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Title: Bond-Based Peridynamics: a Tale of Two Poisson’s Ratios

Abstract

This paper explores the restrictions imposed by bond-based peridynamics, particularly with respect to plane strain and plane stress models. We begin with a review of the derivations in Gerstle et al. (2005) wherein for isotropic materials a Poisson’s ratio restriction of $$\frac{1}{4}$$ for plane strain and $$\frac{1}{3}$$ for plane stress is deduced. Next, we show Cauchy’s relations are an intrinsic limitation of bond-based peridynamics and specialize these restrictions to plane strain and plane stress models. This generalizes the results from Gerstle et al. (2005) and demonstrates that the Poisson’s ratio restrictions described in Gerstle et al. (2005) are merely a consequence of Cauchy’s relations for isotropic materials. We conclude with a discussion of the validity of peridynamic plane strain and plane stress models formulated from two-dimensional bond-based peridynamic models.

Authors:
 [1]; ORCiD logo [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1649523
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Peridynamics and Nonlocal Modeling
Additional Journal Information:
Journal Volume: 2; Journal Issue: 3; Journal ID: ISSN 2522-896X
Publisher:
Springer Nature
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Trageser, Jeremy E., and Seleson, Pablo. Bond-Based Peridynamics: a Tale of Two Poisson’s Ratios. United States: N. p., 2020. Web. https://doi.org/10.1007/s42102-019-00021-x.
Trageser, Jeremy E., & Seleson, Pablo. Bond-Based Peridynamics: a Tale of Two Poisson’s Ratios. United States. https://doi.org/10.1007/s42102-019-00021-x
Trageser, Jeremy E., and Seleson, Pablo. Mon . "Bond-Based Peridynamics: a Tale of Two Poisson’s Ratios". United States. https://doi.org/10.1007/s42102-019-00021-x. https://www.osti.gov/servlets/purl/1649523.
@article{osti_1649523,
title = {Bond-Based Peridynamics: a Tale of Two Poisson’s Ratios},
author = {Trageser, Jeremy E. and Seleson, Pablo},
abstractNote = {This paper explores the restrictions imposed by bond-based peridynamics, particularly with respect to plane strain and plane stress models. We begin with a review of the derivations in Gerstle et al. (2005) wherein for isotropic materials a Poisson’s ratio restriction of $\frac{1}{4}$ for plane strain and $\frac{1}{3}$ for plane stress is deduced. Next, we show Cauchy’s relations are an intrinsic limitation of bond-based peridynamics and specialize these restrictions to plane strain and plane stress models. This generalizes the results from Gerstle et al. (2005) and demonstrates that the Poisson’s ratio restrictions described in Gerstle et al. (2005) are merely a consequence of Cauchy’s relations for isotropic materials. We conclude with a discussion of the validity of peridynamic plane strain and plane stress models formulated from two-dimensional bond-based peridynamic models.},
doi = {10.1007/s42102-019-00021-x},
journal = {Journal of Peridynamics and Nonlocal Modeling},
number = 3,
volume = 2,
place = {United States},
year = {2020},
month = {4}
}

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