13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Random elasto-plastic lattice modeling of damage in fibrous materials Keqiang Hu1,*, Zengtao Chen1, K. C. Li2, X. Frank Xu3 1 Department of Mechanical Engineering, University of New Brunswick, Fredericton, NB, Canada E3B 5A3 2 Department of Chemical Engineering, University of New Brunswick, Fredericton, NB, Canada E3B 5A3 3 School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China * Corresponding author: ckhu@unb.ca, keqianghu@163.com Abstract A random elasto-plastic lattice network model is developed to simulate the damage behavior of fibrous materials. Elasto-plastic bar elements are used to construct a regular lattice network with the random element strength distributions to simulate the randomness of the continuum fibrous materials. The structural response of the elasto-plastic lattice network under displacement controlled loading is studied using finite element method. Small deformation theory is used and the modified Newton-Raphson algorithm is applied to solve the nonlinear finite element equations. The effects of correlation length of the strength distribution of bar elements on the global behaviors are studied. Keywords Damage, Random elasto-plastic lattice, Nonlinear finite element method, Correlation length 1. Introduction Complexity of failure is reflected from sensitivity of strength to small defects and wider scatter of macroscopic behaviors. The information of materials at micro-scale is random and can only be partially measurable, which leads to the complicated failure mechanisms for the random heterogeneous materials [1-3]. Various types of lattice type models such as central force model, electrical fuse model, bond-bending model, and beam-type model have been used to study progressive damage of heterogeneous materials, such as concrete, rock, ceramics and paper. It is a relatively simple but powerful technique to identify microcracking, crack branching, crack tortuosity and bridging, thus allowing the fracture process to be followed until complete failure [4-8]. A comprehensive review of the lattice models for micromechanics applications can be found in Ostoja-Starzewski [9]. The failure properties of fibrous materials have been a subject of research for the past decades [10-12]. As the structure of fibrous material is inhomogeneous, the role of disorder has great influence on the mechanical and rheological properties, and statistical growth models can simulate the heterogeneous fibrous materials well. The fibers in fibrous materials are full of imperfections and exhibit a wide variety, of natural origin, in dimensions and mechanical properties, and the mechanical properties of fibrous materials can be varied significantly by selecting different types of fibers [13]. Paper, a material known to everybody, has a fibrous network structure consisting of wood fibers. A random geometry fiber network model [14] was considered to study the special elastic orthotropy of machine-made papers, which has anisotropy in the two principal directions, the machine direction (MD) and the cross direction (CD). It was shown that the random geometry may lead to a macroscopic property of special elastic orthotropy [14]. A two-dimensional beam network model was proposed as a micromechanics model to simulate paper’s failure process due to sequential breakages of fibers and/or bonds, and the numerical results showed the effects of fiber length and the ratio of fiber strength to bond strength on the failure characteristics of paper [7]. In this paper, a random elasto-plastic lattice model is proposed according to the equivalence of strain energy instead of the true network structure in fibrous materials. The concept of unit cell is
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