13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- 0 1 3 0 1 2 4 0 0 1 3 5 0 1 2 4 2 0 0 0 1 2 4 0 1 2 2 2 , , 2 , n n t A B n C D t n f A cc f B cc c f A cc c f B cc c f B cc c f B cc δ δ Δ = ⋅ ⋅ = ⋅ = ⋅ = ⋅ Δ = ⋅ ⋅ = ⋅ ⋅ l l l (8) The coefficient in Eq.(8) are respectively 2 2 2 0 0 0 0 1 2 2 2 2 3 2 4 5 2 , , exp , exp 1 , 1 , 1 n n n t n t n t n n n n q A B c c c q q c c c φ φ δ δ δ δ δ δ ⎛ ⎞ ⎛ ⎞ Δ Δ = = = − = − ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ Δ Δ = − + ⋅ = + = − l l (9) In [3], Zhang and Gao proposed a remedy method for element size sensitivity, which essentially embedded the fracture energy into the constitutive relation. By adjusting the material parameters at fracture tip, AVIB can keep the strain energy release rate constant. According to the idea of AVIB, the adjusted parameters at crack tip is 0 0 0 0 , , , n n t t A A B B λ λ δ λδ δ λδ = = = = % % % % (10) where λis the adjustment coefficient. The adjustment coefficient takes the following values for different cases. ( ) ( ) ( )( ) 2 2 2 2 1 2 for 3D 3 1 for 2D-stress 2 1 1 2 for 2D-strain 2 t t t J hE J hE J hE ν λ π ε ν λ λ ε ν ν λ ε − ⎧ ⎪ = ⎪ ⎪ − ⎪ =⎨ = ⎪ ⎪ + − ⎪ = ⎪⎩ (11) in which J is the intrinsic J-integral of material; his the element size, as h c S = (12) where S is the area of an element and cis a geometrical factor. In the numerical examples discussed in the next section, take 4 2 c = . 3 . Criterion of crack tip element When using the present method, it is necessary to identity the element of crack tip. Usually, the
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