Rens Robbie, Lerner Edan
Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands.
Eur Phys J E Soft Matter. 2019 Sep 4;42(9):114. doi: 10.1140/epje/i2019-11888-5.
A widely studied model for gels or biopolymeric fibrous materials are networks with central force interactions, such as Hookean springs. Less commonly studied are materials whose mechanics are dominated by non-central force interactions such as bond-bending potentials. Inspired by recent experimental advancements in designing colloidal gels with tunable interactions, we study the micro- and macroscopic elasticity of two-dimensional planar graphs with strong bond-bending potentials, in addition to weak central forces. We introduce a theoretical framework that allows us to directly investigate the limit in which the ratio of characteristic central-force to bending stiffnesses vanishes. In this limit we show that a generic isostatic point exists at [Formula: see text], coinciding with the isostatic point of frames with central-force interactions in two dimensions. We further demonstrate the emergence of a stiffening transition when the coordination is increased towards the isostatic point, which shares similarities with the strain-induced stiffening transition observed in biopolymeric fibrous materials, and coincides with an auxeticity transition above which the material's Poisson's ratio approaches -1 when bond-bending interactions dominate.
对于凝胶或生物聚合物纤维材料，一个被广泛研究的模型是具有中心力相互作用的网络，例如胡克弹簧。而力学由诸如键弯曲势等非中心力相互作用主导的材料则较少被研究。受近期在设计具有可调相互作用的胶体凝胶方面的实验进展启发，我们研究了除弱中心力外还具有强键弯曲势的二维平面图的微观和宏观弹性。我们引入了一个理论框架，使我们能够直接研究特征中心力与弯曲刚度之比消失的极限情况。在此极限下，我们表明在[公式：见原文]处存在一个通用的等静力点，这与二维中具有中心力相互作用的框架的等静力点一致。我们进一步证明，当配位数朝着等静力点增加时会出现硬化转变，这与在生物聚合物纤维材料中观察到的应变诱导硬化转变相似，并且与负泊松比转变相吻合，在该转变之上，当键弯曲相互作用占主导时，材料的泊松比接近 -1。
