13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- displacement analysis, therefore all the following calculations were done only in the second hypothesis. By using the densities of the materials mentioned previously the total mass of the sandwich panel resulted as 1.335 kg, from which the mass of the sheets is 65% (0.864 kg), of the core is 31% (0.418 kg), and of the adhesive as 4% (0.053 kg). It is to observe that the mass of proposed chiral foam core represents 35% of the mass corresponding to a compact core made from the same foam and having the same overall sizes, which is of 1.2 kg. Data were considered in the SI system, therefore in the figures displacements were obtained in meters, and stresses in N/m2 (106 N/m2 = 1 N/mm2 = 1 MPa). Figure 4. The core discretized with 8-node brick-type finite elements Figure 5. Geometry of the basic semi-block of the meta-tetrachiral core 3. Evaluation of in-plane auxetic properties of the core The chiral core was initially analyzed separately in order to establish the coefficients of transversal contraction (or of transversal swelling), notated as xyν and yx ν . The displacements in the plane XY (median plane of the core) were established in two situations (Fig. 4): I displacements blocked in the direction X on the edge AD and an imposed displacement on the opposite edge (UX = 1 mm); II displacements blocked in the direction Y on the edge AB and an imposed displacement on the opposite edge (UY = 1 mm). In general, if xL and yL are the overall dimensions of the panel (length and width), the two values of the “Poisson’s coefficients”, associated to the situations defined in I and II are to be calculated with the relations: ( ) ( ) x I x y I y xy L L L L/ / / , , Δ =−Δ ν , ( ) ( ) y II y x II x yx L L L L/ / / , , Δ =−Δ ν . (1)
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