Shivers Jordan L, MacKintosh Fred C
Department of Chemical and Biomolecular Engineering, <a href="https://ror.org/008zs3103">Rice University</a>, Houston, Texas 77005, USA.
<a href="https://ror.org/04hfg7v94">Center for Theoretical Biological Physics</a>, <a href="https://ror.org/008zs3103">Rice University</a>, Houston, Texas 77005, USA.
Phys Rev E. 2024 Jul;110(1-1):014502. doi: 10.1103/PhysRevE.110.014502.
Stretching an elastic material along one axis typically induces contraction along the transverse axes, a phenomenon known as the Poisson effect. From these strains, one can compute the specific volume, which generally either increases or, in the incompressible limit, remains constant as the material is stretched. However, in networks of semiflexible or stiff polymers, which are typically highly compressible yet stiffen significantly when stretched, one instead sees a significant reduction in specific volume under finite strains. This volume reduction is accompanied by increasing alignment of filaments along the strain axis and a nonlinear elastic response, with stiffening of the apparent Young's modulus. For semiflexible networks, in which entropic bending elasticity governs the linear elastic regime, the nonlinear Poisson effect is caused by the nonlinear force-extension relationship of the constituent filaments, which produces a highly asymmetric response of the constituent polymers to stretching and compression. The details of this relationship depend on the geometric and elastic properties of the underlying filaments, which can vary greatly in experimental systems. Here, we provide a comprehensive characterization of the nonlinear Poisson effect in an affine network model and explore the influence of filament properties on essential features of both microscopic and macroscopic response, including strain-driven alignment and volume reduction.
沿一个轴拉伸弹性材料通常会导致沿横向轴收缩，这种现象称为泊松效应。根据这些应变，可以计算比容，随着材料被拉伸，比容通常会增加，或者在不可压缩极限下保持不变。然而，在半柔性或刚性聚合物网络中，这些网络通常具有高度可压缩性，但在拉伸时会显著变硬，人们反而会看到在有限应变下比容显著减小。这种体积减小伴随着细丝沿应变轴的排列增加以及非线性弹性响应，表观杨氏模量变硬。对于半柔性网络，其中熵弯曲弹性控制线性弹性区域，非线性泊松效应是由组成细丝的非线性力-伸长关系引起的，这会导致组成聚合物对拉伸和压缩产生高度不对称的响应。这种关系的细节取决于基础细丝的几何和弹性特性，在实验系统中这些特性可能有很大差异。在这里，我们在仿射网络模型中对非线性泊松效应进行了全面表征，并探讨了细丝特性对微观和宏观响应的基本特征的影响，包括应变驱动的排列和体积减小。
