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

Jeremy Trageser; Pablo Seleson

doi:10.1007/s42102-019-00021-x

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

Jeremy Trageser, Pablo Seleson

Multiscale Methods

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

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 14 for plane strain and 13 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.

Original language	English
Pages (from-to)	278-288
Number of pages	11
Journal	Journal of Peridynamics and Nonlocal Modeling
Volume	2
Issue number	3
DOIs	https://doi.org/10.1007/s42102-019-00021-x
State	Published - Sep 2020

Funding

Research sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U. S. Department of Energy. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

Funders	Funder number
U.S. Department of Energy
National Nuclear Security Administration	DE-NA0003525
Oak Ridge National Laboratory

Keywords

Bond-based peridynamics
Cauchy’s relations
Plane strain
Plane stress

Access to Document

10.1007/s42102-019-00021-x

Cite this

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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{\textquoteright}s ratio restriction of 14 for plane strain and 13 for plane stress is deduced. Next, we show Cauchy{\textquoteright}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{\textquoteright}s ratio restrictions described in Gerstle et al. (2005) are merely a consequence of Cauchy{\textquoteright}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.",

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

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