Finite strain homogenization of periodic rod networks with application to semi-flexible biopolymers

Abstract

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.