Discrete model of dislocations in fractional nonlocal elasticity

Vasily E. Tarasov
2016 Journal of King Saud University: Science  
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
more » ... range interactions is suggested. We also propose a fractional generalization of interacting atomic chains (IAC) model of dislocations by considering long-range interacting chains.
doi:10.1016/j.jksus.2015.04.001 fatcat:t72xhrhrgnakhgxx3wqp5pcsm4