13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- problem. Hence, the idea of the present method can be depicted by Fig.1. At the K-dominant zone which experience large deformation, the AVIB constitutive model is used while at the rest zone where the deformation is small, the linear elastic constitutive model is adopted. Fig.1 Depiction of the constitutive approach to fracture simulation. In VIB theory[4], the solid is considered to consist of randomized discrete material particles on micro scale and the constitutive relation is directly derived from the interactions between material particles. The AVIB generalizes the original VIB model in that the shear deformation effect between material particles is considered via Xu-Needleman potential. Therefore, the AVIB can represent material with different Poisson ratios. The micro structure of AVIB is shown in Fig.1. Material particle Virtual bond (a) tΔ nΔ ξ 0ℓ εξ 0ℓ ξℓ (b) Fig.2 Micro structure of AVIB and micro bond deformation (εdenotes the strain tensor; ξthe bond orientation vector; 0 l the original bond length) The micro bond can be described by the following simplified Xu-Needleman potential[5] 2 2 ( ) exp 1 1 exp n n t n n n n t U q q φ φ δ δ δ ⎡ ⎤ ⎛ ⎞⎛ ⎞ ⎛ ⎞ Δ Δ Δ Δ = − − + − + − ⎢ ⎥ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ ⎠⎝ ⎠ ⎝ ⎠ ⎣ ⎦ (1) where nΔ , tΔ are respectively the normal and shear bond deformation. In AVIB, they are calculated as ( ) 0 2 2 2 0 T n T T T t Δ = ⎡ ⎤ Δ = − ⎢ ⎥ ⎣ ⎦ ξ εξ ξ ε εξ ξ εξ l l (2)
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