Journal of Elasticity

, Volume 125, Issue 1, pp 137–137 | Cite as

Erratum to: Cohesive Dynamics and Brittle Fracture

  • Robert Lipton

Erratum to: J Elast (2015) DOI   10.1007/s10659-015-9564-z

There is a mislabeling of the angle in Fig. 3 the angle written as \(\psi\) should be \(\theta\). There is a missing differential \(d\theta\) in the multiple integral appearing in (1.10). The correct equation reads
$$\mathcal{G}_{c}^{\epsilon}=\frac{2}{V_{d}}\int_{0}^{\epsilon}\int_{0}^{2\pi}\int_{z}^{\epsilon}\int_{0}^{\arccos(z/\zeta)}\mathcal{W}^{\epsilon}(\mathcal{S}_{c}^{+},\zeta)\zeta^{2}\sin{\psi}\,d\psi\,d\zeta\,d\theta\,dz. $$
In second line of the statement of Theorem 4.1 both the interval \(0\leq \beta<1\) and the equation \(\beta=2\alpha-1\) are irrelevant and should not appear. The correct statement of the Theorem is

Theorem 4.1

Dependence of the process zone on the radius of the peridynamic horizon
$$\mathcal{L}^{d}\left(PZ^{\epsilon}(\overline{\theta},t) \right)\leq \frac{\epsilon}{\overline{\theta}m f(\overline{r}^{2})}\times \frac{C(t)}{2}, \quad \textit{for}\ 0\leq t\leq T. $$

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of MathematicsLouisiana State UniversityBaton RougeUSA

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