Variable horizon in a peridynamic medium

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

doi:10.2140/jomms.2015.10.591

Variable horizon in a peridynamic medium

Journal Article · Thu Dec 10 00:00:00 EST 2015 · Journal of Mechanics of Materials and Structures

DOI:https://doi.org/10.2140/jomms.2015.10.591· OSTI ID:1311296

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)

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.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: ORNL LDRD Director's R&D; USDOE Office of Science (SC)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1311296

Journal Information:: Journal of Mechanics of Materials and Structures, Journal Name: Journal of Mechanics of Materials and Structures Journal Issue: 5 Vol. 10; ISSN 1559-3959

Publisher:: Mathematical Science PublishersCopyright Statement

Country of Publication:: United States

Language:: English

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Cited By (11)

Quasinonlocal coupling of nonlocal diffusions Li, Xingjie Helen; Lu, Jianfeng arXiv https://doi.org/10.48550/arxiv.1607.03940	preprint	January 2016
A quasinonlocal coupling method for nonlocal and local diffusion models Du, Qiang; Li, Xingjie Helen; Lu, Jianfeng arXiv https://doi.org/10.48550/arxiv.1704.00348	preprint	January 2017
A non-ordinary peridynamics implementation for anisotropic materials Hattori, Gabriel; Trevelyan, Jon; Coombs, William M. arXiv https://doi.org/10.48550/arxiv.1710.06827	preprint	January 2017
Reduction of integration domain in Triebel-Lizorkin spaces Rutkowski, Artur arXiv https://doi.org/10.48550/arxiv.1810.11353	preprint	January 2018
A review of Local-to-Nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics D'Elia, Marta; Li, Xingjie; Seleson, Pablo arXiv https://doi.org/10.48550/arxiv.1912.06668	preprint	January 2019
Dual-horizon peridynamics: Dual-horizon peridynamics Ren, Huilong; Zhuang, Xiaoying; Cai, Yongchang International Journal for Numerical Methods in Engineering, Vol. 108, Issue 12 https://doi.org/10.1002/nme.5257	journal	July 2016
Voronoi-based peridynamics and cracking analysis with adaptive refinement: Voronoi-based peridynamics and cracking analysis with adaptive refinement Gu, Xin; Zhang, Qing; Xia, Xiaozhou International Journal for Numerical Methods in Engineering, Vol. 112, Issue 13 https://doi.org/10.1002/nme.5596	journal	August 2017
An implicit dual‐based approach to couple peridynamics with classical continuum mechanics Bie, Yehui; Li, She; Hu, Xin International Journal for Numerical Methods in Engineering, Vol. 120, Issue 12 https://doi.org/10.1002/nme.6182	journal	August 2019
Superposition-based coupling of peridynamics and finite element method Sun, Wei; Fish, Jacob Computational Mechanics, Vol. 64, Issue 1 https://doi.org/10.1007/s00466-019-01668-5	journal	February 2019
A new peridynamic formulation with shear deformation for elastic solid Ren, Huilong; Zhuang, Xiaoying; Rabczuk, Timon Journal of Micromechanics and Molecular Physics, Vol. 01, Issue 02 https://doi.org/10.1142/s2424913016500090	journal	July 2016
Peridynamics review Javili, Ali; Morasata, Rico; Oterkus, Erkan Mathematics and Mechanics of Solids, Vol. 24, Issue 11 https://doi.org/10.1177/1081286518803411	journal	October 2018

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