Field Dislocation Mechanics and Phase Field Crystal models

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.

References in corpus (23)

• Modeling Elasticity in Crystal Growth
• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• An Exactly Solvable Phase-Field Theory of Dislocation Dynamics, Strain Hardening and Hysteresis in Ductile Single Crystals
• Phase-field Crystals with Elastic Interactions
• Diffusive Atomistic Dynamics of Edge Dislocations in Two Dimensions
• Size effects and idealized dislocation microstructure at small scales: predictions of a phenomenological model of Mesoscopic Field Dislocation Mechanics: Part I
• Renormalization group approach to multiscale simulation of polycrystalline materials using the phase field crystal model
• Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics
• Amplitude expansion of the binary phase field crystal model
• Phase field crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures
• Consistent Hydrodynamics for Phase Field Crystals
• Dislocation dynamics and crystal plasticity in the phase field crystal model
• Deriving phase field crystal theory from dynamical density functional theory: consequences of the approximations
• Mesoscale model of dislocation motion and crystal plasticity
• Phase-field-crystal models and mechanical equilibrium
• A coarse-grained phase-field crystal model of plastic motion
• Finite Element Approximation of Finite Deformation Dislocation Mechanics
• A unification of finite deformation $J_2$ Von-Mises plasticity and quantitative dislocation mechanics
• Non-linear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene
• Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal model
• An efficient numerical framework for the amplitude expansion of the phase-field crystal model
• Mechanical relaxation and fracture of phase field crystals
• Elastic constants of stressed and unstressed materials in the phase field crystal model

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