Variable horizon in a peridynamic medium
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 positiondependent 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 localnonlocal coupling. Computational examples, including dynamic fracture in a onedimensional model with localnonlocal coupling, illustrate the methods.
 Authors:

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 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Mechanics of Materials and Structures
 Additional Journal Information:
 Journal Volume: 10; Journal Issue: 5; Journal ID: ISSN 15593959
 Publisher:
 Mathematical Science Publishers
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 36 MATERIALS SCIENCE; elasticity; nonlocality; local–nonlocal coupling; peridynamics
 OSTI Identifier:
 1311296
Silling, Stewart A., Littlewood, David J., and Seleson, Pablo. Variable horizon in a peridynamic medium. United States: N. p.,
Web. doi:10.2140/jomms.2015.10.591.
Silling, Stewart A., Littlewood, David J., & Seleson, Pablo. Variable horizon in a peridynamic medium. United States. doi:10.2140/jomms.2015.10.591.
Silling, Stewart A., Littlewood, David J., and Seleson, Pablo. 2015.
"Variable horizon in a peridynamic medium". United States.
doi: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 positiondependent 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 localnonlocal coupling. Computational examples, including dynamic fracture in a onedimensional model with localnonlocal 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 = {2015},
month = {12}
}