软双层组织中的冲击波
Impact waves in soft bilayer tissues
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中文总结 AI 辅助
本研究通过半解析解和有限元模拟，研究了软双层组织中冲击波的传播，揭示了瞬态位移场与导波模式群速度的联系，并表明层刚度和厚度变化显著影响波场特征，为多层软材料的非侵入性力学表征提供了理论基础。
中文摘要 AI 辅助
在本研究中，我们在非线性弹性框架内，研究了置于无摩擦刚性基底上的预应力可压缩超弹性双层中冲击波的传播。利用傅里叶-拉普拉斯变换，推导了由局部表面冲击引起的瞬态位移场的半解析解，并通过驻相法获得了其长时间渐近行为。进一步进行了有限元模拟以验证理论预测。结果建立了瞬态位移场的特征特征与导波模式群速度之间的直接联系，揭示了色散传播和模态贡献如何塑造观测到的波形。随后，考虑了对应于人体关节软骨、牙龈和皮肤的三个代表性双层模型，以检验层刚度和厚度变化的影响。结果表明，结构和材料变化可以显著改变冲击波的空间分布、到达位置和特征速度。特别是，在某些参数范围内，高阶模式可以对位移响应做出显著贡献，使得波场的主要特征不能总是仅由基模来表征。这些发现表明，瞬态波测量包含的信息超出了单一特征表面波速度所捕获的内容，并为解释多层软材料中的瞬态波场以及未来的非侵入性力学表征提供了理论基础。
英文摘要
In this study, we investigate impact-wave propagation in a pre-stressed compressible hyperelastic bilayer resting on a frictionless rigid substrate within the framework of nonlinear elasticity. Semi-analytical solutions for the transient displacement fields induced by localized surface impulses are derived using the Fourier-Laplace transform, and their long-time asymptotic behavior is obtained through the method of stationary phase. Finite element simulations are further performed to validate the theoretical predictions. The results establish a direct connection between characteristic features of the transient displacement fields and the group velocities of the guided-wave modes, revealing how dispersive propagation and modal contributions shape the observed waveforms. Three representative bilayer models corresponding to human articular cartilage, gingiva, and skin are then considered to examine the effects of variations in layer stiffness and thickness. The results show that structural and material variations can substantially modify the spatial distribution, arrival positions, and characteristic velocities of impact waves. In particular, higher-order modes can make significant contributions to the displacement response in certain parameter regimes, such that the dominant features of the wavefield cannot always be characterized by the fundamental mode alone. These findings demonstrate that transient-wave measurements contain mechanical information beyond that captured by a single characteristic surface-wave velocity and provide a theoretical basis for interpreting transient wavefields in multilayered soft materials and for future non-invasive mechanical characterization.
发表机构
- Tianjin University（天津大学）
- University of Galway（戈尔韦大学）
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