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# 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

DOI: http://dx.doi.org/10.4310/CMS.2007.v5.n4.a6

#### Authors

#### 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.

#### Keywords

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

#### 2010 Mathematics Subject Classification

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