Discrete model of dislocations in fractional nonlocal elasticity

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• 作者：Vasily E. Tarasov ^{tarasov@theory.sinp.msu.ru" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fractional derivative ; Fractional difference ; Dislocation ; Nonlocal continuum ; Long-range interaction ; Frenkel&ndash ; Kontorova model
• 刊名：Journal of King Saud University - Science
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：28
• 期：1
• 页码：33-36
• 全文大小：346 K

文摘

Discrete models of dislocations in fractional nonlocal materials are suggested. The proposed models are based on fractional-order differences instead of finite differences of integer orders that are usually used. The fractional differences allow us to describe long-range interactions in materials. In continuous limit the suggested discrete models give continuum models of dislocations in nonlocal continua. Fractional generalization of the Frenkel–Kontorova model by using long-range interactions is suggested. We also propose a fractional generalization of interacting atomic chains (IAC) model of dislocations by considering long-range interacting chains.