Migration of inflated cavities in graded hyperelastic solids
Abstract
The inflation of a pre-existing, fluid-filled cavity is a timeless topic in the finite-deformation analysis of soft materials. However, classical solutions for cavity inflation rely on radially symmetric material properties, leaving unresolved the effects of non-radial stiffness heterogeneity that are commonly present in biological tissues and engineered soft materials. In this work, we investigate the quasi-static inflation of a pressurized cavity in a hyperelastic solid with shear modulus varying monotonically along a reference Cartesian direction. Finite-element simulations reveal that, beyond an initial small-inflation regime, the most pronounced symmetry-breaking response is the migration of the cavity toward the more compliant end of the material, while nonspherical distortion remains comparatively weak. To analytically quantify this migration-dominated response, we develop a Rayleigh--Ritz reduced-order framework to determine the strain-energy-minimizing migration amplitude for prescribed gradation parameters and inflation level. Without using fitted parameters, the Rayleigh--Ritz framework recovers key features of the cavity migration that are intimately linked to the mechanical gradation parameters. The identification of centroid migration as a salient geometric signal, together with the reduced-order prediction of its evolution, suggests a roadmap for inverse characterization of graded materials through cavity-inflation experiments.
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BibTeX
@misc{zhu2026migration,
title = {{Migration of inflated cavities in graded hyperelastic solids}},
author = {Zhiren Zhu and Jonathan B. Estrada},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27689},
eprint = {2608.27689},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27689},
}
RIS
TY - UNPB
TI - Migration of inflated cavities in graded hyperelastic solids
AU - Zhiren Zhu
AU - Jonathan B. Estrada
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27689
UR - https://arxiv.org/abs/2608.27689
AB - The inflation of a pre-existing, fluid-filled cavity is a timeless topic in the finite-deformation analysis of soft materials. However, classical solutions for cavity inflation rely on radially symmetric material properties, leaving unresolved the effects of non-radial stiffness heterogeneity that are commonly present in biological tissues and engineered soft materials. In this work, we investigate the quasi-static inflation of a pressurized cavity in a hyperelastic solid with shear modulus varying monotonically along a reference Cartesian direction. Finite-element simulations reveal that, beyond an initial small-inflation regime, the most pronounced symmetry-breaking response is the migration of the cavity toward the more compliant end of the material, while nonspherical distortion remains comparatively weak. To analytically quantify this migration-dominated response, we develop a Rayleigh--Ritz reduced-order framework to determine the strain-energy-minimizing migration amplitude for prescribed gradation parameters and inflation level. Without using fitted parameters, the Rayleigh--Ritz framework recovers key features of the cavity migration that are intimately linked to the mechanical gradation parameters. The identification of centroid migration as a salient geometric signal, together with the reduced-order prediction of its evolution, suggests a roadmap for inverse characterization of graded materials through cavity-inflation experiments.
ER -