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Viet Dung Luong et. al., Vol. 7, No. 2, 2021
Fig. 3. Experimental setup for shock testing on the vibration table.
Fig. 4. Example of a half-sine shock pulse and corresponding response.
Shock tests were performed on the same boxes introduced in previous section using a servo-hydraulic vibration table connected to a real-time vibration controller (SEREME, France) programmed to generate shocks of various shapes and intensities. As in most mechanical shock test procedures, fixturing of the package on the shock test machine may have significant influence on the test results. In this study, the box is fixed on the vibration table by a structure consisting of link bars connected to the table by bolts as shown in Fig. (3). The box is preloaded with a total mass of 8.4 kg. The test procedure for repetitive shock experiment is as follows: the vibration table generates a shock in the vertical direction and the response of the system shown in Fig. (4) is recorded. A box is subjected to repetitive shock with the same intensity until a visible damage is observed on the box. The damaged box is then removed and replaced by a new one to undergo a series of shocks with another level of intensity. The acceleration and velocity change are the two parameters recorded and plotted in the testing procedure. With this procedure, we obtain the Damage Boundary Curve (DBC) which is constructed from the critical acceleration and the critical velocity change when the box is damaged. 3. Material Model To efficiently simulate the mechanical behavior of a corrugated cardboard box, we need to use a homogenization model instead using the full 3D model to reduce the preparation of the model and the computational times. The homogenization consists in representing the corrugated-core sandwich panel by a homogeneous plate. 3.1 Governing equations The dynamic boundary value problem (BVP) in a 3D cartesian frame is written in a strong form as: ݑߩ ሷ ൌ ߪ ǡ ݂ (1) where ݑ are the displacement vector components, ߩ is the density value, ߪ are the stress tensor components, and ݂ are the body force components. The kinematic relations for the strain rates are given as follows: ߝ ሶ ൌ ͳ ʹ ൫ ݑ ሶ ǡ ݑ ሶ ǡ ൯ൌ ߝ ሶ ߝ ሶ (2) where ߝ are the strain tensor components, ߝ and ߝ are the components of the elastic and plastic strain tensors. The constitutive equations relating stress rates and elastic strain rates are given by: ߪ ሶ ൌ ܥ ߝ ሶ (3) where ܥ is the matrix of elastic moduli. Considering the decomposition of the strain rate tensor into elastic and plastic components, the Hooke’s law is written in the following form: ߪ ሶ ൌ ܥ ൫ ߝ ሶ െ ߝ ሶ ൯ (4)
Journal of Applied and Computational Mechanics, Vol. 7, No. 2, (2021), 820-830
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