Amjad S N, Picu R C
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.
Soft Matter. 2022 Jan 5;18(2):446-454. doi: 10.1039/d1sm01546j.
Stress relaxation in network materials with permanent crosslinks is due to the transport of fluid within the network (poroelasticity), the viscoelasticity of the matrix and the viscoelasticity of the network. While relaxation associated with the matrix was studied extensively, the contribution of the network remains unexplored. In this work we consider two and three-dimensional stochastic fiber networks with viscoelastic fibers and explore the dependence of stress relaxation on network structure. We observe that relaxation has two regimes - an initial exponential regime, followed by a stretched exponential regime - similar to the situation in other disordered materials. The stretch exponent is a function of density, fiber diameter and the network structure, and has a minimum at the transition between the affine and non-affine regimes of network behavior. The relaxation time constant of the first, exponential regime is similar to the relaxation time constant of individual fibers and is independent of network density and fiber diameter. The relaxation time constant of the second, stretched exponential regime is a weak function of network parameters. The stretched exponential emerges from the heterogeneity of relaxation dynamics on scales comparable with the mesh size, with higher heterogeneity leading to smaller stretch exponents. In composite networks of fibers whose relaxation time constant is selected from a distribution with set mean, the stretch exponent decreases with increasing the coefficient of variation of the fiber time constant distribution. As opposed to thermal glass formers and colloids, in these athermal systems the dynamic heterogeneity is introduced by the network structure and does not evolve during relaxation. While in thermal systems the control parameter is the temperature, in this athermal case the control parameter is a non-dimensional structural parameter which describes the degree of non-affinity of the network.
具有永久交联的网络材料中的应力松弛是由于网络内流体的传输（多孔弹性）、基体的粘弹性和网络的粘弹性。虽然与基体相关的松弛已得到广泛研究，但网络的贡献仍未被探索。在这项工作中，我们考虑具有粘弹性纤维的二维和三维随机纤维网络，并探讨应力松弛对网络结构的依赖性。我们观察到松弛有两个阶段——一个初始指数阶段，随后是一个拉伸指数阶段——类似于其他无序材料的情况。拉伸指数是密度、纤维直径和网络结构的函数，并且在网络行为的仿射和非仿射阶段之间的转变处有一个最小值。第一个指数阶段的松弛时间常数与单个纤维的松弛时间常数相似，并且与网络密度和纤维直径无关。第二个拉伸指数阶段的松弛时间常数是网络参数的弱函数。拉伸指数源于与网格尺寸相当的尺度上松弛动力学的不均匀性，不均匀性越高，拉伸指数越小。在其松弛时间常数从具有设定均值的分布中选择的纤维复合网络中，拉伸指数随着纤维时间常数分布的变异系数增加而减小。与热玻璃形成体和胶体不同，在这些无热系统中，动态不均匀性是由网络结构引入的，并且在松弛过程中不会演变。在热系统中，控制参数是温度，而在这种无热情况下，控制参数是一个无量纲结构参数，它描述了网络的非仿射程度。
