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Research Papers

Effect of Network Architecture on the Mechanical Behavior of Random Fiber Networks

[+] Author and Article Information
M. R. Islam

Department of Mechanical,
Aerospace and Nuclear Engineering,
Rensselaer Polytechnic Institute,
Troy, NY 12180

R. C. Picu

Department of Mechanical,
Aerospace and Nuclear Engineering,
Rensselaer Polytechnic Institute,
Troy, NY 12180
e-mail: picuc@rpi.edu

1Corresponding author.

Manuscript received April 5, 2018; final manuscript received May 7, 2018; published online June 4, 2018. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 85(8), 081011 (Jun 04, 2018) (8 pages) Paper No: JAM-18-1192; doi: 10.1115/1.4040245 History: Received April 05, 2018; Revised May 07, 2018

Fiber-based materials are prevalent around us. While microscopically these systems resemble a discrete assembly of randomly interconnected fibers, the network architecture varies from one system to another. To identify the role of the network architecture, we study here cellular and fibrous random networks in tension and compression, and in the context of large strain elasticity. We observe that, compared to cellular networks of same global parameter set, fibrous networks exhibit in tension reduced strain stiffening, reduced fiber alignment, and reduced Poisson's contraction in uniaxial tension. These effects are due to the larger number of kinematic constraints in the form of cross-links per fiber in the fibrous case. The dependence of the small strain modulus on network density is cubic in the fibrous case and quadratic in the cellular case. This difference persists when the number of cross-links per fiber in the fibrous case is rendered equal to that of the cellular case, which indicates that the different scaling is due to the higher structural disorder of the fibrous networks. The behavior of the two network types in compression is similar, although softening induced by fiber buckling and strain localization is less pronounced in the fibrous case. The contribution of transient interfiber contacts is weak in tension and important in compression.

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Figures

Grahic Jump Location
Fig. 1

Illustration of (a) cellular and (b) fibrous network (green lines represent fibers and red lines are cross-links) in 3D. Both networks have volume fraction ϕ=3% and other parameters as shown in Table 1.

Grahic Jump Location
Fig. 2

Nominal stress–stretch behavior of cellular (dashed lines) and cross-linked networks (solid lines) for three volume fractions: (a) uniaxial tension and (b) uniaxial compression. Each stress–strain curve is obtained by averaging the response of three replicas of the stochastic microstructure with the same set of network parameters (ϕ,lb,Nc). The bars shown for volume fraction (ϕ=3%, blue squares in the two figures) represent the range of the three realizations. Similar level of variability is observed for the other volume fractions, but bars are not shown for clarity. The inset in (b) shows a detail of the compression curves of cellular networks. The vertical axis is normalized by fiber modulus (Ef) in both (a) and (b).

Grahic Jump Location
Fig. 3

Scaling of the small strain modulus (E0) with the network density (ρ) and bending length (lb) for (a) cellular and (b) fibrous networks. Data in (b) are shown for two cross-link densities: fully cross-linked case with p = 1 (circles) and partially cross-linked with p = 0.69 (triangles). The vertical dashed lines and change of symbol color indicate the transition from bending to stretching-dominated regimes and corresponding scalings.

Grahic Jump Location
Fig. 4

Variation of tangent modulus (Et) as a function of stress under tension for (a) cellular and (b) fibrous networks with various volume fractions. The vertical axis is normalized by the small strain network modulus, E0 and the horizontal axis is normalized by the stress at transition from regime I to II. Results for the fibrous network with ϕ=3% and with various values of p are shown in (c). The axes of the plots in the insets are normalized by the fiber modulus, Ef, in order to avoid distorting the actual shape of the curves.

Grahic Jump Location
Fig. 5

Variation of the (a) incremental Poisson's ratio, νi, and (b) orientation index, P2, under uniaxial tension for both network types (here, p = 1 for fibrous networks). The arrows indicated the transitions between the three regimes.

Grahic Jump Location
Fig. 6

(a) Effect of interfiber contacts on the compressive stress–strain response for cellular and fibrous networks with volume fraction ϕ=3%, p = 1 and lb/lc=0.036 and (b) the evolution of the density of interfiber contacts (pc) with stretch for cellular (black circles) and cross-linked networks (blue triangles), compared with Toll's model of Eq. (4) (continuous line).

Grahic Jump Location
Fig. 7

Variation of the mean contact force (CF) at interfiber contacts during compression for cellular and fibrous networks with ϕ=3%. The contact force is normalized by D2 and by the modulus of the fiber material.

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