有限预拉伸软纤维中的弹性波速度
Elastic wave velocities in finitely pre-stretched soft fibers
AI总结：
本文基于 small-on-large 理论建立有限预拉伸软纤维的弹性波传播模型，给出并验证P/S波速度公式，揭示本构、可压缩性、预应力及弦-梁振动竞争的影响。
摘要：
软纤维中的弹性波速度会随材料本构和轴向应力水平而变化，是许多技术应用中力学信号的重要度量。在本工作中，我们基于小扰动叠加于大变形的 small-on-large 理论，建立了有限预拉伸软纤维中线性弹性波传播的模型。文中给出了纵波（Primary，P波）和横波（Secondary，S波）速度的公式，并通过数值模拟以及蜘蛛丝的实验数据进行了验证。研究考察了材料本构、可压缩性和预应力对波传播的影响。我们发现，随着预应力增加，P波速度的变化高度依赖于应力-应变曲线的凹凸性；相比之下，无论采用何种本构模型，S波速度都会增大。对于P波和S波而言，可压缩纤维中速度的变化都比近不可压缩纤维中更显著。此外，针对极小预应力，我们基于 Rayleigh 梁理论提出了修正的S波速度公式，揭示了“弦振动”与“梁振动”之间的竞争机制。这可为软纤维的精确力学表征提供可靠的理论基础，并为轻质、可调的波操控器件开辟路径。
英文摘要：
Elastic wave velocity in a soft fiber that varies depending on material constitution and axial stress level is an essential measure of mechanical signals in many technical applications. In this work, based on the small-on-large theory, we establish a model of linear elastic wave propagation in a finitely pre-stretched soft fiber. The formulas of longitudinal (Primary, P-) and transverse (Secondary, S-) wave velocities are provided and validated by numerical simulations as well as by experimental data on spider silk. The influences of material constitution, compressibility, and pre-stress on the wave propagation are investigated. We found that with increasing pre-stress, the variation of P-wave velocity highly relies on the concavity of the stress-strain curve. In contrast, an increase of S-wave velocity exhibits regardless of any constitutive model. For both P- and S-waves, the variation of the velocities is more significant in a compressible fiber than that in a nearly-incompressible one. Moreover, for minuscule pre-stress, we propose a modified formula for S-wave velocity based on the Rayleigh beam theory, which reveals the competition mechanism between "string vibration" and "beam vibration." This may provide a reliable theoretical basis for precise mechanical characterization of soft fibers and open a route for lightweight, tunable wave manipulation devices.
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