Pressurized solids are ubiquitous in nature. Mechanical properties of biological tissues arise from cell turgor pressure and membrane elasticity. Flat contact between cells generate nonlinear forces. In this work, cells are idealized as pressurized elastic membranes in frictionless contact with one another. Contact forces are experimentally measured on rubber-like membranes and computed using finite element analysis (FEA). FEA matches experimental force-indentation relationships from small to large indentations. With the chosen dimensionless numbers, data gather on a master curve. The isobaric force exhibits a 4/3 power law over 1.5 decades of indentation. Forces for other thermodynamic processes (adiabatic, isothermal/osmotic and isochoric) are interpolated from isobaric data. Regarding stiffness, the isochoric process is superlinear contrary to the sublinear isobaric stiffness. Simple force-indentation relationships are given for each process.

中文翻译：

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壁之间的加压膜：热力学过程改变力和刚度


加压固体在自然界中无处不在。生物组织的机械特性由细胞膨胀压力和膜弹性产生。细胞之间的平面接触产生非线性力。在这项工作中，细胞被理想化为彼此无摩擦接触的加压弹性膜。通过实验测量类橡胶膜上的接触力，并使用有限元分析 (FEA) 进行计算。 FEA 匹配从小压痕到大压痕的实验力-压痕关系。使用选定的无量纲数字，数据收集在主曲线上。等压力在 1.5 个压痕范围内表现出 4/3 幂律。其他热力学过程（绝热、等温/渗透和等容）的力是根据等压数据插值得出的。关于刚度，等容过程是超线性的，与亚线性等压刚度相反。每个过程都给出了简单的力-压痕关系。