# Finite Element Simulation of the Flat Crush Behavior of Corrugated Packages
## 1 Introduction  
Recently, with emerging environmental problems worldwide, paper-based cushioning materials that can replace polymer-based ones, such as EPS (Expanded Polystyrene), EPE (Expanded Polyethylene), and EPU (Expanded Polyurethane), have gained interest in the packaging field.  
The most representative paper-based packaging material is the corrugated paperboard, which is an orthotropic engineering structure. The mechanical and directional properties of the corrugated paperboard depend on its structural shape and the properties of the constituent paperboards [1, 2, 3].  
Until recently, experimental methods have been primarily applied to the design problems and used for characteristic understanding of the various corrugated packages based on corrugated paperboards. However, these methods have limitations from both time and economical perspectives. In addition, it is impossible to quantitatively analyze the effect of each component of the corrugated paperboard on the mechanical strengths, such as the edgewise compression strength and flat crush resistance. Therefore, severalrecent studies have applied finite element analysis (FEA) to the design of corrugated packages [2; 3; 4; 5; 6; 7; 8; 9].  
Most FEA studies have focused on analyzing the mechanisms of buckling, failure, stability, and adherence strength of the corrugated paperboard [4; 5; 6; 10; 11], and investigating the compression and flexural behavior of the different flute types [7]. Some FEA studies [8; 12; 13] have also attempted to replace the conventional semi-empirical equations by optimizing the board combinations of corrugated paperboard to analyze the performance and strength of their boxes and to develop FEA simulations. In addition, some researchers [3; 8] conducted FEA on the various specimens of standard for the edgewise compression strength of corrugated paperboard worldwide, and compared and analyzed their results according to the specimen shape. [PERSON] and [PERSON] [8] conducted FEA for edgewise compression test (ECT) specimens based on the recommendations of the FEFCO No.8 testing standard [14]. They found that the difference in the ECT values according to the frictional contact conditions between the modeled test specimen and the rigid surface of the testing machine was less than 3% in A/F (A-flute) and C/F (C-flute), and approximately 15% in B/F (B-flute). [PERSON] et al. [3] analyzed the edgewise compression behaviors of DW (single-wall) (A/F and B/F) and DW (double-wall) (AB/F and BB/F) corrugated paperboards that are commonly used in South Korea [15] with three standardized methods (KS M 7063-1 method A [16], TAPPI T 838 [17], and FEFCO No.8 [15]), using FEA simulations and experimental methods. They reported that the edgewise compression strength obtained by the FEA and the experiment differed due to the contact condition between the liner and flute in the FE modeling of the corrugated paperboard. Moreover, the difference between the standards by the experiment and the FEA was qualitatively consistent.  
In this study, FEA for flat crush behavior, which is its out-of-plane characteristic, was conducted for each of the two types of SW (A/F and B/F) and DW (AB/F and BB/F) corrugated paperboards, which are commonly used in Korea. The effects of each component of the corrugated paperboard on the flat crush behavior were analyzed qualitatively. In addition, the applicability of the FEA-based computer simulation was analyzed through empirical experiments on the FEA results.