2
Advances in Materials Science and Engineering
Table 1: Parameters of linear elastic material [18].
Numerical value
Unit MPa MPa MPa MPa MPa MPa
Name
Twin wall corrugated board
7600 4020
𝐸 𝑥 𝐸 𝑦 𝐸 𝑧
Elastic modulus
38
2140
𝐺 𝑥𝑦 𝐺 𝑥𝑧 𝐺 𝑦𝑧 𝑉 𝑥𝑦 𝑉 𝑥𝑧 𝑉 𝑦𝑧
Shear modulus
20 70
Figure 1: Twin corrugated wall board structure.
— — —
0.34 0.01 0.01
Poisson’s ratio
and structures composed of corrugated board a difficult task [4]. Numerous studies have been focused on the properties of corrugated cardboard and external environment’s effects on the performance of corrugated carton [5–10]. Gilchrist et al. [4] have developed nonlinear finite element mod- els for corrugated board configurations. Results from the finite element simulations correlated reasonably well with the analogous experimental measurements performed using actual corrugated board specimens. Biancolini and Brutti [11] have developed a finite element “corrugated board” by means of a dedicated homogenization procedure in order to investigate the buckling of a complete package. The FEM model of the package, assembled with this new element, can accurately predict the experimental data of incipient buckling observed during the standard box compression test, despite the few degrees of freedom and the minimal computational effort. Biancolini [12] also presented a numerical approach to evaluating the stiffness parameters for corrugated board. The method is based on a detailed micromechanical rep- resentation of a region of corrugated board modelled by means of finite elements. Conde et al. [13] have developed a methodology for modelling corrugated board adhesive joints subjected to shear, considered to be the main load in most of these joints. The corrugated board adhesive joint model reproduced quite well the stiffness obtained in the test samples, as well as the failure load with a deviation of less than 14%. Biancolini et al. [1] compared results obtained from the simplified formula, an extended formula, and two numerical models developed by authors using finite elements (FE): an FE model realised with homogenised elements and an FE model representing the entire corrugation geometry. Numer- ical results of the capability to resist stacking loads obtained with FE models were consistent with experimental results. Haj-Ali et al. [14] presented a refined nonlinear finite ele- ment modeling approach for analyzing corrugated cardboard material and structural systems. This method can accurately predict overall mechanical behavior and ultimate failure for wide range corrugated systems. Talbi et al. [15] presented an analytical homogenization model for corrugated cardboard and its numerical implementation in a shell element. The shape and size of flute have an important effect on the performance of corrugated cardboard. However, there are no strict standards of flute size parameter to achieve the best elasticity and compressive strength of corrugated cardboard. There is also little literature regarding the finite element
kg/m 3
Density
404.5
Table 2: Parameters of rigid plate material.
Name
Numerical value
Unit
12
N/m 2 kg/m 3
Elastic modulus
1.0 × 10
1.0 × 10 − 8
Density
Poisson’s ratio
0.3
—
analysis of flute size. Yuan et al. [16, 17] have developed a model of UV-shaped corrugated cardboard by ANSYS. The results show that the closer the model to the U-shaped flute, the larger the corrugated board strain becomes. It is consistent with the empirical data, which prove the feasibility of finite element analysis method. In this paper, we focus on the investigation of nonlinear finite element analysis of the fluted corrugated sheet in the corrugated cardboard based on software SolidWorks2008. The shape and size of flute will be discussed with the help of SolidWorks and compared with the empirical data. 2. Modeling SolidWorks2008 has powerful structural modeling functions, among which Cosmos/Works is a function module which is specially used to make finite element analysis on structure. The model of common UV-shaped corrugated board is shown in Figure 2. In Figure 2, 𝐿 is flute length, 𝐻 is flute height, ℎ is facing paper thickness, 𝛿 is fluting paper thickness, 𝜃 is flute angle, and 𝑟 is arc radius. The principal aim of this work is to study the fluted corru- gated sheet. So we added a piece of rigid plate with large elastic modulus on upper facing paper (as shown in Figure 3) to eliminate the influence of the facing paper deformation. The maximum stress and strain of the improved model occur in the point in which flute contact with the upper facing paper in all cases. The material parameters of corrugated board model are given in Table 1 [18]. The material parameters of rigid plate model are given in Table 2 from the SolidWorks material library. 3. Results and Discussion 3.1. The Numbers of Flutes in Models. In order to eliminate the influence of the number of flutes in models, a series
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