Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 116, Issue -, Pages 334-349Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2018.03.028
Keywords
Peridynamic theory; Defect propagation; Kink; Phase transformation; Dynamics; Frenkel-Kontorova
Funding
- National Natural Science Foundation of China [11521202]
- Chinese Scholarship Council
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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. (C) 2018 Elsevier Ltd. All rights reserved.
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