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Variable-order particle dynamics: formulation and application to the simulation of edge dislocations.

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Variable-order (VO) fractional operators model edge dislocation dynamics under shear stress. This approach captures complex transitions and bond changes without prior assumptions, enabling simulation of dislocation sliding and coalescence.

Keywords:
edge dislocationsevolutionary differential equationsfractional calculusvariable-order operators

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Area of Science:

  • Materials Science
  • Computational Physics
  • Applied Mathematics

Background:

  • Edge dislocations are crucial in material deformation.
  • Modelling dislocation dynamics involves complex linear-to-nonlinear transitions.
  • Fractional calculus offers advanced tools for complex system dynamics.

Purpose of the Study:

  • To apply variable-order (VO) fractional operators for modelling edge dislocation dynamics.
  • To simulate material microscopic structure using a particle dynamic approach.
  • To capture complex dynamic transitions and bond evolution during dislocation motion.

Main Methods:

  • Utilized a particle dynamic approach with discrete masses and inter-particle forces.
  • Introduced VO fractional operators to the constitutive model.
  • Simulated dislocation motion without assuming trajectories or nonlinear sections.

Main Results:

  • VO operators successfully modelled linear-to-nonlinear dynamic transitions.
  • The formulation captured bond creation and annihilation during dislocation movement.
  • Simulations demonstrated the ability to model dislocation sliding and coalescence.
  • The model's evolutionary nature requires only initial dislocation positions.

Conclusions:

  • VO fractional operators provide a powerful, assumption-free method for edge dislocation dynamics.
  • This approach enhances the simulation of material deformation and failure mechanisms.
  • Fractional calculus presents new perspectives for advanced materials modelling.