The hydrogel can be regarded as a system comprising of a three-dimensional (3D) polymer network entrapping water in intermolecular space. Contributions of polymeric fibers and water to macrostresses of hydrogels are usually separated by fitting stress–strain relations from experiments. In this paper, we developed a new method to determine the two contributions by applying triaxial loads on a 3D micro-fiber network model, in which not only the uniaxial tension or uniaxial compression direction, but also the other two lateral directions are applied with external loads for keeping the unchanged volume of the fiber network model throughout the loading process. The lateral forces on the model can be regarded as the forces of water on the micro-fiber network at boundaries, since the lateral boundary conditions of hydrogels under uniaxial loading are completely free. With the calculation of the effective areas of polymeric fibers and water on the lateral surfaces, the hydrostatic pressure of water can be derived in each loading step, and further, the contributions of polymeric fibers and water to macrostresses of hydrogels in uniaxial loading direction can be determined quantitatively. The results show that in small deformation (the strain is less than about 10%), contributions of the water and polymeric fibers are of the same order of magnitude. In larger deformation, polymeric fibers are decisive in the contribution to stresses in tension, while water takes the dominant contribution in compression. Therefore, the difference in the contribution of water in tension and compression can explain the phenomenon of different initial elastic moduli of hydrogels in tension and compression. The method recommended in this paper can be used to learn the contributions of polymeric fibers and water in hydrogels with diverse fiber contents and even under multi-axial loading.

中文翻译：

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一种使用 3D 微纤维网络模型研究聚合物纤维和水分别对拉伸和压缩水凝胶应力贡献的新方法

水凝胶可以被认为是一个由三维 (3D) 聚合物网络组成的系统，该网络将水捕获在分子间空间中。聚合物纤维和水对水凝胶宏观应力的贡献通常通过拟合实验中的应力-应变关系来分离。在本文中，我们开发了一种通过在 3D 微纤维网络模型上施加三轴载荷来确定两个贡献的新方法，其中不仅单轴拉伸或单轴压缩方向，而且其他两个横向方向都被施加外部加载以在整个加载过程中保持光纤网络模型的体积不变。模型上的侧向力可以看作是边界处微纤维网络上的水力，因为水凝胶在单轴载荷下的横向边界条件是完全自由的。通过计算聚合物纤维和水在侧面的有效面积，可以得出水在每个加载步骤中的静水压力，进一步，聚合物纤维和水对水凝胶单轴加载方向宏观应力的贡献可以是定量确定。结果表明，在小变形（应变小于约 10%）中，水和聚合物纤维的贡献处于同一数量级。在较大的变形中，聚合物纤维对拉伸应力的贡献起决定性作用，而水在压缩中起主要作用。所以，水在拉伸和压缩中贡献的差异可以解释水凝胶在拉伸和压缩中的初始弹性模量不同的现象。本文推荐的方法可用于了解聚合物纤维和水在具有不同纤维含量的水凝胶中甚至在多轴载荷下的贡献。