Influence of kernel functions on dynamic fracture in the bond-based peridynamics

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Table 1

Different kernel functions W^¯ (ξ, δ) and their corresponding constants c(0, δ) for 1D and 2D cases.

Function type	W^¯ (ξ, δ)	1D c(0, δ)	2D plane stress c(0, δ)	2D plane strain c(0, δ)
Constant [9]	1	$\frac{2 E}{A δ^{2}}$	$\frac{9 E}{π h δ^{3}}$	$\frac{48 E}{5 π h δ^{3}}$
Triangular [9]	$1 - \frac{\| ξ \|}{δ}$	$\frac{6 E}{A δ^{2}}$	$\frac{36 E}{π h δ^{3}}$	$\frac{192 E}{5 π h δ^{3}}$
Gaussian [16]	$e^{- {(\frac{2 ξ}{δ})}^{2}}$	$\frac{8 e^{4} E}{A δ^{2} (e^{4} - 1)}$	$\frac{96 e^{4} E}{(e^{4} \sqrt{π} \erf (2) - 4) h π δ^{3}}$	$\frac{512 e^{4} E}{5 (e^{4} \sqrt{π} \erf (2) - 4) h π δ^{3}}$

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