Peridynamic bond-associated correspondence model: Stability and convergence properties

Hailong Chen; Benjamin W. Spencer

doi:10.1002/nme.5973

Peridynamic bond-associated correspondence model: Stability and convergence properties

Hailong Chen, Benjamin W. Spencer

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

39 Scopus citations

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, ie, zero-energy modes, which 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 show how the bond-associated correspondence model satisfies the requirement for material stability. The convergence behavior is also examined. 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.

Original language	English
Pages (from-to)	713-727
Number of pages	15
Journal	International Journal for Numerical Methods in Engineering
Volume	117
Issue number	6
DOIs	https://doi.org/10.1002/nme.5973
State	Published - Feb 10 2019

Bibliographical note

Funding Information:
This work has been supported through the INL Laboratory Directed Research & Development (LDRD) Program under DOE Idaho Operation Office contract DE-AC07-05ID14517. This manuscript has been authored by Battelle Energy Alliance, LLC under contract DE-AC07-05ID14517 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.

Publisher Copyright:
Published 2018. This article is a U.S. Government work and is in the public domain in the USA.

Keywords

Peridynamics
bond-associated deformation gradient
correspondence model
material instability
zero-energy modes

ASJC Scopus subject areas

Numerical Analysis
Engineering (all)
Applied Mathematics

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10.1002/nme.5973

Cite this

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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, ie, zero-energy modes, which 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 show how the bond-associated correspondence model satisfies the requirement for material stability. The convergence behavior is also examined. 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.",

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N2 - 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, ie, zero-energy modes, which 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 show how the bond-associated correspondence model satisfies the requirement for material stability. The convergence behavior is also examined. 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.

AB - 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, ie, zero-energy modes, which 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 show how the bond-associated correspondence model satisfies the requirement for material stability. The convergence behavior is also examined. 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.

KW - Peridynamics

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KW - zero-energy modes

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Peridynamic bond-associated correspondence model: Stability and convergence properties

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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