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

TL;DR

This paper models elastic inclusions within crystalline materials using a mesoscale phase-field crystal approach, successfully reproducing classical elastic inclusion solutions and highlighting microscopic effects on mechanical response.

Contribution

It introduces a spatially-dependent parameter in the phase-field crystal model to simulate eigenstrain in elastic inclusions, bridging microscopic structure and macroscopic elasticity.

Findings

Stress field matches Eshelby solution

Microscopic lattice effects influence elastic response

Model effectively captures eigenstrain in crystalline inclusions

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.