Nonlinear Elasticity: From Single Chain to Networks and Gels
Nonlinear Elasticity: From Single Chain to Networks and Gels
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DOI：
10.1021/ma400478f
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发表时间：
2013-05-14
期刊：
影响因子：
5.5
通讯作者：
Dobrynin, Andrey V.
中科院分区：
文献类型：
--
作者：
Carrillo, Jan-Michael Y.;MacKintosh, Fred C.;Dobrynin, Andrey V.
生物和聚合物网络表现出高度非线性的应力-应变行为，表现在随着变形增加而变硬的材料中。利用理论分析和分子动力学模拟相结合的方法，我们建立了一个网络形变模型，该模型通过将网络和凝胶的宏观应变硬化行为与网络链的分子参数相关联来描述网络和凝胶的非线性力学性质。我们的方法的出发点是具有不同弯曲刚性的离散链的力/伸长关系。推导出的网络自由能表达式是第一变形不变量和链伸长率的普适函数，它取决于完全伸展构象中未受扰动的链尺寸与链尺寸之比。对于单轴和剪切变形的非线性剪切模数和微分剪切模数的模型预测与网络的分子动力学模拟结果以及肌动蛋白、胶原、纤维蛋白、波形蛋白、神经丝和果胶等生物聚合物网络的实验数据都非常吻合。
Biological and polymeric networks show highly nonlinear stress-strain behavior manifested in materials that stiffen with increasing deformation. Using a combination of the theoretical analysis and molecular dynamics simulations, we develop a model of network deformation that describes nonlinear mechanical properties of networks and gels by relating their macroscopic strain hardening behavior to molecular parameters of the network strands, The starting point of our approach is a nonlinear force/elongation relation for discrete chains with varying bending rigidity. The derived expression for the network free energy is a universal function of the first deformation invariant and chain elongation ratio that depends on a ratio of the unperturbed chain size to chain dimension in a fully extended conformation. The model predictions for the nonlinear shear modulus and differential shear modulus for uniaxial and shear deformations are in very good agreement with both the results of molecular dynamics simulations of networks and with experimental data for biopolymer networks of actin, collagen, fibrin, vimentin, neurofilaments, and pectin.