Topology effects on nonaffine behavior of semiflexible fiber networks

Abstract

Filamentous semiflexible networks define the mechanical and physical properties of many materials such as cytoskeleton. In the absence of a distinct unit-cell, Mikado fiber network model is the most commonly used algorithm for representing the microstructure of these networks in numerical models. Nevertheless, certain types of filamentous structures such as collagenous tissues, at early stages of their development, are assembled by growth of individual fibers from random nucleation sites. In this work, we develop a computational model to investigate the mechanical response of such networks by characterizing their nonaffine behavior. We show that that the deformation of these networks is nonaffine at all length scales. Furthermore, similar to Mikado networks, the degree of nonaffinity in these structures decreases with increasing the probing length scale, the network fiber density, and/or the flexibility of constituting filaments. Nevertheless, despite the lower coordination number of these networks, their deformation field is more affine than that of the Mikado networks with the same fiber density and fiber mechanical properties.

Colloidal particle gel models using many-body potential interactions

“…There exists a strain-softening response for low volume fraction gels in which the normalized differential modulus strictly decreases to values less than 1. This strain softening response has been also observed experimentally and numerically in soft gels of different nature and under various loading conditions as well as systems whose microstructure is fibrillar such as polymer fiber networks [7,10,15,[21][22][23][24][25][26]. Similar to the SRG model, the variation of the normalized shear stiffness is significant at the lowest volume fraction φ = 0.05 and becomes less significant with increasing the volume fraction.…”

Non-affinity in multi-material mechanical metamaterials

“…The degree of non-affinity was defined as 29 , 31 where is the total number of nodes in the structure, is the local displacement of the i th node of the multi-material structure, and is the corresponding displacement of the i th node of a corresponding single-material lattice structure (Fig. 1 d).…”

“…Non-affine deformation can be characterized in terms of a degree of non-affinity ( ) or non-affine correlation functions 14 , 29 , 30 . The degree of non-affinity is a scalar parameter that depends on the length scale 31 and applied strain 15 , 19 , 21 .…”

“…The degree of non-affinity is a scalar parameter that depends on the length scale 31 and applied strain 15,19,21 . There are also other metrics of non-affinity that are based on strain energy 15,19,31,32 or a comparison of the local deformations with affine deformations 14,29,30,[33][34][35][36][37][38][39] .…”

Nonlinear Mechanical Properties of Prestressed Branched Fibrous Networks

“…Previous studies have shown that the mechanical response of random networks is a function of their architecture and mechanical properties of their fibrous constituents (7)(8)(9)(10)(11)(12)(13)(14)(15). Furthermore, the specific architecture of random networks has been shown to have significant influence on certain aspects of their mechanical response (16,17). Biological networks often appear either as 1) cross-linked (z % 4) networks in which fibers are interconnected by cross-linking proteins or as 2) branched (z % 3) networks in which the fibers are split into other fibers at the branching points (18).…”