# Prediction of Deflection Due to Multistage Loading of a Corrugated Package
## 2 Finite Element Modeling of a Corrugated Package  
As shown in Figure 1, a corrugated fiberboard was manufactured by bonding the wavy corrugating medium (flute) between the liners. In the production process, the direction of the flow of the equipment is the machine direction (MD), the direction orthogonal to the flat MD is the count machine direction (CD), and the direction perpendicular to the corrugated fiberboard's surface is the thickness direction (z-direction). As shown in Figure 1, the liner and corrugating media have orthotropic properties during the manufacturing process; however, the combined corrugated fiberboard also has orthotropic properties because of the unique characteristics of the flute. In addition, the tensile and compressive direction characteristics are different and exhibit nonlinear properties [13]. Therefore, in this study, we assumed that the corrugated package has a linear behavior. The corrugated fiberboard is classified into several types according to the number of combinations of liners and corrugating media, as well as the shape of the applied flute. In this study, the DW corrugated fiberboard of the EB-flute (EB/F) was targeted. The DW corrugated fiberboard of the EB/F consists of two flutes (E-flute (E/F) and B-flute (B/F)) and three liners (outer, middle, and inner liner), as shown on the left side of Figure 2. The flute height and flute pitch of E/F range from 1.4 to 1.6 mm and 3.33 to 3.19 mm, respectively, and the flute height and flute pitch of E/F range from 2.5 to 2.8 mm and 6.25 to 5.77 mm, respectively. The board combination of the target corrugated fiberboard was (SC300 surface coating+) KA180/K180(E/F)/S120/K180(B/F)/K180 (SC: outer BKP + inner Manila waste paper (BKP--bleached kraft pulp); KA: 30% outer liner containing UKP + 40% AOCC + 30% KOCC (UKP--unbleached kraft pulp; AOCC--American old corrugated container; KOCC--Korean old corrugated container, K180 and S120; 100% KOCC). The measured total thickness of the corrugated fiberboard was approximately 5 mm. Abaqus laminar material constants were determined to define the anisotropic properties of the liner, assuming that the areas of the E/F corrugating medium, the intermediate liner, and the B/F corrugating medium between the outer and inner liners were combined for simplification and homogenization and were defined as the core. The core was also defined by the same Abaqus laminar material constants as those of the liner. As shown in Figure 2, the laminated structure of the liner and the corrugating medium was defined by the Abaqus composite model and consisted of an outer liner, core, and inner liner. In the simplified model of Figure 2, \(t\) is the ratio of the thickness occupied by the liner and the core with a total thickness of the corrugated fiberboard of 5 mm. To simplify the model, we considered the thicknesses of the outer and inner liners to be equal, with an average thickness of 0.2 mm. Figure 1: Definitions of the directions of the corrugated fiberboard and corrugated package [5; 13]: CD, count machine direction; MD, machine direction. The power-law creep model of Equation (2) was applied to predict the time-dependent deflection with respect to the compression load of the target corrugated package, wherein we assumed that the creep behaviors of the liner and core were the same. The box was modeled in 3D based on the drawings of the target corrugated package. As [PERSON] (2014) mentioned, the continuum shell element was applied as the basic element type of the corrugated fiberboard because it is more suitable for predicting the changes over time than conventional shell elements and advantageous for handling contact between the packages.