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arXiv · 2608.27689

Migration of inflated cavities in graded hyperelastic solids

Zhiren Zhu·Jonathan B. Estrada
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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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Zhiren Zhu, Jonathan B. Estrada. 2026-08-27. Migration of inflated cavities in graded hyperelastic solids. https://arxiv.org/abs/2608.27689

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