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

Research output: Contribution to journalResearch articleContributedpeer-review



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.


Original languageEnglish
Article number100067
JournalExamples and Counterexamples
Publication statusPublished - 2022

External IDs

unpaywall 10.1016/j.exco.2022.100067
Scopus 85131401010
ORCID /0000-0002-4217-0951/work/142237444



  • Elastic inclusion, Eshelby problem, Phase-field crystal, Lattice deformation