A one-dimensional peridynamic model of defect propagation and its relation to certain other continuum models. (July 2018)

• Record Type: Journal Article
• Authors: Wang, Linjuan; Abeyaratne, Rohan
• Is Part Of: Journal of the mechanics and physics of solids. Volume 116(2018)
• Page Start: 334
• Page End: 349
• Publication Date: 2018-07
• Subjects: Peridynamic theory -- Defect propagation -- Kink -- Phase transformation -- Dynamics -- Frenkel–Kontorova; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2018.03.028
• Languages: English
• ISSNs: 0022-5096

Abstract

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.