The elastic inclusion problem in the (amplitude) phase field crystal model

Abstract

In many processes for crystalline materials such as precipitation, heteroepitaxy, alloying, and phase transformation, lattice expansion or compression of embedded domains occurs. This can significantly alter the mechanical response of the material. Typically, these phenomena are studied macroscopically, thus neglecting the underlying microscopic structure. Here we present the prototypical case of an elastic inclusion described by a mesoscale model, namely a coarse-grained phase-field crystal model. A spatially-dependent parameter is introduced into the free energy functional to control the local spacing of the lattice structure, effectively prescribing an eigenstrain. The stress field obtained for an elastic inclusion in a 2D triangular lattice is shown to match well with the analytic solution of the Eshelby inclusion problem.

6 pages; 3 figures

References in corpus (6)

• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• Renormalization group theory for the phase field crystal equation
• A coarse-grained phase-field crystal model of plastic motion
• Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview
• Mesoscale Defect Motion in Binary Systems: Effects of Compositional Strain and Cottrell Atmospheres
• Dislocation nucleation in the phase field crystal model

Cited by in corpus (3)

• Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview
• A Non-Isothermal Phase-Field Crystal Model with Lattice Expansion: Analysis and Benchmarks
• Explicit temperature coupling in phase-field crystal models of solidification