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.
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (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. doi: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 = {Mon Apr 27 00:00:00 EDT 2020},
month = {Mon Apr 27 00:00:00 EDT 2020}
}
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