Peridynamic stress is the static first Piola–Kirchhoff Virial stress

The peridynamic stress formula proposed by Lehoucq and Silling (2008) is cumbersome to be implemented in numerical computations. In this paper, we show that the peridynamic stress tensor has the exact mathematical expression as that of the first Piola–Kirchhoff static Virial stress originated from t...

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Bibliographic Details
Published in:International journal of solids and structures 2022-04, Vol.241, p.111478, Article 111478
Main Authors: Li, Jun, Li, Shaofan, Lai, Xin, Liu, Lisheng
Format: Article
Language:English
Subjects:
Bond based peridynamics
Crack tips
Exact solutions
Finite element method
Fracture
Materials failure
Mathematical models
Nonlocal continuum mechanics
Peridynamic stress
Stress concentration
Stress distribution
Tensors
Virial stress
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Summary:The peridynamic stress formula proposed by Lehoucq and Silling (2008) is cumbersome to be implemented in numerical computations. In this paper, we show that the peridynamic stress tensor has the exact mathematical expression as that of the first Piola–Kirchhoff static Virial stress originated from the Irving–Kirkwood–Noll formalism (Irving and Kirkwood, 1905; Noll, 1955) through the Hardy–Murdoch procedure (Hardy, 1982; Murdoch, 1983), which offers a simple and clear expression for numerical calculations of peridynamic stress. Several numerical verifications have been carried out to validate the accuracy of the proposed peridynamic stress formula in predicting the stress states in the vicinity of the crack tip and other sources of stress concentration. By evaluating the peridynamic stress in the prototype microelastic brittle (PMB) material model of bond-based peridynamics, it is found that the PMB material model may exhibit nonlinear constitutive behaviors at large deformations. The stress fields calculated through the proposed peridynamic stress formula show good agreements with these calculated by using finite element methods, analytical solutions, as well as experimental data, demonstrating the merit of the peridynamic stress formula in predicting stress states for material failure problems.
ISSN:0020-7683
1879-2146
DOI:10.1016/j.ijsolstr.2022.111478