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Title: Peridynamic bond-associated correspondence model: Stability and convergence properties

Abstract

The correspondence approach is a powerful technique that permits the usage of standard constitutive models from local theory within a peridynamic formulation. However, the conventional correspondence formulation suffers from material instability, i.e. zero-energy modes, that must be controlled for it to be applied in practice. The recently-introduced correspondence reformulation based on the use of a bond-associated deformation gradient can inherently remove the material instability. In this paper, we characterize some important properties, i.e. balance of linear momentum, balance of angular momentum and material stability, of the bond-associated correspondence model. The convergence behavior is also examined. Here, the accuracy of this approach is further demonstrated by comparing model predictions against local reference solutions and results from the conventional correspondence model with penalty stabilization for both two-dimensional and three-dimensional problems.

Authors:
ORCiD logo [1]; 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.:
Idaho National Laboratory LDRD program; USDOE
OSTI Identifier:
1572458
Alternate Identifier(s):
OSTI ID: 1481217
Report Number(s):
INL/JOU-17-43494-Rev001
Journal ID: ISSN 0029-5981
Grant/Contract Number:  
AC07-05ID14517
Resource Type:
Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Volume: 117; Journal Issue: 6; Journal ID: ISSN 0029-5981
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Peridynamics; Zero-energy modes; Correspondence model

Citation Formats

Chen, Hailong, and Spencer, Benjamin W. Peridynamic bond-associated correspondence model: Stability and convergence properties. United States: N. p., 2018. Web. doi:10.1002/nme.5973.
Chen, Hailong, & Spencer, Benjamin W. Peridynamic bond-associated correspondence model: Stability and convergence properties. United States. doi:10.1002/nme.5973.
Chen, Hailong, and Spencer, Benjamin W. Tue . "Peridynamic bond-associated correspondence model: Stability and convergence properties". United States. doi:10.1002/nme.5973. https://www.osti.gov/servlets/purl/1572458.
@article{osti_1572458,
title = {Peridynamic bond-associated correspondence model: Stability and convergence properties},
author = {Chen, Hailong and Spencer, Benjamin W.},
abstractNote = {The correspondence approach is a powerful technique that permits the usage of standard constitutive models from local theory within a peridynamic formulation. However, the conventional correspondence formulation suffers from material instability, i.e. zero-energy modes, that must be controlled for it to be applied in practice. The recently-introduced correspondence reformulation based on the use of a bond-associated deformation gradient can inherently remove the material instability. In this paper, we characterize some important properties, i.e. balance of linear momentum, balance of angular momentum and material stability, of the bond-associated correspondence model. The convergence behavior is also examined. Here, the accuracy of this approach is further demonstrated by comparing model predictions against local reference solutions and results from the conventional correspondence model with penalty stabilization for both two-dimensional and three-dimensional problems.},
doi = {10.1002/nme.5973},
journal = {International Journal for Numerical Methods in Engineering},
number = 6,
volume = 117,
place = {United States},
year = {2018},
month = {10}
}

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