Bond-associated deformation gradients for peridynamic correspondence model

Chen, Hailong

doi:10.1016/j.mechrescom.2018.04.004

Title: Bond-associated deformation gradients for peridynamic correspondence model

Abstract

Non-ordinary state-based peridynamic correspondence material model is known to have issues with material instability, i.e. the existence of zero-energy modes, due to non-unique mapping between deformation states and force states via the conventional peridynamic deformation gradient. In this paper, an alternative approach in which the deformation gradient hence force state are computed specifically for each individual bond is proposed to eliminate the material instability. Bond-associated deformation gradient is calculated based on deformation states of material points within an individual bond’s proximity, termed here as the bond-associated family, rather than a material point’s whole family. This bond-associated deformation gradient can better represent the force state of each individual bond from the deformation states of material points in its proximity, and hence inherently resolves issues of material instability in the conventional correspondence material model. Parametric study on bond-associated horizon size indicates that the optimal size should be no less than the material point’s horizon size but smaller than two times of that value. Comparisons against reference solutions using finite element method establish the validity and accuracy of the proposed formulation.

Authors:

^[1]

Idaho National Lab. (INL), Idaho Falls, ID (United States)

Publication Date:: Mon Apr 16 00:00:00 EDT 2018

Research Org.:: Idaho National Laboratory (INL), Idaho Falls, ID (United States)

Sponsoring Org.:: USDOE Office of Energy Efficiency and Renewable Energy (EERE)

OSTI Identifier:: 1631716

Alternate Identifier(s):: OSTI ID: 1548501

Report Number(s):: INL/JOU-18-45154-Rev000
Journal ID: ISSN 0093-6413; TRN: US2201018

Grant/Contract Number:: AC07-05ID14517

Resource Type:: Accepted Manuscript

Journal Name:: Mechanics Research Communications

Additional Journal Information:: Journal Volume: 90; Journal Issue: C; Journal ID: ISSN 0093-6413

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; Peridynamics; Correspondence model; Stability; Zero-energy modes; Deformation gradient

Citation Formats


                    Chen, Hailong. Bond-associated deformation gradients for peridynamic correspondence model.  United States: N. p., 2018. 
Web.  doi:10.1016/j.mechrescom.2018.04.004.

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                    Chen, Hailong. Bond-associated deformation gradients for peridynamic correspondence model.  United States.  https://doi.org/10.1016/j.mechrescom.2018.04.004

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                    Chen, Hailong. Mon .  
"Bond-associated deformation gradients for peridynamic correspondence model".  United States.  https://doi.org/10.1016/j.mechrescom.2018.04.004.  https://www.osti.gov/servlets/purl/1631716.

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@article{osti_1631716,

  title        = {Bond-associated deformation gradients for peridynamic correspondence model},

  author       = {Chen, Hailong},

  abstractNote = {Non-ordinary state-based peridynamic correspondence material model is known to have issues with material instability, i.e. the existence of zero-energy modes, due to non-unique mapping between deformation states and force states via the conventional peridynamic deformation gradient. In this paper, an alternative approach in which the deformation gradient hence force state are computed specifically for each individual bond is proposed to eliminate the material instability. Bond-associated deformation gradient is calculated based on deformation states of material points within an individual bond’s proximity, termed here as the bond-associated family, rather than a material point’s whole family. This bond-associated deformation gradient can better represent the force state of each individual bond from the deformation states of material points in its proximity, and hence inherently resolves issues of material instability in the conventional correspondence material model. Parametric study on bond-associated horizon size indicates that the optimal size should be no less than the material point’s horizon size but smaller than two times of that value. Comparisons against reference solutions using finite element method establish the validity and accuracy of the proposed formulation.},

  doi          = {10.1016/j.mechrescom.2018.04.004},

  journal      = {Mechanics Research Communications},

  number       = C,

  volume       = 90,

  place        = {United States},

  year         = {Mon Apr 16 00:00:00 EDT 2018},

  month        = {Mon Apr 16 00:00:00 EDT 2018}

}

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Works referenced in this record:

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Works referencing / citing this record:

Improved method for zero-energy mode suppression in peridynamic correspondence model
journal, June 2019

Wan, Ji; Chen, Zhuang; Chu, Xihua
Acta Mechanica Sinica, Vol. 35, Issue 5
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Mixed peridynamic formulations for compressible and incompressible finite deformations
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Mixed peridynamic formulations for compressible and incompressible finite deformations
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Bode, Tobias; Weißenfels, Christian; Wriggers, Peter
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Peridynamic bond-associated correspondence model: Stability and convergence properties
journal, November 2018

Chen, Hailong; Spencer, Benjamin W.
International Journal for Numerical Methods in Engineering, Vol. 117, Issue 6
DOI: 10.1002/nme.5973

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Title: Bond-associated deformation gradients for peridynamic correspondence model

Abstract

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