A sharp-interface model for diffusional evolution of precipitates in visco-plastic materials.

Research output: Contribution to journalResearch articleContributedpeer-review



This paper describes a 3D implementation of the sharp-interface theory for material heterogeneities and is, hence, able to identify equilibrium shapes of precipitates in superalloys. The theory is adopted from Morton E. Gurtin and extended by crystal plasticity in the bulk. Crystal plasticity relaxes stresses at the phase interface, which leads to subsequent coalescence of the precipitates. The fully implicit model employs the extended finite element method (XFEM) in conjunction with level sets. The level set is advected in a velocity field computed by the stress-modified Gibbs-Thomson interface condition. Mechanical equilibrium and level set update are solved in a staggered procedure. Jump quantities are treated by means of a suitable enriched least square smoothing. Multiple schemes for the computation of curvature of surfaces in the context of the XFEM are presented and compared. Equilibrium shapes at different levels of misfit are computed. A cuboidal equilibrium shape is retrieved in a rotated mesh in order to quantify mesh-independence, a linear volume-time relationship during Ostwald ripening is reproduced and merging of particles under tension is reported.


Original languageEnglish
Article number114440
JournalComputer Methods in Applied Mechanics and Engineering
Early online date13 Jan 2022
Publication statusPublished - 1 Mar 2022

External IDs

Scopus 85122649837
unpaywall 10.1016/j.cma.2021.114440
ORCID /0000-0001-9453-1125/work/142237979



  • Crystal plasticity, Curvature schemes, Heterogeneities, Phase transformation, Sharp-interface theory, XFEM

Library keywords