Liu Zezhou, Bouklas Nikolaos, Hui Chung-Yuen
Sibley School of Mechanical and Aerospace Engineering, Field of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA.
Global Station for Soft Matter, GI-CoRE, Hokkaido University, Sapporo, Japan.
Proc Math Phys Eng Sci. 2020 Jan;476(2233):20190761. doi: 10.1098/rspa.2019.0761. Epub 2020 Jan 29.
In the past decade, many experiments have indicated that the surfaces of soft elastic solids can resist deformation by surface stresses. A common soft elastic solid is a hydrogel which consists of a polymer network swollen in water. Although experiments suggest that solvent flow in gels can be affected by surface stress, there is no theoretical analysis on this subject. Here we study the solvent flow near a line load acting on a linear poroelastic half space. The surface of this half space resists deformation by a constant, isotropic surface stress. It can also resist deformation by surface bending. The time-dependent displacement, stress and flow fields are determined using transform methods. Our solution indicates that the stress field underneath the line load is completely regularized by surface bending-it is bounded and continuous. For small surface bending stiffness, the line force is balanced by surface stresses; these forces form what is commonly known as 'Neumann's triangle'. We show that surface stress reduces local pore pressure and inhibits solvent flow. We use our line load solution to simulate the relaxation of the peak which is formed by applying and then removing a line force on the poroelastic half space.
在过去十年中，许多实验表明，软弹性固体表面可通过表面应力抵抗变形。常见的软弹性固体是水凝胶，它由在水中溶胀的聚合物网络组成。尽管实验表明凝胶中的溶剂流动会受到表面应力的影响，但对此主题尚无理论分析。在此，我们研究作用于线性多孔弹性半空间上的线载荷附近的溶剂流动。该半空间的表面通过恒定的各向同性表面应力抵抗变形。它也可以通过表面弯曲来抵抗变形。使用变换方法确定随时间变化的位移、应力和流场。我们的解表明，线载荷下方的应力场通过表面弯曲完全正则化——它是有界且连续的。对于小的表面弯曲刚度，线力由表面应力平衡；这些力形成了通常所说的“诺伊曼三角形”。我们表明，表面应力会降低局部孔隙压力并抑制溶剂流动。我们使用线载荷解来模拟通过在多孔弹性半空间上施加然后移除线力而形成的峰值的松弛过程。
