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December 2007 On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity
Etienne Emmrich, Olaf Weckner
Commun. Math. Sci. 5(4): 851-864 (December 2007).

Abstract

The non-local peridynamic theory describes the displacement field of a continuous body by the initial-value problem for an integro-differential equation that does not include any spatial derivative. The non-locality is determined by the so-called peridynamic horizon $\delta$ which is the radius of interaction between material points taken into account. Well-posedness and structural properties of the peridynamic equation of motion are established for the linear case corresponding to small relative displacements. Moreover the limit behavior as $\delta \rightarrow 0$ is studied.

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Etienne Emmrich. Olaf Weckner. "On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity." Commun. Math. Sci. 5 (4) 851 - 864, December 2007.

Information

Published: December 2007
First available in Project Euclid: 3 January 2008

zbMATH: 1133.35098
MathSciNet: MR2375050

Subjects:
Primary: 35Q72, 74B05, 74B99, 74H10, 74H20, 74H25

Rights: Copyright © 2007 International Press of Boston

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Vol.5 • No. 4 • December 2007
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