13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- 4. Numerical calculations Finite element calculations are carried out to predict the dynamic response of the corrugated sandwich plates with sinusoidal plate cores. All simulations have been carried out using ABAQUS/Explicit code. Eight-node linear brick elements with reduced integration (Type C3D8R) are used to model the face sheets and core webs in ABAQUS/CAE software. The uniform distributed impulsive loading I per area is applied to the top face sheet of the sandwich plate as a uniform initial velocity 0 s t V I hρ = [10,12]. Periodic boundary conditions are applied at each end of the repeating unit in x direction, and symmetrical boundary conditions about the centerline are adopted. The computational model of the corrugated sandwich plate is shown in Fig. 1(b). All the contact of the plates is modeled by using a general contact algorithm with a frictionless contact option in ABAQUS/Explicit. The vertical, horizontal and rotational displacements of nodes at the ends of the plate are zero. The face sheets and core web are made of stainless steel with yield strength 400MPa Yσ = , Young’s modulus 200GPa sE = , yield strain 0.2% Yε = , elastic Poisson’s ratio 0.3 ev = , density 3 7850kg m sρ = and linear hardening modulus 12 t Y E σ = , respectively. It is assumed that the face sheets and core web materials have sufficient ductility to be able to sustain deformation without fracture. The face sheets and core webs are modeled as 2J flow theory of plasticity. 5. Results and discussion 5.1. Effect of the asymmetric factor Comparisons of the analytical solutions and numerical results for the normalized maximum deflection 1w of the bottom face sheets and the nondimensional structural response time fT for the asymmetric sandwich plates subjected to 0.25 I = are shown in Figs. 4(a) and (b), respectively. The sandwich plates with sinusoidal plate core have 0.1 cH = , 0.08 h = , 45 φ= o, 0.055 ρ= and 1m L= . In Fig. 4(a), it is seen the analytical solutions based on Eq. (7) are in good agreement with the numerical results and underestimates the numerical ones a little. Actually, the discrepancies between the analytical and numerical solutions lie in that the analytical procedure does not consider the effects of the wrinkling of face sheets and cores, the strain hardening of the metal material, the effect of shear force and the reduction in momentum provided by the supports in the core compression phase. The discrepancies in high impulsive loading may be due to the assumption that there is full densification of the core in the analytical solution while in the numerical solution there is no distinct densification in the core. In Fig. 4(a), it is seen that the numerical result for the smallest maximum deflection occurs in the case of 0.5 α= . Moreover, seen the deformed configurations at the impulse value 0.25 I = in Figs. 5(a) and (b), the deformation of top and bottom face sheets in the case of 2 α= both almost keeps horizontal at the midspan, while the top face sheet of the sandwich plate in the case of 0.5 α= occurs more evident deformation in the location far away the core web relative to the location bonded to the core. In Fig. 4(b), the analytical
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