Abstract
A closed finite-dimensional system of dynamical equations for an unbounded periodic set of edge dislocations obtained previously from homogenization reasoning (Berdichevsky in J Mech Phys Solids 106:95–132, 2017) is rederived in this paper using some elementary means.
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Notes
Indeed, in this case \(\xi _{i}^{+}+m^{2}P^{\prime }/2m_{+}m_{-}\) with \( i\eqslantgtr 2\) do not change, while \(\xi _{1}^{+}+m^{2}P^{\prime }/2m_{+}m_{-}\) changes for \(m_{+}\gamma \).
References
Berdichevsky, V.L.: A continuum theory of edge dislocations. J. Mech. Phys. Solids 106, 95–132 (2017)
Hirth, J.P., Lothe, J.: Theory of Dislocations. Wiley, New York (1982). Sect. 19-5
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Berdichevsky, V.L. Dynamic equations for a periodic set of edge dislocations. Arch Appl Mech 89, 425–436 (2019). https://doi.org/10.1007/s00419-018-1408-4
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DOI: https://doi.org/10.1007/s00419-018-1408-4