczuk, Timon
- Journal of Micromechanics and Molecular Physics, Vol. 01, Issue 02
Quasinonlocal coupling of nonlocal diffusions
preprint, January 2016
- Li, Xingjie Helen; Lu, Jianfeng
- arXiv
A quasinonlocal coupling method for nonlocal and local diffusion models
preprint, January 2017
- Du, Qiang; Li, Xingjie Helen; Lu, Jianfeng
- arXiv
A non-ordinary peridynamics implementation for anisotropic materials
preprint, January 2017
- Hattori, Gabriel; Trevelyan, Jon; Coombs, William M.
- arXiv
Reduction of integration domain in Triebel-Lizorkin spaces
preprint, January 2018
- Rutkowski, Artur
- arXiv
A review of Local-to-Nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics
preprint, January 2019
- D'Elia, Marta; Li, Xingjie; Seleson, Pablo
- arXiv