The corrugated board packaging industry is increasingly using advanced numerical tools to design and estimate the load capacity of its products. This is why numerical analyses are becoming a common standard in this branch of manufacturing. Such trends cause either the use of advanced computational models that take into account the full 3D geometry of the flat and wavy layers of corrugated board, or the use of homogenization techniques to simplify the numerical model. The article presents theoretical considerations that extend the numerical homogenization technique already presented in our previous work. The proposed here homogenization procedure also takes into account the creasing and/or perforation of corrugated board (i.e., processes that undoubtedly weaken the stiffness and strength of the corrugated board locally). However, it is not always easy to estimate how exactly these processes affect the bending or torsional stiffness. What is known for sure is that the degradation of stiffness depends, among other things, on the type of cut, its shape, the depth of creasing as well as their position or direction in relation to the corrugation direction. The method proposed here can be successfully applied to model smeared degradation in a finite element or to define degraded interface stiffnesses on a crease line or a perforation line.

Bending stiffness (BS) is one of the two most important mechanical parameters of corrugated board. The second is edge crush resistance (ECT). Both are used in many analytical formulas to assess the load capacity of corrugated cardboard packaging. Therefore, the correct determination of bending stiffness is crucial in the design of corrugated board structures. This paper focuses on the analytical determination of BS based on the known parameters of the constituent papers and the geometry of the corrugated layers. The work analyzes in detail the dependence of the bending stiffness of an asymmetric, five-layer corrugated cardboard on the sample arrangement. A specimen bent so that the layers on the lower wave side are compressed has approximately 10% higher stiffness value. This is due to imperfections, which are particularly important in the case of compression of very thin liners. The study showed that imperfection at the level of a few microns causes noticeable drops in bending stiffness. The method has also been validated by means of experimental data from the literature and simple numerical finite element model (FEM). The obtained compliance of the computational model with the experimental model is very satisfactory. The work also included a critical discussion of the already published data and observations of other scientists in the field.

In the modern world, all manufacturers strive for the optimal design of their products. This general trend is recently also observed in the corrugated board packaging industry. Colorful prints on displays, perforations in shelf-ready-packaging and various types of ventilation holes in trays, although extremely important for ergonomic or functional reasons, weaken the strength of the box. To meet the requirements of customers and recipients, packaging manufacturers outdo each other with new ideas for the construction of their products. Often the aesthetic qualities of the product become more important than the attention to maintaining the standards of the load capacity of the packaging (which, apart from their attention-grabbing functions, are also intended to protect transported products). A particular flaps design (both top and bottom) and its influence on the strength of the box are investigated in this study. An updated analytical–numerical approach is used here to predict the strength of packaging with various flap offsets. Experimental results indicated a significant decrease in the static load-bearing capacity of packaging in the case of shifted flap creases. The simulation model proposed in our previous work has been modified and updated to take into account this effect. The results obtained by the model presented in this paper are in satisfactory agreement with the experimental data.

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.

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.