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Mechanical response of random nanofiber networks with defined network parameters and microstructures. 

A balance between model complexity, accuracy, and computational cost is a central concern in numerical simulations. In particular, for stochastic fiber networks, the non-affine deformation of fibers, related non-linear geometric features due to large global deformation, and size effects can significantly affect the accuracy of the computer experiment outputs and increase the computational cost. In this work, we systematically investigate methodological aspects of fiber network simulations with a focus on the output accuracy and computational cost in models with cellular (Voronoi) and fibrous (Mikado) network architecture. We study both p and h-refinement of the discretizations in finite element solution procedure, with uniform and length-based adaptive h-refinement strategies. The analysis is conducted for linear elastic and viscoelastic constitutive behavior of the fibers, as well as for networks with initially straight and crimped fibers. With relative error as the determining criterion, we provide recommendations for mesh refinement, comment on the necessity of multiple realizations, and give an overview of associated computational cost that will serve as guidance toward minimizing the computational cost while maintaining a desired level of solution accuracy. 

Abstract Many engineering materials are made from fibers, and fibrous assemblies are often compacted during the fabrication process. Compression leads to the formation of contacts between fibers, and this causes stiffening. The relation between the uniaxial stress, S, and the volume fraction of fibers, φ, is of power law form. The derivation of this relation based on micromechanics considerations takes as input the structural evolution represented by the dependence of the mean segment length of the network, lc, on the current density, ρ (ρ is defined as the total length of fiber per unit volume of the network). In this work, we revisit this problem while considering that the mean segment length should be defined exclusively by fiber contacts that transmit load. We use numerical simulations of the compression of crimped fiber assemblies to show that, when using this definition, ρ∼1/lc2 at large enough strains. Purely geometric considerations require that ρ∼1/lc, and we observe that this applies in the early stages of compaction. In pre-stressed networks, the density–mean segment length scaling is of the form ρ∼1/lc2 at all strains. This has implications for the relation between stress and the fiber volume fraction. For both ρ versus lc scalings, S∼(φn−φ0n), where φ0 is the initial or reference fiber volume fraction; however, n = 3 when ρ∼1/lc and n = 2 for ρ∼1/lc2. These predictions are compared with experimental data from the literature. 

This article addresses the structure-properties relation in network materials, with focus on the effect of the crosslink connectivity. Three regimes of behavior are outlined, and a new non-affine relaxation mechanism is described.