On the nonlinear Eshelby inclusion problem and its isomorphic growth limit
Name
bonavia-et-al-2025-on-the-nonlinear-eshelby-inclusion-problem-and-its-isomorphic-growth-limit.pdf
Description
Published version
Size
6.23 MB
Format
Adobe PDF
Checksum (MD5)
6e6d384e99d90b24e0aa27ed438bf22d
Author(s)
Bonavia, Joseph E
Chockalingam, S
Cohen, Tal
Date Issued
January 2026
Journal
Mathematics and Mechanics of Solids
Publisher
SAGE Publications
Citation
Bonavia JE, Chockalingam S, Cohen T. On the nonlinear Eshelby inclusion problem and its isomorphic growth limit. Mathematics and Mechanics of Solids. 2026;31(1):140-171.
Version
Final published version
Abstract
In the late 1950s, Eshelby’s linear solutions for the deformation field inside an ellipsoidal inclusion and, subsequently, the infinite matrix in which it is embedded were published. The solutions’ ability to capture the behavior of an orthotropically symmetric shaped inclusion made it invaluable in efforts to understand the behavior of defects within, and the micromechanics of, metals and other stiff materials throughout the rest of the 20th century. Over half a century later, we wish to understand the analogous effects of microstructure on the behavior of soft materials, both organic and synthetic, but in order to do so, we must venture beyond the linear limit, far into the nonlinear regime. However, no solutions to these analogous problems currently exist for non-spherical inclusions. In this work, we present an accurate semi-inverse solution for the elastic field in an isotropically growing spheroidal inclusion embedded in an infinite matrix, both made of the same incompressible neo-Hookean material. We also investigate the behavior of such an inclusion as it grows infinitely large, demonstrating the existence of a non-spherical asymptotic shape and an associated asymptotic pressure. We call this the isomorphic limit, and the associated pressure the isomorphic pressure.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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Creative Commons Attribution-Noncommercial
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1177/10812865251319798
