The role of structure in the nonlinear mechanics of cross-linked semiflexible polymer networks

Abstract

The microstructural basis of the characteristic nonlinear mechanics of biopolymer networks remains unclear. We present a 3D network model of realistic, cross-linked semiflexible fibers to study strain-stiffening and the effect of fiber volume-occupancy. We identify two structural parameters, namely, network connectivity and fiber entanglements, that fully govern the nonlinear response from small to large strains. The results also reveal distinct deformation mechanisms at different length scales and, in particular, the contributions of heterogeneity at short length scales.

Finite-strain, finite-size mechanics of rigidly cross-linked biopolymer networks

“…Large deformations of individual filaments, including buckling, must also be taken into account. This can be achieved using a semiflexible, worm-like chain model 16,28,30 , or e.g. large deformation Timoshenko beam elements 15 .…”

“…Biopolymer networks display a remarkable range of mechanical properties; they can be extremely extensible 6,7 and exhibit strong strain-stiffening [6][7][8][9] to ensure cell and tissue integrity 8 . The mechanical characteristics of branched, athermal biopolymer networks derive from the individual strand behavior 10,11 , the angle distribution between filaments 12 , the number of branchpoints per coherent fiber 13 and the network topology [14][15][16] . In this work, we study the finite-strain mechanical characteristics of reconstituted, cross-linked collagen type I and fibrin networks in the low-frequency limit.…”

“…Previous modeling work on the mechanics of disorganized fiber networks have been largely concerned with regular lattices with variable filament stiffness 20,21 , random network geometries 12,14,16,[22][23][24][25][26] and networks created through a simulated polymerization process 27 . An important generic result is that the hyperelastic response of low-connectivity networks is due to the excitation of nonaffine, bending-dominated modes of deformation at small strains, followed by a transition to stretching-dominated filament deformation at large network strains 12,13,20,23 .…”

Modeling of Fibrin Gels Based on Confocal Microscopy and Light-Scattering Data

“…These studies, motivated by the still-unclear physical mechanism underlying the highly nonlinear elasticity that is the basis of the strain-stiffening behavior that characterizes almost all known biopolymer fibrous networks, have spurred the development of many network models aimed at reproducing the observed mechanical properties of the various systems. Most of these models have been implemented in two dimensions (10)(11)(12)(13)(14)(15), but with the advent of confocal imaging, 3D models are becoming more and more popular (16)(17)(18)(19)(20)(21). The common feature of all of these models is that they are validated by comparing mainly their mechanical properties with those of the real network they aim to reproduce, and very little attention is paid to the agreement between the static and structural/morphological properties of the real gel versus those of the in silico network.…”

Effects of Migrating Cell-Induced Matrix Reorganization on 3D Cancer Cell Migration

“…Among these factors, the physical remodeling of 3D ECM can change the microstructure of the matrix 27 and result in multiple implications on cell migration. Firstly, mechanical contraction of ECM has been shown to facilitate cell migration.…”