The main aim of this Special Issue in Materials was to collect interesting and innovative works on the mechanics of corrugated and composite materials ....
Knowing the material properties of individual layers of the corrugated plate structures and the geometry of its cross-section, the effective material parameters of the equivalent plate can be ...calculated. This can be problematic, especially if the transverse shear stiffness is also necessary for the correct description of the equivalent plate performance. In this work, the method proposed by Biancolini is extended to include the possibility of determining, apart from the tensile and flexural stiffnesses, also the transverse shear stiffness of the homogenized corrugated board. The method is based on the strain energy equivalence between the full numerical 3D model of the corrugated board and its Reissner-Mindlin flat plate representation. Shell finite elements were used in this study to accurately reflect the geometry of the corrugated board. In the method presented here, the finite element method is only used to compose the initial global stiffness matrix, which is then condensed and directly used in the homogenization procedure. The stability of the proposed method was tested for different variants of the selected representative volume elements. The obtained results are consistent with other technique already presented in the literature.
In the field of corrugated board production and packaging optimization, the advent of Artificial Intelligence (AI) has initiated a paradigm shift. This paper presents a brief analysis of AI’s role in ...revolutionizing both the production of corrugated board and the design of corrugated packaging. It explores the integration of AI in the homogenization process of complex corrugated board structures into single-layer, shallow shell-based computational models, aiming to improve and accelerate load-bearing calculations. This work presents also how AI’s predictive and analytical capabilities are pivotal in achieving efficiency, sustainability, and cost-effectiveness in the corrugated board industry.
This paper presents analytical methods for estimating the static top-to-bottom compressive strength of simple corrugated packaging, in which the torsional and shear stiffness of corrugated cardboard ...as well as the panel depth-to-width ratio are included. The methods are compared herein with a basic and more detailed buckling description with the successful McKee formula, which is over fifty years old but still widely used among packaging designers and quality control departments. Additionally, the assumptions and applied simplifications used in the literature are analyzed, and the limits of applicability of different versions of the selected methods are checked. Finally, all approaches are verified with the experiment results of various packaging designs made of corrugated cardboard. The results show that, for certain proportions of dimensions of simple flap boxes, simplified methods give an even two times larger estimation error than the analytical approach proposed in the paper. Furthermore, it is evidenced that including all flexural, torsional and shear stiffnesses in the buckling force estimation gives a very precise prediction of the box compressive strength for the full range of package dimensions.
This paper presents mixed analytical/numerical method for estimating the static top-to-bottom compressive strength of corrugated packaging with different ventilation openings and holes, in which the ...torsional and shear stiffness of corrugated cardboard as well as the panel depth-to-width ratio are included. Analytical framework bases on Heimerls assumption with a modification to a critical force, which is here computed by a numerical algorithm. The proposed method is compared herein with the successful McKee formula and is verified with the large number of experiment results of various packaging designs made of different qualities of corrugated cardboard. The results show that, for various hole dimensions or location of openings in no-flap and flap boxes, the estimation error may be reduced up to three times than in the simple analytical approach.
There are many possible sources of potential geometrical inaccuracies in each layer of corrugated board during its manufacture. These include, among others, the processes of wetting the corrugated ...layers during profiling, the process of accelerated drying, the gluing process, and any mechanical impact of the pressure rollers on the cardboard. Work taking into account all the above effects in numerical modeling is not well described in the literature. Therefore, this article presents a simple and practical procedure that allows us to easily account for geometric imperfections in the calculation of the effective stiffness of corrugated board. As a main tool, the numerical homogenization based on the finite element method (FE) was used here. In the proposed procedure, a 3D model of a representative volumetric element (RVE) of a corrugated board is first built. The numerical model can include all kinds of geometrical imperfections and is used to calculate the equivalent tensile and bending stiffnesses. These imperfections were included in the 3D numerical model by appropriate modeling of individual layers, taking into account their distorted shape, which was obtained on the basis of a priori buckling analysis. This paper analyzes different types of buckling in order to find the most representative one. The proposed procedure is easy to implement and fully scalable.
This paper presents a modified analytical formula for estimating the static top-to-bottom compressive strength of corrugated board packaging with different perforations. The analytical framework is ...based here on Heimerl’s assumption with an extension from a single panel to a full box, enhanced with a numerically calculated critical load. In the proposed method, the torsional and shear stiffness of corrugated cardboard, as well as the panel depth-to-width ratio is implemented in the finite element model used for buckling analysis. The new approach is compared with the successful though the simplified McKee formula and is also verified with the experimental results of various packaging designs made of corrugated cardboard. The obtained results indicate that for boxes containing specific perforations, simplified methods give much larger estimation error than the analytical–numerical approach proposed in the article. To the best knowledge of the authors, the influence of the perforations has never been considered before in the analytical or analytical–numerical approach for estimation of the compressive strength of boxes made of corrugated paperboard. The novelty of this paper is to adopt the method presented to include perforation influence on the box compressive strength estimation.
In the present work, an analytical equation describing the plate torsion test taking into account the transverse shear stiffness in sandwich plates is derived and numerically validated. Transverse ...shear becomes an important component if the analyzed plate or shell is thick with respect to the in-plane dimensions and/or its core has significantly lower stiffness than the outer faces. The popular example of such a sandwich plate is a corrugated cardboard, widely used in the packaging industry. The flat layers of a corrugated board are usually made of thicker (stronger) material than that used for the corrugated layer, the role of which is rather to keep the outer layers at a certain distance, to ensure high bending stiffness of the plate. However, the soft core of such a plate usually has a low transverse shear stiffness, which is often not considered in the plate analysis. Such simplification may lead to significant calculation errors. The paper presents the generalization of the Reissner’s analytical formula, which describes the torsional stiffness of the plate sample including two transverse shear stiffnesses. The paper also presents the implementation of the numerical model of the plate torsion test including the transverse shear stiffnesses. Both approaches are compared with each other on a wide range of material parameters and different aspect ratios of the specimen. It has been proved that both analytical and numerical formulations lead to an identical result. Finally, the performance of presented formulations is compared with other numerical models using commercial implementation of various Reissner–Mindlin shell elements and other analytical formulas from the literature. The comparison shows good agreement of presented theory and numerical implementation with other existing approaches.
The methods of separation of microalgae has a significant impact in the economic aspects of their cultivation. In this study, pine bark was used as a substrate for immobilization of microalgal ...biomass cultivated in raw municipal sewage. The experiment was conducted in cylindrical photobioreactors (PBRs) with circulation of wastewater. Biomass was cultivated for 42 days. After that time, abundant growth of the biofilm with microalgae on the surface of pine bark as well as improvement of the quality of treated sewage were observed. The efficiency of removal of nutrients from wastewater was 64-81% for total nitrogen and 97-99% for total phosphorus. Moreover, the concentration of suspended solids in sewage was reduced, which resulted in a decrease in turbidity by more than 90%. Colorimetric analysis and Volatile Matter (VM) content in the substrate showed a decrease in the Higher Heating Value (HHV) and concentration of VM due to the proliferation of biofilm.
In a description of materials for orthotropic panels with a soft and/or corrugated core, it is important to correctly determine all constitutive parameters. In laboratory practice, the determination ...of transverse shear modulus is often overlooked. This paper presents a method for determining this property based on a plate torsion test and a correctly formulated analytical description. It has been proved that the transverse shear effect in some cases cannot be omitted because it significantly influences the mechanical behavior of corrugated board. The method of transverse shear modeling used so far can be modified to eliminate dimensionless, physically unjustified coefficient and replace them with coefficients that have a physical basis. It is shown here that such modification leads to results with lower error. The effective modeling of transverse shear effects enables a more conscious design of corrugated board structures, where the final goal is to obtain packaging with high strength and durability but low material consumption.
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