A one-dimensional peridynamic model of defect propagation and its relation to certain other continuum models
Name
Abeyaratne_A one-dimensional.pdf
Description
Accepted version
Size
499.12 KB
Format
Adobe PDF
Checksum (MD5)
79f259f77cd9ddc380a28d3961cf33c1
Author(s)
Wang, Linjuan
Abeyaratne, Rohan
Date Issued
2018
Journal
Journal of the Mechanics and Physics of Solids
Publisher
Elsevier BV
Version
Author's final manuscript
Abstract
© 2018 Elsevier Ltd 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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.JMPS.2018.03.028
