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

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.