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arXiv · 1803.09586

A One-Dimensional Peridynamic Model of Defect Propagation and its Relation to Certain Other Continuum Models

Linjuan Wang·Rohan Abeyaratne
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Abstract

The peridynamic model of a solid does not involve spatial gradients of the displacement field and is therefore well suited for studying defect propagation. Here, bond-based peridynamic theory is used to study the equilibrium and steady propagation of a lattice defect -- a kink -- in one dimension. The material transforms locally, from one state to another, as the kink passes through. The kink is in equilibrium if the applied force is less than a certain critical value that is calculated, and propagates if it exceeds that value. The kinetic relation giving the propagation speed as a function of the applied force is also derived. In addition, it is shown that the dynamical solutions of certain differential-equation-based models of a continuum are the same as those of the peridynamic model provided the micromodulus function is chosen suitably. A formula for calculating the micromodulus function of the equivalent peridynamic model is derived and illustrated. This ability to replace a differential-equation-based model with a peridynamic one may prove useful when numerically studying more complicated problems such as those involving multiple and interacting defects.

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Linjuan Wang, Rohan Abeyaratne. 2018-03-26. A One-Dimensional Peridynamic Model of Defect Propagation and its Relation to Certain Other Continuum Models. https://doi.org/10.1016/j.jmps.2018.03.028

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