梯度超弹性固体中膨胀空腔的迁移
Migration of inflated cavities in graded hyperelastic solids
AI总结：
该研究针对剪切模量沿笛卡尔方向单调变化的超弹性固体，通过有限元模拟和Rayleigh-Ritz降阶框架，揭示了受压空腔向材料更柔顺端迁移的规律，为梯度材料的逆表征提供了新方法。
AI中文摘要：
预先存在的充满流体的空腔的膨胀是软材料有限变形分析中的一个经典课题。然而，经典的空腔膨胀解依赖于径向对称的材料属性，无法解决生物组织和工程软材料中常见的非径向刚度异质性的影响。本工作中，我们研究了超弹性固体中受压空腔的准静态膨胀，该超弹性固体的剪切模量沿参考笛卡尔方向单调变化。有限元模拟显示，在初始的小膨胀阶段之后，最显著的对称性破缺响应是空腔向材料更柔顺的一端迁移，而非球形变形则相对较弱。为了解析量化这种以迁移为主导的响应，我们开发了Rayleigh-Ritz降阶框架，以确定给定梯度参数和膨胀水平下使应变能最小化的迁移幅度。在不使用拟合参数的情况下，Rayleigh-Ritz框架重现了与力学梯度参数密切相关的空腔迁移的关键特征。将质心迁移识别为显著的几何信号，结合其演化的降阶预测，为通过空腔膨胀实验对梯度材料进行逆表征提供了一条可行路径。
英文摘要：
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.
