Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation

Garbowski, Tomasz; Knitter-Piątkowska, Anna; Mrówczyński, Damian

doi:10.3390/ma14143786

Cited by 28 publications

(41 citation statements)

References 32 publications

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“…One cannot forget that there are many factors that diminish the compression strength of corrugated paperboard boxes [59], such as openings, ventilation holes and perforations or indentations [60][61][62][63][64][65], shifted creases on the flaps [66], time and conditions of storage [67,68], and stacking load [47,69,70]. The influence of the box geometry as well as the composition and arrangement of the corrugated board layers on the change of the buckling force, edge crushing (ECT), and the compressive box strength resistance (BCT) are the elements that need to be considered when assessing the load capacity of the box.…”

Section: Introductionmentioning

confidence: 99%

Non-Local Sensitivity Analysis and Numerical Homogenization in Optimal Design of Single-Wall Corrugated Board Packaging

2022

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The optimal selection of the composition of corrugated cardboard dedicated to specific packaging structures is not an easy task. The use of lighter boards saves material, but at the same time increases the risk of not meeting the guaranteed load capacity. Therefore, the answer to the question “in which layer the basis weight of the paper should be increased?” is not simple or obvious. The method proposed here makes it easy to understand which components and to what extent they affect the load-bearing capacity of packages of various dimensions. The use of numerical homogenization allows for a quick transformation of a cardboard sample, i.e., a representative volume element (RVE) into a flat plate structure with effective parameters describing the membrane and bending stiffness. On the other hand, the use of non-local sensitivity analysis makes it possible to find the relationship between the parameters of the paper and the load capacity of the packaging. The analytical procedures presented in our previous studies were used here to determine (1) the edge crush resistance, (2) critical load, and (3) the load capacity of corrugated cardboard packaging. The method proposed here allows for obtaining a comprehensive and hierarchical list of the parameters that play the most important role in the process of optimal packaging design.

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Section: Introductionmentioning

confidence: 99%

Non-Local Sensitivity Analysis and Numerical Homogenization in Optimal Design of Single-Wall Corrugated Board Packaging

2022

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“…In order to validate the results presented in Table 4 , the numerical homogenization procedure (for details see recent works by Garbowski and Gajewski [ 9 ] or Garbowski et al [ 10 ]) of the cross-section of corrugated board BE-650 (see Figure 18 ) was used. The numerical homogenization technique used the geometrical and constitutive parameters presented in Table 1 and Table 2 .…”

Section: Discussionmentioning

confidence: 99%

“…Numerous approaches to sandwich element strength determination, including for corrugated cardboard, can be found in the literature. Analytical methods, starting already in the 1950s, were presented, e.g., in [ 1 , 2 , 3 , 4 , 5 ], whereas numerical methods can be found in [ 6 , 7 , 8 , 9 , 10 , 11 ], and analytical-numerical techniques in [ 12 , 13 , 14 , 15 , 16 ]. Analytical calculations of the edge crush resistance of cellular paperboard, both in MD and CD, based on the paperboard’s geometric parameters and the mechanical properties of the materials used for its production, was discussed by Kmita-Fudalej et al [ 17 ].…”

Section: Introductionmentioning

confidence: 99%

“…In such a case a good solution is to implement a method called homogenization. This approach efficiently allows us to simplify multi-layer models into single-layered model, described by the effective properties of the composite [ 9 , 10 , 20 ]. The application of this technique has the benefits of significant savings in computation time while maintaining the accuracy of the results.…”

Section: Introductionmentioning

confidence: 99%

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New Edge Crush Test Configuration Enhanced with Full-Field Strain Measurements

2021

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The standard edge crush test (ECT) allows the determination of the crushing strength of the corrugated cardboard. Unfortunately, this test cannot be used to estimate the compressive stiffness, which is an equally important parameter. This is because any attempt to determine this parameter using current lab equipment quickly ends in a fiasco. The biggest obstacle is obtaining a reliable measurement of displacements and strains in the corrugated cardboard sample. In this paper, we present a method that not only allows for the reliable identification of the stiffness in the loaded direction of orthotropy in the corrugated board sample, but also the full orthotropic material stiffness matrix. The proposed method uses two samples: (a) traditional, cut crosswise to the wave direction of the corrugated core, and (b) cut at an angle of 45°. Additionally, in both cases, an optical system with digital image correlation (DIC) was used to measure the displacements and strains on the outer surfaces of samples. The use of a non-contact measuring system allowed us to avoid using the measurement of displacements from the crosshead, which is burdened with a large error. Apart from the new experimental configuration, the article also proposes a simple algorithm to quickly characterize all sought stiffness parameters. The obtained results are finally compared with the results obtained in the homogenization procedure of the cross-section of the corrugated board. The results were consistent in both cases.

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“…Most homogenization studies centre on isolated flutings or single-wall corrugated boards, though some of them also consider double-walled corrugated panels [41,94,98,[105][106][107]. Moreover, most of the existing literature on corrugated cardboard models focuses on homogenization methods, with few practical applications in actual designs.…”

Section: Homogenization Techniquesmentioning

confidence: 99%

Efficient Design of Thin Wall Seating Made of a Single Piece of Heavy-Duty Corrugated Cardboard

et al. 2021

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Corrugated cardboard has waved cores with small flutes that prevent the use of detailed numerical models of whole structures. Many homogenization methods in the literature overcome this drawback by defining equivalent homogeneous plates with the same mechanical behaviour at a macro-mechanical scale. However, few homogenization works have considered complete structures, focusing mainly on beams or plates. For the first time, this study explores the application of homogenization approaches to larger structures as an aid in their design process. We also considered triple-wall boards rather than single- and double-wall configurations commonly addressed in the literature. To this end, we adapted the homogenization methods proposed by Talbi and Duong to analyze thin-walled stools made of triple-wall corrugated cardboard. Using a progressive design process, we performed an efficient stool design by removing material zones with lower stresses, with 35% less material, 35% lower vertical deflections, and 66% lower stresses than the initial design. Unlike other corrugated cardboard stools, this design comprises just one folded piece instead of three, thus saving storage space. These results demonstrate the utility of homogenization techniques as an aid in the design process of whole structures made of corrugated cardboard. Further research will consider buckling analysis.

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Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation

Cited by 28 publications

References 32 publications

Non-Local Sensitivity Analysis and Numerical Homogenization in Optimal Design of Single-Wall Corrugated Board Packaging

Non-Local Sensitivity Analysis and Numerical Homogenization in Optimal Design of Single-Wall Corrugated Board Packaging

New Edge Crush Test Configuration Enhanced with Full-Field Strain Measurements

Efficient Design of Thin Wall Seating Made of a Single Piece of Heavy-Duty Corrugated Cardboard

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