On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity

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.

Keywords

linear elasticity, non-local theory, peridynamic equation, Navier equation

2010 Mathematics Subject Classification

74B05, 74B99, 74H10, 74H20, 74H25

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Published 1 January 2007