Vol. 10, No. 5, 2015

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Variable horizon in a peridynamic medium

Stewart A. Silling, David J. Littlewood and Pablo Seleson

Vol. 10 (2015), No. 5, 591–612
DOI: 10.2140/jomms.2015.10.591
Abstract

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
Milestones
Received: 6 January 2015
Accepted: 21 April 2015
Published: 10 December 2015
Authors
Stewart A. Silling
Multiscale Science Department
Sandia National Laboratories
P.O. Box 5800
MS 1322
Albuquerque, NM 87185-1320
United States
David J. Littlewood
Multiscale Science Department
Sandia National Laboratories
P.O. Box 5800
MS 1322
Albuquerque, NM 87185-1320
United States
Pablo Seleson
Computer Science and Mathematics Division
Oak Ridge National Laboratory
P.O. Box 2008
Oak Ridge, TN 37831
United States