Sun Chuanpeng, Chernysh Irina N, Weisel John W, Purohit Prashant K
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA.
Department of Cell and Developmental Biology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA.
Proc Math Phys Eng Sci. 2020 Dec;476(2244):20200643. doi: 10.1098/rspa.2020.0643. Epub 2020 Dec 16.
Several biological materials are fibre networks infused with fluid, often referred to as fibrous gels. An important feature of these gels is that the fibres buckle under compression, causing a densification of the network that is accompanied by a reduction in volume and release of fluid. Displacement-controlled compression of fibrous gels has shown that the network can exist in a rarefied and a densified state over a range of stresses. Continuum chemo-elastic theories can be used to model the mechanical behaviour of these gels, but they suffer from the drawback that the stored energy function of the underlying network is based on neo-Hookean elasticity, which cannot account for the existence of multiple phases. Here we use a double-well stored energy function in a chemo-elastic model of gels to capture the existence of two phases of the network. We model cyclic compression/decompression experiments on fibrous gels and show that they exhibit propagating interfaces and hysteretic stress-strain curves that have been observed in experiments. We can capture features in the rate-dependent response of these fibrous gels without recourse to finite-element calculations. We also perform experiments to show that certain features in the stress-strain curves of fibrous gels predicted by our model can be found in the compression response of blood clots. Our methods may be extended to other tissues and synthetic gels that have a fibrous structure.
几种生物材料是充满液体的纤维网络，通常被称为纤维凝胶。这些凝胶的一个重要特征是，纤维在压缩下会发生弯曲，导致网络致密化，同时伴随着体积减小和液体释放。对纤维凝胶进行位移控制的压缩实验表明，在一定应力范围内，网络可以处于稀薄状态和致密状态。连续介质化学弹性理论可用于模拟这些凝胶的力学行为，但它们存在一个缺点，即基础网络的储能函数基于新胡克弹性，无法解释多相的存在。在此，我们在凝胶的化学弹性模型中使用双阱储能函数来捕捉网络的两相存在。我们对纤维凝胶的循环压缩/解压实验进行建模，并表明它们呈现出在实验中观察到的传播界面和滞后应力-应变曲线。我们无需借助有限元计算就能捕捉这些纤维凝胶的速率依赖性响应中的特征。我们还进行了实验，以表明我们模型预测的纤维凝胶应力-应变曲线中的某些特征可以在血凝块的压缩响应中找到。我们的方法可能会扩展到其他具有纤维结构的组织和合成凝胶。
