Communications in Mathematical Sciences

Volume 5 (2007)

Number 4

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

Pages: 851 – 864



Etienne Emmrich

Olaf Weckner


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.


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

2010 Mathematics Subject Classification

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

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