13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- continuum cell E E= (3) Figure 3. Correlated Weibull RF samples. The relationship in Eq. (3) is based on the space periodicity of the current regular lattice, which is constructed by arranging the hexagonal unit cell as shown in Figure 4 periodically. The numbers in Figure 4 denote the corresponding nodes. For a regular lattice model, as shown in Figure 2 and Figure 4, the energies of the cell and its continuum equivalent, respectively, are ∑ = ⋅ = 6 1 ( ) ( ) 2 1 b b b cell E F u (4) 2 2 σ ε ijkm ij km V continuum dV VC E ε ε = ⋅ =∫ (5) where, b stands for the b th spring element, ijkm C are material parameters, σ is the stress tensor and ε is the strain tensor. In the two-dimensional (2D) setting, the volume of the unit cell is 3 2 2 l t V = , with t being the thickness of the continuum counterpart of the unit cell and l being the spacing of neighboring unit cells which is equal to the length of the element. Consider the regular triangular network of Figure 2 with central force interactions only, which are described, for each element b, by j b j b i b j b ij i n n u F k u ( ) ( ) ( ) ( ) α = = (6) where ( )bα is the spring constant of half-lengths of the central interactions. The unit vectors ( )b n at respective angles ( )bθ of the first three α springs are
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