Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK.
Soft Matter. 2016 Aug 10;12(32):6749-56. doi: 10.1039/c6sm01029f.
We develop a continuum theory for equilibrium elasticity of a network of crosslinked semiflexible filaments, spanning the full range between flexible entropy-driven chains to stiff athermal rods. We choose the 3-chain constitutive model of network elasticity over several plausible candidates, and derive analytical expressions for the elastic energy at arbitrary strain, with the corresponding stress-strain relationship. The theory fits well to a wide range of experimental data on simple shear in different filament networks, quantitatively matching the differential shear modulus variation with stress, with only two adjustable parameters (which represent the filament stiffness and the pre-tension in the network, respectively). The general theory accurately describes the crossover between the positive and negative Poynting effect (normal stress on imposed shear) on increasing the stiffness of filaments forming the network. We discuss the network stability (the point of marginal rigidity) and the phenomenon of tensegrity, showing that filament pre-tension on crosslinking into the network determines the magnitude of linear modulus G0.
我们为交联半弹性纤维网络的平衡弹性开发了连续统理论，涵盖了从柔性熵驱动链到刚性非热棒的整个范围。我们选择了 3 链网络弹性本构模型而不是几个合理的候选者，并为任意应变量下的弹性能量导出了解析表达式，以及相应的应力-应变关系。该理论与不同纤维网络中简单剪切的广泛实验数据拟合良好，定量匹配了微分剪切模量随应力的变化，仅使用两个可调参数（分别代表纤维刚度和网络中的预张力）。一般理论准确地描述了网络形成的纤维刚度增加时正和负 Poynting 效应（施加剪切的正应力）之间的交叉。我们讨论了网络稳定性（边缘刚硬点）和张拉整体现象，表明交联成网络的纤维预张力决定了线性模量 G0 的大小。
