AI 中文总结
该研究针对因固液相互作用弱化的多孔弹性介质，建立了多孔弹性变形、骨架弱化与溶质传输耦合的数学模型，揭示了流致单轴压缩下孔隙闭合的不同参数 regime，推导了慢弱化系统的孔隙闭合时间近似。
AI 中文摘要
多孔弹性材料（如聚合物组织支架、多孔岩石和水凝胶）会因固体骨架与间隙流体中的化学物质相互作用而发生弱化。我们开发了一种针对多孔弹性材料的数学模型，以提供关于材料弱化如何影响系统随时间变化的力学特性的基础机制见解。该模型将大变形多孔弹性理论与溶质的平流-扩散方程耦合，此外，我们引入了材料刚度的衰减方程，其衰减速率取决于溶质浓度。通过这种方式，我们描述了多孔弹性变形、骨架弱化以及溶质在材料内传输三者之间的耦合关系。我们利用数值和分析技术，揭示了弱化多孔弹性材料在流作用下的单轴压缩行为，并确定了使材料弱化促进下游边界孔隙闭合的参数范围。我们明确了三类参数范围：（1）无孔隙闭合的稳态；（2）有限时间内发生孔隙闭合；（3）孔隙瞬时闭合；其中情况（2）是通过在系统中引入弱化现象发现的。我们深入分析了不同行为与系统时间尺度分离之间的关系，对于弱化速率较慢的系统，我们将多孔弹性弛豫与弱化的时间尺度之比视为小参数，推导出了孔隙闭合时间的 leading-order（主导阶）近似，并研究了该近似的准确性以及时间尺度变得可比时出现的新行为。
英文摘要
Poroelastic materials, such as polymer tissue scaffolds, porous rocks, and hydrogels, can weaken due to interactions between the solid skeleton and chemical species in the interstitial fluid. We develop a mathematical model for a poroelastic material to provide fundamental mechanistic insight into how weakening the material can affect the time-varying mechanics of the system. Our model couples large-deformation poroelasticity with an advection-diffusion equation for the solute. Furthermore, we introduce a decay equation for the material stiffness, whose rate of decay depends on the solute concentration. In this way, we describe a three-way coupling between poroelastic deformation, weakening of the skeleton and transport of solute through the material. We exploit numerical and analytical techniques to reveal the flow-driven uniaxial compression of a weakening poroelastic material and determine parameter regimes for which weakening the material facilitates pore closure at the downstream boundary. We identify parameter regimes in which (1) a steady state is attained without pore closure, (2) pore closure occurs at a finite time or (3) the pores close instantaneously; we uncover case (2) through the introduction of weakening into the system. We provide insights into the relationship between the differing behaviours and the separation between the timescales of the system. For systems with slow weakening, we derive a leading-order approximation for the time of pore closure, treating the ratio of the timescales of poroelastic relaxation and weakening as a small parameter, and investigate the accuracy of this approximation and the new behaviours that arise when these timescales become comparable.
Comments30 pages, 6 figures, Submitted to Journal of Fluid Mechanics
