Equivalence model for analyzing nonlinear mechanical behavior of Corrugated Core Composite Panel

In this study, we propose to build an equivalent 2D model to replace the 3D model of corrugated composite sheets, by the method of homogenization, to study the nonlinear mechanical behavior of corrugated core composite sheets. This model helps to significantly reduce the calculation time as well as the model building time. The model homogeneity is confirmed by comparing the numerical simulation results of the 2D model and the 3D model.
Nội dung trích xuất từ tài liệu:
Equivalence model for analyzing nonlinear mechanical behavior of Corrugated Core Composite Panel 92 108 Tuyển tập công trình Hội nghị Cơ học toàn quốc lần thứ XI, Hà Nội, 02-03/12/2022 Equivalence model for analyzing nonlinear mechanical behavior of Corrugated Core Composite Panel Luong Viet Dung*, Dao Lien Tien, and Duong Pham Tuong Minh Thai Nguyen University of Technology *Email: luongvietdung@tnut.edu.vn Abstract. A corrugated core composite panel is one of the material structures that is becoming more and more popular in many fields such as the aviation industry, and shipbuilding. In order to use this material effectively, it is necessary to understand its mechanical behavior of them. Up to now, the calculation of these structures has been mentioned by many authors, however, the calculation is still very difficult. Especially when studying their nonlinear mechanical behavior. In this study, we propose to build an equivalent 2D model to replace the 3D model of corrugated composite sheets, by the method of homogenization, to study the nonlinear mechanical behavior of corrugated core composite sheets. This model helps to significantly reduce the calculation time as well as the model building time. The model homogeneity is confirmed by comparing the numerical simulation results of the 2D model and the 3D model. Keywords: Homogenization, Finite element, Simulation, Corrugated, Composite panel1. Introduction Sandwich panels have been widely used in many fields such as in aerospace industries, marine,mechanical and civil engineering applications. This is due to the high stiffness and high strength-to-weight ratio of the sandwich panels. The sandwich panel structure consists of lightweight core and rigidouter layers. The core may consist of a continuous or discrete structural component. Core shapes arediverse such as corrugation, honeycomb, foam, triangle, etc. In which, corrugated cardboard is widelyused in product packaging. Carton is made up of layers of paper, corrugated, usually at least 2 layers ofpaper and one layer of corrugated board. Corrugated cardboard panels are one of the most complicatedorthotropic sandwich panels. By using the finite element method, the mechanical behavior of the panelsis determined, but with the complex 3D modeling of the corrugated board, numerical modeling andsimulation will be time consuming and may not be possible with large panels. The homogenizationmethod is used to simplify the simulation process; the corrugated board will be replaced by equivalentsolid 3D or 2D sheet. Aboura et al. [1] also developed a homogeneous analysis model based onmultilayer laminate theory and compared its results with numerical and experimental results, Biancolini[2] used FE numerical method to evaluate the stiffness parameters, Carlsson et al. [3,4] have presentedhomogenous properties such as cross-sectional stiffness and flexural stiffness of corrugated board byanalytical method, Nordstrand and colleagues [5,6,7] have demonstrated some of the properties ofcorrugated board by analytical methods, but these studies are limited to the behavior of the corrugatedboard in the elastic region. In this paper, we propose a homogenization model to determine the parameters of the cardboardin the plastic region. Numerical simulation of tests was performed for homogeneous model panel andthe 3D structure panel. This homogeneity model is confirmed by comparing the results obtained betweenthe two models.2. Homogenization model2.1. Material studies 93Equivalence model for analyzing nonlinear mechanical behavior of Corrugated Core Composite Panel 109 We used corrugated cardboard material in this study with the properties shown in Figure 1 andgiven in Table 1. The manufacturing process gives three characteristic directions: the machine direction(MD), the cross direction (CD), and the thickness direction (ZD). Figure 1. Geometric structure and the directions of the corrugated cardboard panel Table 1. Properties of the papers Paper Ex Ey G xy ν xy E0 n a b c d ε0 (MPa) (MPa) (MPa) 1,3 2433.2 859.91 0.0829 1077.2 96.45 4.97 1.0 2.498 2.498 1.622 0.48e-3 2 1130.4 625.85 0.0717 303.05 87.31 4.247 1.0 2.178 2.178 1.871 0.92e-32.2. Homogenization model The homogenization method is based on Mindlins theory for thick or composite panels. Itassumes that a segment that is straight and perpendicular to the mean surface remains straight but notperpendicular to the mean surface after the deformation. This assumption makes it possible to take intoaccount the deformations of transverse shearing. On the mean surface of a panel, we define the x and yaxes on the surface and the z axis perpendicular to the surface (Figure 2), Mindlins theory assumes thefollowing displacement field: uq= u + z β x  vq = v + z β y (1)  w q = wwhere u q , v q and w q are the displacements of a point q ...