Variable horizon in a peridynamic medium

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

doi:10.2140/jomms.2015.10.591

Title: 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:

Silling, Stewart A. ^[1]; Littlewood, David J. ^[1]; Seleson, Pablo ^[2]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Publication Date:: Thu Dec 10 00:00:00 EST 2015

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:: Journal Article: 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; local–nonlocal 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.

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                    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

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                    Silling, Stewart A., Littlewood, David J., and Seleson, Pablo. 2015.  
        "Variable horizon in a peridynamic medium".  United States.  https://doi.org/10.2140/jomms.2015.10.591.  https://www.osti.gov/servlets/purl/1311296.

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@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},

  url          = {https://www.osti.gov/biblio/1311296},
  journal      = {Journal of Mechanics of Materials and Structures},

  issn         = {1559-3959},

  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}

}

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Title: Variable horizon in a peridynamic medium

Abstract

Citation Formats

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A Morphing framework to couple non-local and local anisotropic continua
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Non-ordinary state-based peridynamic analysis of stationary crack problems
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