谐波型软材料与刚性楔体相互作用的应力奇点

IF 5.3 2区 工程技术 Q1 MECHANICS
Kui Miao, Qiang Zhang, Ming Dai, Cun-Fa Gao
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引用次数: 0

摘要

在软弹性材料中嵌入刚性楔的复合结构在生物医学设备、软机器人和柔性电子产品中非常普遍。由于软质材料与刚性楔体的弹性模量存在明显的不匹配,在楔体角附近可能会出现严重的应力集中,进而导致软基质破裂等结构破坏。软基质与刚性楔体之间的相互作用在文献中得到了广泛的研究,但主要是在线性弹性和小变形假设的背景下进行的。关于软质材料中嵌入的刚性楔具有几何和本构非线性的相关研究非常有限,线弹性中的方程和结论是否仍然适用尚不清楚。本文给出了在大变形条件下,刚性楔体与类软橡胶基体完美结合的局部弹静力场的渐近分析,该基体被建模为谐波型超弹性材料。渐近结果表明,楔角附近的局部应力和变形梯度的奇异性仅取决于楔角(这与相应的基于线弹性的结果形成鲜明对比)。此外,我们证明了当前超弹性情况的渐近奇异解是有条件的楔角(它们只存在于楔角的特定范围内),表明严重的体积畸变可能发生在楔角附近的楔角的某些锐角(这不能用线性弹性理论捕获)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stress singularities in soft materials of harmonic type interacting with a rigid wedge
Composite structures of rigid wedges embedded in soft elastic materials are prevalent in biomedical devices, soft robotics, and flexible electronics. Due to significant mismatches in the elastic moduli between soft materials and rigid wedges, severe stress concentrations may occur in the vicinity of the wedge corner, which may further lead to certain structural failure such as rupture of the soft matrices. The interactions between soft matrices and rigid wedges have been widely studied in the literature but mainly in the context of linear elasticity and small deformation assumptions. Relevant studies about rigid wedges embedded in soft materials exhibiting geometric and constitutive nonlinearities are extremely limited and it remains unclear whether the equations and conclusions in linear elasticity are still applicable. In this paper, we present an asymptotic analysis of the local elastostatic field for the case of a rigid wedge perfectly bonded to a soft rubber-like matrix which is modelled as a hyperelastic material of harmonic type under large deformations. The asymptotic results demonstrate that the singularity behavior of the local stress and deformation gradient near the wedge corner depend solely on the angle of the wedge (which is in sharp contrast to corresponding linear elasticity-based results). In addition, we show that asymptotic singular solutions for the current hyperelastic case are conditional on the angle of the wedge (they exist only for a specific range of the angle of the wedge), indicating that severe volumetric distortion may occur in the vicinity of the wedge corner for certain acute angles of the wedge (which fails to be captured with the use of linear elasticity theory).
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来源期刊
CiteScore
8.70
自引率
13.00%
发文量
606
审稿时长
74 days
期刊介绍: EFM covers a broad range of topics in fracture mechanics to be of interest and use to both researchers and practitioners. Contributions are welcome which address the fracture behavior of conventional engineering material systems as well as newly emerging material systems. Contributions on developments in the areas of mechanics and materials science strongly related to fracture mechanics are also welcome. Papers on fatigue are welcome if they treat the fatigue process using the methods of fracture mechanics.
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