Periodic image effects in dislocation modelling

By Wei Cai, Vasily V. Bulatob, Jinpeng Chang, Ju Li, Sidney Yip. 2003

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Core structure and Peierls potential of screw dislocations in α-Fe from first principles: cluster versus dipole approaches (2007, methodology): “We have calculated the deviation from the anisotropic elastic energy, as obtained from a Madelung summation based only on the values of the elastic constants as inputs [9] (http://micro.”
Enabling strain hardening simulations with dislocation dynamics (2006, background): “The conditional convergence problem (Cai et al 2003) associated with long range interactions can be avoided at the top-most level of the hierarchy by numerically solving an infinite series expression with appropriate corrections (Challacombe et al 1997).”
A non-singular continuum theory of dislocations (2006, methodology): “Solids 54 (2006) 561–587 579 compare the result with the energy of the same configuration predicted by the continuum elasticity theory (Cai et al., 2001, 2003).”
Ab initio modeling of dislocation core properties in metals and semiconductors (2017, methodology): “Several inequivalent arrays can be devised, but quadrupolar arrangements should in most cases be preferred because they minimize the Peach-Koehler force due to image dislocations [32,40,41,60,74,75].”