The nonlinear stress–strain response of synthetic and biological networks and gels manifested in a monotonic increase of an instantaneous modulus is a result of the nonlinear deformation of individual network strands. To describe this behavior, we develop a nonlinear network deformation model, which relates macroscopic stress–strain response with force-elongation behavior of polymer chains with bending rigidity and extendable bonds. In particular, network mechanical properties such as structural shear modulus, extensibility ratio, and bond deformation modulus are expressed in terms of chain bending constant, Kuhn length, bond elastic constant, and chain sizes in undeformed and fully extended states. The chain deformation model is tested by molecular dynamics simulations of deformation of coarse-grained chains with harmonic and finitely extensible nonlinear elastic (FENE) bonds and is applied to analyze the DNA deformation data. The network model predictions are confirmed by molecular dynamics simulations of diamond networks made of coarse-grained chains and are used to describe experimental data for biological networks of collagen, fibrin, and neurofilaments.

中文翻译：

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具有可扩展键的链和网络的变形模型

合成和生物网络和凝胶的非线性应力-应变响应表现为瞬时模量的单调增加，这是单个网络链的非线性变形的结果。为了描述这种行为，我们建立了一个非线性网络变形模型，该模型将宏观应力-应变响应与具有弯曲刚度和可延伸键的聚合物链的力-伸长行为联系起来。尤其是，网络力学性能（例如结构剪切模量，延伸率和键变形模量）以链弯曲常数，库恩长度，键弹性常数和未变形和完全伸展状态下的链大小表示。通过具有谐波和有限可扩展非线性弹性（FENE）键的粗粒链变形的分子动力学模拟，测试了链变形模型，并将其用于分析DNA变形数据。网络模型的预测已通过由粗颗粒链制成的钻石网络的分子动力学模拟得到证实，并用于描述胶原，纤维蛋白和神经丝的生物网络的实验数据。