13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- correlation length d increases from 1 to 3. It can be seen the phenomena of “strain softening” after the maximum stress value is reached, which corresponds to the decreasing external loads when the stiffness of the system becomes smaller after some elements become plastic. By checking the linear part of the stress-strain curve, we can get the Young’s modulus of the lattice network as E E GPa c 0.5 1= ≈ , which indicates that the effect of the elasto-plastic properties of the elements will lead to the decrease of the Young’s modulus. The macroscopic strength of the fibrous material decreases with reduction of the correlation length, which equivalent to increase of the sample size, this is consistent with the statistical size effect, even when plasticity is presented. 6. Conclusions In this study a random lattice network model is introduced to simulate the damage behavior of heterogeneous fibrous materials. Elasto-plastic bar elements are used to construct a regular triangular lattice with the random field strength distributions to characterize the randomness of the continuum fibrous materials. The material properties and geometric size of the elements in the lattice networks are calibrated based on the equivalence of the elastic strain energy. Nonlinear finite element method has been applied to study the structural response of the lattice network under external tensile loading. The correlation length of the strength distribution of bar elements has great influence on the strength of the random lattice networks. The macroscopic strength of the fibrous material decreases with reduction of the correlation length, which is equivalent to increase of the sample size. Acknowledgements The present work is supported by the Atlantic Innovation Fund, and is gratefully acknowledged. References [1] K. Hu, X.F. Xu, Probabilistic upscaling of material failure using random field model. Algorithms, 2 (2009) 750-763. [2] X.F. Xu, X. Chen, L.H. Shen, A Green-function-based multiscale method for uncertainty quantification of finite body random heterogeneous materials. Comput Struct, 87 (2009) 1416-1426. [3] Z. Yang, X.F. Xu, A heterogeneous cohesive model for quasi-brittle materials considering spatially varying random fracture properties. Comput Methods Appl Mech Engrg, 197 (2008) 4027-4039. [4] Z.P. Bazant, M.R. Tabbara, M.T. Kazemi, G. Pijaudier-Cabot, Random particle model for fracture of aggregate or fibre composites. J Eng Mech, ASCE, 116 (1990) 1686-1705. [5] W.A. Curtin, H. Scher, Brittle fracture in disordered materials: a spring network model. J Mater Res, 5 (1990) 535-553. [6] E. Schlangen, J.G.M. van Mier, Simple lattice model for numerical simulation of fracture of concrete materials and structures. Mater Struct, 25 (1992) 534-542. [7] J.X. Liu, Z.T. Chen, K.C. Li, A 2-D lattice model for simulating the failure of paper. Theor Appl Fract Mech, 54 (2010) 1-10. [8] B.L. Karihaloo, P.F. Shao, Q.Z. Xiao, Lattice modeling of the failure of particle composites.
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