A numerical study on mechanical properties of low-density two-dimensional networks of crosslinked long fibers




Mane, Soham Manohar

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In this dissertation, we study mechanical properties of low-density two-dimensional (2D) networks by finite element methods. Fiber-based materials are prevalent in nature and in engineering applications. To understand the relationship between the effective mechanical properties and the underlying microstructures, we consider a variety of periodic and random 2D networks of crosslinked long fibers. The linearly elastic properties of periodic 2D networks (e.g., square, triangular and Kagome) are well understood. However, for low-density networks, cooperative buckling of the fiber segments can take place at small strains, leading to nonlinear, anisotropic elastic behaviors. A transition from stretch to bending and then back to stretch dominated deformation is predicted for the Kagome and triangular networks. For random 2D networks, the stress-strain behavior is statistically isotropic and slightly nonlinear under uniaxial tension, dominated by stretch of the fibers aligned closely to the loading direction. Meanwhile, stochastic buckling occurs continuously in the random networks, leading to significant lateral contraction. Consequently, while the effective Young’s modulus follows a nearly linear scaling with respect to the relative density, the effective Poisson’s ratio exhibits a transition from stretch to bending dominated mode as the relative density decreases. The comparison between the periodic and random 2D networks highlights the profound effects of the network topology on the effective elastic properties. Furthermore, we study the strength of 2D periodic networks. First we present the elastic beam models to predict the effective tensile strength of the rotated square, triangular and Kagome networks. Next we conduct finite element analyses to simulate the damage initiation and progression in the periodic 2D networks assuming elastic-brittle fibers. For the Kagome networks subject to uniaxial tension in the y-direction, four different failure modes (including post-buckling modes) are predicted, depending on the relative density and the fiber strength. The elastic beam model does not consider the nonlinear elastic behavior due to buckling and thus generally overestimates the tensile strength. Moreover, for Kagome networks consisting of many unit cells, the effective tensile strength depends on the boundary conditions, and the presence of a crack-like defect could reduce the strength considerably.


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