Cioroianu Adrian R, Storm Cornelis
Department of Applied Physics and Institute for Complex Molecular Systems, Eindhoven University of Technology, P. O. Box 513, NL-5600 MB Eindhoven, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052601. doi: 10.1103/PhysRevE.88.052601. Epub 2013 Nov 4.
When loaded in simple shear deformation, polymeric materials may develop so-called normal stresses: stresses perpendicular to the direction of the applied shear. These normal stresses are intrinsically nonlinear: basic symmetry considerations dictate they may only enter at O(γ(2)), with γ the dimensionless shear strain. There is no fundamental restriction on their sign, and normal stresses may be positive (pushing outward) or negative (pulling inward). Most materials tend to dilate in the normal direction, but a wide variety of biopolymer networks including fibrin and actin gels have been reported to present anomalously large, negative normal stresses-a feature which has been ascribed to the intrinsic elastic nonlinearity of semiflexible fibers. In this work, we present analytical results on a model nonlinear network, which we expand to the required nonlinear order to show that due to geometric, rather than elastic, nonlinearities (negative) normal stresses generically arise in filamentous networks-even in networks composed of linear, Hookean springs. We investigate analytically and numerically how the subsequent addition of elastic nonlinearities, nonaffine deformations, and filament persistence through cross-linkers augment this basic behavior.
当在简单剪切变形中加载时，聚合物材料可能会产生所谓的法向应力：垂直于外加剪切方向的应力。这些法向应力本质上是非线性的：基本的对称性考虑表明它们只能在O(γ(2))阶出现，其中γ是无量纲剪切应变。它们的符号没有基本限制，法向应力可以是正的（向外推）或负的（向内拉）。大多数材料倾向于在法向方向上膨胀，但据报道，包括纤维蛋白和肌动蛋白凝胶在内的多种生物聚合物网络呈现出异常大的负法向应力——这一特征归因于半柔性纤维的固有弹性非线性。在这项工作中，我们给出了一个模型非线性网络的分析结果，我们将其扩展到所需的非线性阶数，以表明由于几何而非弹性非线性，丝状网络中通常会出现（负）法向应力——即使在由线性胡克弹簧组成的网络中也是如此。我们通过分析和数值方法研究了随后添加弹性非线性、非仿射变形以及通过交联剂实现的细丝持久性如何增强这种基本行为。
