13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- both cell-wall and sphere is 2700 Kg/m3, elastic modulus is 69Gpa, poisson's ratio is 0.3. Mesh sensitivity studies revealed that additional mesh refinements did not improve the accuracy of the calculations appreciably. The automatic single-surface contact type with the principle simple, rarely arouse the hourglass effect, no numerical noise and the momentum conservation accurate penalty function method is adopted. 3 Equivalent processing Cell-wall was assumed to be 'two force rod' model as shown in Figure 2. Young's modulus and density of cell-wall matrix are sE and sρ. The tensile load and internal force distribution on 1X and 2X direction can be found out through the force equilibrium condition. Then according to harmonize deformation of cell-wall, the relation of equivalent stress and strain can be established. Figure 2. Triangle-grid structure under two cases of compression load [18] The relative density is defined as * / s ρ ρ ρ = ，where *ρis the equivalent density of grid structure，and sρ is the density of cell-wall matrix. The material parameters of equivalent homogeneous shell [18]are: Relative density: * 2 2 2 2 3 2 3 sin60 s T T L L ρ ρ ρ = = = ,Young's modulus: 2 1 2 2 2 3 3 3 s s T E E E E L ρ = = = , Poisson's ratio: 12 21 1 3 υ υ = = , Shear modulus: 2 12 2 3 8 4 s s T G E E L ρ = = 4 Result analysis and discussion When structure is subjected to an impact load, the governing equations can be expressed as following [19]: Equation of mass conservation: 0 0 ij V V ρ ρ ′ = (1) where ρ′ denotes the current density, ij V represents the current volume, and 0ρ denotes the initial density. Equation of momentum conservation: , ij j i i f u σ ρ ρ ′ ′ + = & (2) where ijσ represents the Cauchy stress, if represents the body force density, and iu&denotes the acceleration. Equation of energy conservation: ( ) ij ij E Vs p q V ε = − + & & & (3)
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