Field Dislocation Mechanics and Phase Field Crystal models

TL;DR

This paper introduces a new phase field crystal model formulation that accurately captures dislocation dynamics and elastic effects, extending plasticity theories to microscopic scales with independent variables for phase, density, and elastic distortion.

Contribution

It presents a consistent phase field crystal model that separates phase, density, and elastic distortion variables, enabling detailed dislocation motion modeling in stressed solids.

Findings

Model describes dislocation motion in stressed solids.

Extends plasticity equations to phase field crystal framework.

Applicable to both finite and small deformations.

Abstract

A new formulation of the Phase Field Crystal model is presented that is consistent with the necessary microscopic independence between the phase field, reflecting the broken symmetry of the phase, and both mass density and elastic distortion. Although these quantities are related in equilibrium through a macroscopic equation of state, they are independent variables in the free energy, and can be independently varied in evaluating the dissipation functional that leads to the model governing equations. The equations obtained describe dislocation motion in an elastically stressed solid, and serve as an extension of the equations of plasticity to the Phase Field Crystal setting. Both finite and small deformation theories are considered, and the corresponding kinetic equations for the fields derived.