Sharma A, Sheinman M, Heidemann K M, MacKintosh F C
Department of Physics and Astronomy, Vrije Universiteit, Amsterdam, The Netherlands.
Institute for Numerical and Applied Mathematics, Göttingen University, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052705. doi: 10.1103/PhysRevE.88.052705. Epub 2013 Nov 8.
Experiments have shown that elasticity of disordered filamentous networks with compliant crosslinks is very different from networks with rigid crosslinks. Here, we model and analyze filamentous networks as a collection of randomly oriented rigid filaments connected to each other by flexible crosslinks that are modeled as wormlike chains. For relatively large extensions we allow for enthalpic stretching of crosslink backbones. We show that for sufficiently high crosslink density, the network linear elastic response is affine on the scale of the filaments' length. The nonlinear regime can become highly nonaffine and is characterized by a divergence of the elastic modulus at finite strain. In contrast to the prior predictions, we do not find an asymptotic regime in which the differential elastic modulus scales linearly with the stress, although an approximate linear dependence can be seen in a transition from entropic to enthalpic regimes. We discuss our results in light of recent experiments.
实验表明，具有柔顺交联的无序丝状网络的弹性与具有刚性交联的网络有很大不同。在此，我们将丝状网络建模并分析为一组随机取向的刚性细丝，它们通过被建模为蠕虫状链的柔性交联相互连接。对于相对较大的伸长，我们考虑交联主链的焓拉伸。我们表明，对于足够高的交联密度，网络的线性弹性响应在细丝长度尺度上是仿射的。非线性区域可能变得高度非仿射，其特征是在有限应变下弹性模量发散。与先前的预测相反，我们没有发现微分弹性模量与应力呈线性比例的渐近区域，尽管在从熵区域到焓区域的转变中可以看到近似的线性依赖关系。我们根据最近的实验讨论我们的结果。
