Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Peridynamic stress is the static first Piola-Kirchhoff Virial stress   The peridynamic stress formula proposed by Lehoucq and Silling [1, 2] is
cumbersome to be implemented in numerical computations. Here, we show that the
peridynamic stress tensor has the exact mathematical expression as that of the
first Piola-Kirchhoff static Virial stress originated from Irving-Kirkwood-Noll
formalism [3, 4] through the Hardy-Murdoch procedure [5, 6], 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 proposed peridynamic stress formula in predicting the stress states in the
vicinity of the crack tip and other sources of stress concentration. The
peridynamic stress is evaluated within the bond-based peridynamics with
prototype microelastic brittle (PMB) material model. 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 finite element analysis results,
analytical solutions, and experimental data, demonstrating the promising
potential of derived peridynamic stress formula in simulating the stress states
of problems with discontinuities, especially in the bond-based peridynamics.

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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph