轴对称预应力作用下半柔性聚合物网络的局部力学响应
Local mechanical response in semiflexible polymer networks subjected to an axisymmetric prestress
摘要：
本文对轴对称预应力状态下纤维网的力学响应进行了解析和数值计算，在几何非线性如纤维转动可忽略不计的情况下。这使我们能够专注于纯粹从单个纤维的非线性力-延伸曲线导出的各向异性。各向同性，轴对称和完全各向异性网络的独立弹性系数的数量被枚举，然后推导出表达式的响应，可以测试对例如微观流变学实验的局部施加的力。局部力可以产生各向异性远离应用点，所以非线性连续方程的数值积分被用来确定应力场，和诱导的机械各向异性，在点直接位于后面和前面的一个力方向。蠕虫状链模型的规范化形式的结果，使他们能够很容易地映射到一系列的系统。最后，这些研究结果的相关性，自然发生的系统和未来的调查方向进行了讨论。
英文摘要：
Analytical and numerical calculations are presented for the mechanical response of fiber networks in a state of axisymmetric prestress, in the limit where geometric non-linearities such as fiber rotation are negligible. This allows us to focus on the anisotropy deriving purely from the non-linear force-extension curves of individual fibers. The number of independent elastic coefficients for isotropic, axisymmetric and fully anisotropic networks are enumerated, before deriving expressions for the response to a locally applied force that can be tested against e.g. microrheology experiments. Localised forces can generate anisotropy away from the point of application, so numerical integration of non-linear continuum equations is employed to determine the stress field, and induced mechanical anisotropy, at points located directly behind and in front of a force monopole. Results are presented for the wormlike chain model in normalised forms, allowing them to be easily mapped to a range of systems. Finally, the relevance of these findings to naturally occurring systems and directions for future investigation are discussed.
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