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Variable horizon in
a peridynamic medium
Stewart A. Silling, David J. Littlewood and Pablo Seleson |
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Vol. 10 (2015), No. 5, 591–612
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DOI: 10.2140/jomms.2015.10.591
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Abstract |
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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. |
Keywords
elasticity, nonlocality, local–nonlocal coupling,
peridynamics
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Milestones
Received: 6 January 2015
Accepted: 21 April 2015
Published: 10 December 2015
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Authors |
| Stewart A. Silling | |
| Multiscale Science Department Sandia National Laboratories P.O. Box 5800 MS 1322 Albuquerque, NM 87185-1320 United States |
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| David J. Littlewood | |
| Multiscale Science Department Sandia National Laboratories P.O. Box 5800 MS 1322 Albuquerque, NM 87185-1320 United States |
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| Pablo Seleson | |
| Computer Science and Mathematics
Division Oak Ridge National Laboratory P.O. Box 2008 Oak Ridge, TN 37831 United States |
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