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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:
ORCiD logo [1]
  1. Idaho National Lab. (INL), Idaho Falls, ID (United States)
Publication Date:
Research Org.:
Idaho National Lab. (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
Grant/Contract Number:  
AC07-05ID14517
Resource Type:
Journal Article: 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.
Chen, Hailong. Bond-associated deformation gradients for peridynamic correspondence model. United States. doi:10.1016/j.mechrescom.2018.04.004.
Chen, Hailong. Mon . "Bond-associated deformation gradients for peridynamic correspondence model". United States. doi:10.1016/j.mechrescom.2018.04.004. https://www.osti.gov/servlets/purl/1631716.
@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},
issn = {0093-6413},
number = C,
volume = 90,
place = {United States},
year = {2018},
month = {4}
}

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Works referencing / citing this record:

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

Mixed peridynamic formulations for compressible and incompressible finite deformations
journal, February 2020


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