Strain and interface energy of ellipsoidal inclusions subjected to volumetric eigenstrains: shape factors

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Thermodynamic modeling of the development of non-spherical inclusions as precipitates in alloys is an important topic in computational materials science. The precipitates may have markedly different properties compared to the matrix. Both the elastic contrast and the misfit eigenstrain may yield a remarkable generation of elastic strain energy which immediately influences the kinetics of the developing precipitates. The relevant thermodynamic framework has been mostly based on spherical precipitates. However, the shapes of actual particles are often not spherical. The energetics of such precipitates can be met by adapting the spherical energy terms with shape factors. The well-established Eshelby framework is used to evaluate the elastic strain energy of inclusions with ellipsoidal shapes (described by the axes a, b, and c) that are subjected to a volumetric transformation strain. The outcome of the study is two shape factors, one for the elastic strain energy and the other for the interface energy. Both quantities are provided in the form of easy-to-use diagrams. Furthermore, threshold elastic contrasts yielding strain energy shape factors with the value 1.0 for any ellipsoidal shape are studied.
Original languageEnglish
Pages (from-to)405-411
Number of pages7
JournalArchive of applied mechanics
Issue number?
Early online date3 Jan 2022
Publication statusPublished - Jan 2022

Bibliographical note

Publisher Copyright: © 2021, The Author(s).


  • Interface energy
  • Misfit strain energy
  • Modeling thermodynamics
  • Precipitation
  • Shape factors

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