有限应变均匀化方法在周期性杆网络中的应用：半柔性生物聚合物网络
Finite strain homogenization of periodic rod networks with application to semi-flexible biopolymers
AI总结：
本研究采用有限应变计算均匀化方法，结合特殊柯西杆理论，对8链和14链周期性半柔性生物聚合物网络的响应进行分析，重现其特有力学现象，结果与实验数据吻合，还可表征螺旋杆网络的拉伸行为。
AI中文摘要：
本研究采用有限应变计算均匀化方法，对建模为理想化8链和14链周期性网络的半柔性生物聚合物网络的响应进行表征。我们采用几何精确的特殊柯西杆理论对构成这些8链和14链网络的微观纤维进行建模，该理论可捕捉任意大的微观尺度变形。我们同时开展宏观应变驱动和应力驱动的均匀化分析，以研究宏观单轴拉伸、压缩和简单剪切响应。研究中重现了生物聚合物网络特有的若干现象，包括单轴拉伸下的应变硬化和体积收缩、压缩下的软化以及简单剪切下的反向坡印廷效应。我们发现，微观尺度的非线性与非仿射变形，尤其是微观纤维的弯曲和屈曲，在这些现象中发挥重要作用。我们采用非线性、无缺陷的路径追踪方法获得均匀化问题的后屈曲解，并验证其稳定性。我们还将均匀化结果与生物丝网络单轴拉伸和压缩的实验数据进行对比，发现二者吻合良好。当将8链单胞中的纤维替换为螺旋杆时，我们还能重现近期制备的柔性超结构所展现的拉伸行为。
英文摘要：
In this work, we adopt a finite strain computational homogenization approach to characterize the response of semi-flexible biopolymer networks modeled as idealized 8- and 14-chain periodic networks. We use the geometrically exact special Cosserat rod theory to model the microscale fibers forming these 8- and 14-chain networks. This allows us to capture arbitrarily large microscale deformations. Both macroscopic strain- and stress-driven homogenization are performed to study the macroscopic uniaxial tension, compression and simple shear responses. Several phenomena unique to biopolymer networks are recovered such as strain-stiffening and volume shrinkage under uniaxial tension, softening under compression and reverse Poynting effect under simple shear. We find that nonlinearity and non-affine deformation at microscale, especially bending and buckling of microscale fibers, plays an important role in these phenomena. We obtain the postbuckled solutions of the homogenization problem using a nonlinear, imperfection-free path following approach and also check for their stability. We further compare our homogenization results with experimental data for uniaxial tension and compression of biofilament networks and find good agreement. When the fibers are replaced by helical rods in the 8-chain unit cell, we are also able to capture the enlarged stretching behaviour as shown in recently fabricated compliant metastructures.
