The precise control and structural design of the soft matter of the hydrogel subjected to dynamic loading require an in-depth understanding of its transient wave characteristics. However, for the complex solid–liquid coupling effects of the soft matter of hydrogels, the traditional single-phase wave model is no longer applicable. In this study, a transient wave propagation model that considers the solid–liquid coupling effects and its computational method is proposed. The wave-governing equations of hydrogels are derived based on the mass conservation and dynamic equilibrium equations, where the motions of solid and liquid phases are independently described. After transforming the governing equations into the equivalent weak form, numerical solutions for transient wave propagation in one- and two-dimensional hydrogels are calculated. The accuracy of the proposed model is verified by a comparison between semi-analytical and commercial finite element method solutions. We observe that the travelling and reflection processes of the two types of compression waves, P1 and P2, with different wave speeds are captured when the dynamic coefficient of permeability kf increases. Furthermore, the influence of solid–liquid coupling effects on the transient responses of hydrogels is discussed. The results show that the hydrogels exhibit the dynamic characteristics of a single-phase medium to a certain extent when kf is sufficiently small.

中文翻译：

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水凝胶软物质中瞬态波传播分析


对水凝胶在动态载荷作用下的软物质的精确控制和结构设计需要深入了解其瞬态波特性。然而，对于水凝胶软物质的复杂固液耦合效应，传统的单相波模型已不再适用。在本研究中，提出了一种考虑固液耦合效应的瞬态波传播模型及其计算方法。水凝胶的波控方程是基于质量守恒和动态平衡方程推导的，其中固相和液相的运动是独立描述的。将控制方程转换为等效的弱形式后，计算了一维和二维水凝胶中瞬态波传播的数值解。通过比较半解析法和商用有限元法解，验证了所提模型的准确性。我们观察到，当动态磁导率系数 kf 增加时，具有不同波速的两类压缩波 P1 和 P2 的传播和反射过程被捕获。此外，讨论了固液耦合效应对水凝胶瞬态响应的影响。结果表明，当 kf 足够小时，水凝胶在一定程度上表现出单相介质的动态特性。