A numerical study on tensile strength of low-density Kagome networks made of brittle fibers

In this paper, we present a numerical study on the tensile strength of low-density Kagome networks made of brittle fibers. First, an elastic beam model is employed to analytically predict the effective elastic properties and tensile strength, as well as the critical condition for buckling of the fibers in Kagome networks. A series of finite element analyses are then conducted to simulate the elastic deformation and failure of Kagome networks under tension. The numerical results based on unit-cell models reveal four possible failure modes of the Kagome networks subject to uniaxial tension, summarized in a phase diagram in terms of the relative density and the fiber strength. The pre-buckling failure mode is restricted to cases with relatively high density and low fiber strength. A low-density Kagome network is likely to fail by one of the post-buckling modes, with an effective tensile strength much lower than the prediction by the elastic beam model. For Kagome networks consisting of a large number of unit cells, the effect of boundary conditions on the tensile strength is examined. Under periodic boundary conditions, the effective tensile strength is nearly identical to that predicted by the unit-cell model, independent of the model size. Under a roller boundary condition, with damage initiation near the free edges followed by a diffusive damage progression, the effective tensile strength is lower than that under periodic boundary conditions for the cases of relatively low fiber strengths. Under a clamped boundary condition, the effective tensile strength is higher than that under periodic boundary conditions for the cases of relatively high fiber strengths, where fiber buckling is largely suppressed by the clamped boundaries. Finally, the effect of a crack-like defect on the effective tensile strength is studied for Kagome networks under the clamped boundary condition. With a small defect, the effective strength is nearly independent of the defect size. In contrast, with a relatively long defect, the effective strength decreases almost linearly with the length of the crack-like defect. The effective toughness for damage initiation and steady-state damage progression in the Kagome networks is discussed from an energetic perspective.