This paper proposes a novel approach to represent the geometry of the corrugated board profile during compression by using graphs. Graphs are lighter than images, and the computational time of compression analysis is then significantly reduced compared to using the original image data for the same analysis. The main goal of using such graphs is to gain more knowledge about the mechanical behavior of corrugated boards under compression compared to the current load-deformation curve approach. A node-tracking algorithm is applied to characterize the different phases happening during the compression test in order to predict physical phenomena, including buckling and contact. The main results show that analyzing the nodes provides significant insights into the compression phases, which was not achieved in the current state-of-the-art. The authors believe the object of this research is crucial to better understand the physics of corrugated boards under compression, and it can also be extended to other engineering structures.

Corrugated boards are used for packaging because of their high strength-to-weight ratio, recyclability, and biodegradability. They have an orthotropic sandwich structure with unique characteristics for each direction owing to their flute shape. In this study, the bending behavior was qualitatively analyzed for various variables through an FE-based simulation, and the possibility of an alternative test method for the four-point bending test on a corrugated board was examined through a similarity analysis with the experimental results. The cross-machine direction (CD) bending stiffness through finite element analysis (FEA) simulation was closely related to the thickness of the corrugated board. In AB-flute-double-wall (AB/F-DW), the difference in CD bending stiffness based on the bending direction was approximately 17.2% in the FEA simulation and approximately 10.5% in the experiment. However, the differences in the bending behavior (bending force vs. deflection plot) and bending stiffness based on the phase shift between the two flutes constituting BB-flute-double-wall (BB/F-DW) were insignificant. Overall, the CD bending behavior of the corrugated board was simulated relatively well through FEA simulation. However, it was impossible to simulate the machine-direction (MD) bending behavior through FE-based simulation because of a decrease in convergence and a large error caused by the variability of the contact condition of the modeled test specimen with a non-uniform MD cross-section.

The continuing development of industrialization and increasing population density has led to the emergence of noise as an increasingly common problem, requiring various types of sound absorption and insulation methods to address it. Meanwhile, the recycling of resources to ensure a sustainable future for the planet and mankind is also required. Therefore, this study investigates the potential of corrugated cardboard as a resource for noise reduction. The sound absorption and insulation performance of non-perforated corrugated cardboard (NPCC) were measured, and modified corrugated boards were fabricated by drilling holes either through the surface of the corrugated board alone or through the corrugated board in its entirety. The sound absorption/insulation performance both of perforated corrugated cardboard (PCC), and perforated corrugated cardboard with multi frequency resonators (PCCM) were measured using the transfer function method and the transmission matrix method. To determine the effectiveness of NPCC, PCC, and PCCM in noise reduction, the sound pressure level was analyzed by applying it to a home blender. The results showed PCCM’s sound absorption and insulation performance to be excellent. On the basis of these findings, we propose the use of PMMC as an eco-friendly noise reduction material.

This manuscript critically reviews the design and delivery of spray-dried particles for the achievement of high total lung doses (TLD) with a portable dry powder inhaler. We introduce a new metric termed the product density, which is simply the TLD of a drug divided by the volume of the receptacle it is contained within. The product density is given by the product of three terms: the packing density (the mass of powder divided by the volume of the receptacle), the drug loading (the mass of drug divided by the mass of powder), and the aerosol performance (the TLD divided by the mass of drug). This manuscript discusses strategies for maximizing each of these terms. Spray drying at low drying rates with small amounts of a shell-forming excipient (low Peclet Number) leads to formation of higher density particles with high packing densities. This enables ultrahigh TLD (>100 mg of drug) to be achieved from a single receptacle. Emptying of powder from capsules is directly proportional to the mass of powder in the receptacle, requiring an inhaled volume of about 1 L for fill masses between 40 and 50 mg and up to 3.2 L for a fill mass of 150 mg.

Artificial intelligence is increasingly used in various branches of engineering. In this article, artificial neural networks are used to predict the crush resistance of corrugated packaging. Among the analysed packages were boxes with ventilation openings, packages with perforations, and typical flap boxes, which makes the proposed estimation method very universal. Typical shallow feedforward networks were used, which are perfect for regression problems, mainly when the set of input and output parameters is small, so no complicated architecture or advanced learning techniques are required. The input parameters of the neural networks are selected so as to take into account not only the material used for the production of the packaging, but also the dimensions of the box and the impact of ventilation holes and perforations on the load capacity of individual walls of the packaging. In order to maximize the effectiveness of neural network training process, the group of input parameters was changed so as to eliminate those to which the sensitivity of the model was the lowest. This allowed the selection of the optimal configuration of training pairs for which the estimation error was on the acceptable level. Finally, models of neural networks were selected, for which the training and testing error did not exceed 10%. The demonstrated effectiveness allows to conclude that the proposed set of universal input parameters is suitable for efficient training of a single neural network model capable of predicting the compressive strength of various types of corrugated packaging.

Paper is a material whose mechanical properties are highly dependent on humidity and temperature. Which naturally also builds the relationship between the stiffness and strength of corrugated board and changing weather conditions. In this paper, attention is focused on the dependence of the physical properties of the cardboard on changes in humidity and temperature, which undergo dynamic fluctuations both during the production of corrugated board and during its storage. Two techniques were used to test this effect, namely numerical homogenization and global sensitivity analysis. Both methods were implemented to determine the theoretical relationships between the change in humidity and/or temperature in each layer of corrugated board and its global bending, compression and shear stiffness. The procedure was used to analyze different types of 5-ply and 3-ply cardboard. The obtained results allowed to build a complete map of the relationship between the change in humidity of selected layers and the strength characteristics of the full assembly.

The corrugated board is a versatile and durable material that is widely used in the packaging industry. Its unique structure provides strength and cushioning, while its recyclability and bio-degradability make it an environmentally friendly option. The strength of corrugated board depends on many factors, including the type of individual papers on flat and corrugated layers, the geometry of the flute, temperature, humidity, etc. This paper presents a new approach to analysis geometric features of corrugated boards based on the images. It allows for precise determination of the geometry of the corrugated layer, as well as the thickness of individual papers in all cardboard layers. The experimental set used in the work and the created software are characterized by high reliability and precision of measurement thanks to the use of an identification procedure based on image analysis and evolutionary algorithms. This allows to quickly find the main geometric characteristics of the corrugated board, which in turn leads to the possibility of performing numerical analyzes taking into account the real model of the corrugated board. Calculations made on a real (correctly mapped geometrically) model allow, for example, a more reliable analysis of the composition of the cardboard, and thus also to obtain greater savings in the optimization process.

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 in 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). The particular flaps design (both top and bottom) and their influence on the strength of the box is investigated in this study. The updated analytical-numerical approach is used here to predict the strength of the packaging with various flap’s 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 also this effect. The results obtained by the model presented in the paper are in satisfactory agreement with the experimental data.

The article focuses on derivation of simplified predictive models for identification of overall compressive stiffness and strength of corrugated cardboards. As a representative example an unsymmetrical 5-ply sample (with E and B flute) was used in this study. In order to exclude unreliable displacement measurement in the standard edge crush test, the virtual strain gauges are used. Video extensometry is employed here to collect measurements from the outer surfaces of the sample on both sides. Additional data allows for obtaining real force-displacement curves, which are used in the validation procedure. To emulate the experimental results, beside simple analytical model, also a 3D numerical model fully reflecting the geometry of the corrugated board, based on finite elements method was also built. In both cases a good agreement between the experimental results and the analytical and numerical calculations was observed. This proves that the proposed analytical model can be successfully used to determine the overall stiffness and compressive strength of the corrugated board, provided that the geometry and properties of all the layers of the board are known. The simple model presented in this work enables quick and reliable design and prototyping of new assemblies without the need to manufacture them.

Corrugated board, widely used in the packing industry, is a recyclable and durable material. Its strength and cushioning, influenced by geometry, environmental conditions like humidity and temperature, and paper quality, make it versatile. Double-walled (or five-ply) corrugated board, comprising two flutes and three liners, enhances these properties. This study introduces a novel approach to analyze 5-layered corrugated board, extending a previously published algorithm for single-walled boards. Our method focuses on measuring layer and overall board thickness, flute height, and center lines of each layer. Integrating image processing and genetic algorithms, the research successfully developed an algorithm for precise geometric feature identification of double-walled boards. Images were recorded using a special device with a sophisticated camera and image sensor for detailed corrugated board cross-sections. Demonstrating high accuracy, the method faced limitations only with very deformed or damaged samples. This research contributes significantly to quality control in the packaging industry and paves the way for further automated material analysis using advanced machine learning and image sensors. It emphasizes the importance of sample quality and suggests areas for algorithm refinement to enhance robustness and accuracy.

In the laboratory practice, several standards for testing the bending stiffness of corrugated board are used. There are often cases of tests where the results depend on the way the sample is placed on the supports. The problem arises when the board is five-ply (with two corrugated layers with different corrugation heights) or when the board has asymmetrically selected papers on the flat layers. In this article, we focus our attention on the problem related to boundary conditions, with particular attention to the local effects of the support of the sample. Since the cardboard layers, both flat and corrugated, have a small thickness, a slight deformation of the papers can always be observed at the point of contact between the sample and the support, which affects the readings of the measured stiffness. The paper presents theoretical and numerical analyzes showing how much the method of supporting the sample affects the measured bending stiffness of various samples. Numerical observations were also compared with the results of analyzes presented by other scientists as well as with experimental results.

The article presents a simplified method for determining the strength of a corrugated board packaging subjected to dynamic transport loads. The proposed algorithm consists of several calculation steps: (1) a static analysis of the compressive strength of the package, (2) an analysis of random vibrations in the frequency domain, used to determine the resonance frequencies, and (3) a dynamic analysis of the package loaded with computed resonant frequencies. For this purpose, numerical models of the static compression test of the packaging before and after the dynamic analysis of the package subjected to general transport loads were developed. In order to validate the model, the laboratory packaging compression tests were also performed for samples of boxes with 3-layer cardboard. Thanks to this, it was possible to verify the results of numerical simulations of compression tests for several box geometries. Which, in turn, allowed for the development of a method based on dynamic and post-dynamic (static) numerical analysis, allowing to determine with high accuracy the resistance of selected packaging to vibrations and dynamic loads. The results of the (validated experimentally) numerical analysis prove the usefulness of the simplified method presented here for precise estimation of the load capacity of various packages dynamically loaded during transport.

The shield tunnels inevitably endure various damage with the service time increasing. Meanwhile, steel corrugated plate has been used extensively in multiple conditions and proved effective to strengthen the segmental joints by full-scale tests. A numerical model is proposed to probe the feasibility of using new Stainless Steel Corrugated Plate (SSCP) to reinforce the shield tunnel segments. A new method, called virtual tracking element technology, is employed to achieve the simulation of realistic stress state of the segmental joint. Moreover, the segmental joint component analysis and parametric study are conducted based on the numerical model. The results demonstrate that: (1) the virtual tracking element technology proves valid and efficient to simulate the secondary stress state of segmental joint; (2) SSCP reinforcement is not fully utilized when the grade of segmental concrete is C50 and it has abundant safety margin for potential overload; (3) SSCP reinforcement is well-performed regardless of the burial depth and reinforcement in advance is recommended.

The corrugated board packaging industry is increasingly using advanced numerical tools to design and estimate the load capacity of its products. That is why numerical analyzes are becoming a common standard in this branch of manufacturing. Such trend causes 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.

Corrugated cardboard is an ecological material, mainly because, in addition to virgin cellulose fibers also the fibers recovered during recycling process are used in its production. However, the use of recycled fibers causes slight deterioration of the mechanical properties of the corrugated board. In addition, converting processes such as printing, die-cutting, lamination, etc. cause micro-damage in the corrugated cardboard layers. In this work, the focus is precisely on the crushing of corrugated cardboard. A series of laboratory experiments were conducted, in which the different types of single-walled corrugated cardboards were pressed in a fully controlled manner to check the impact of the crush on the basic material parameters. The amount of crushing (with a precision of 10 micrometers) was controlled by a precise FEMat device, for crushing the corrugated board in the range from 10 to 70 % of its original thickness. In this study, the influence of crushing on bending, twisting and shear stiffness as well as a residual thickness and edge crush resistance of corrugated board was investigated. Then, a procedure based on a numerical homogenization, taking into account a partial delamination in the corrugated layers to determine the degraded material stiffness was proposed. Finally, using the empirical-numerical method, a simplified calculation model of corrugated cardboard was derived, which satisfactorily reflects the experimental results.

Corrugated board is a composite material characterized by strong orthotropy in both the elastic and plastic phases. Additionally, due to its layered structure, which consists of alternately arranged flat and wavy layers of paper, its mechanics becomes complicated. Therefore, a precisely selected set of laboratory tests is needed to correctly identify all the necessary material parameters of cardboard. The work attempts to define a full set of laboratory tests in order to determine material parameters describing the linear-elastic, orthotropic behavior of cardboard and the basic parameters defining popular plasticity criteria, such as the asymmetric orthotropic Hoffman criterion. For this purpose, sensitivity analysis and numerical models of several selected basic laboratory tests were used. Since the aim of the work is to choose appropriate laboratory tests necessary to correctly determine the material parameters of corrugated board (not its individual layers), the numerical models do not contain detailed cardboard geometry, but only its homogenized representation in the form of the flat shell models. All numerical models are based on the nonlinear finite element method and constitutive modelling in the form of UMAT subroutines implemented in the ABAQUS software. Based on the analyses, appropriate measurements and laboratory tests were indicated that are most sensitive to the material parameters sought.

The standard edge crush test (ECT) allows to determine the crushing strength of the corrugated cardboard. Unfortunately, this test cannot be used to estimate the compressive stiffness, which is an equally important parameter. It 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 to reliably identify 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 degrees. Additionally, in both cases, an optical system with digital image correlation (DIC) is used to measure the displacements and strains on the outer surface of samples. The use of a non-contact measuring system allows 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.

As long as the non-contact digital printing is not a common standard in the corrugated packaging industry, corrugated board crushing is a real issue that affects the load capacity of the boxes. Crushing mainly occurs during the converting of corrugated board (e.g. analog flexographic printing or laminating) and is a process that cannot be avoided. However, as show in this study, it can be controlled. In this work, extended laboratory tests were carried out on the crushing of double-walled corrugated board. The influence of fully controlled crushing (with a precision: ±10 μm) in the range from 10 to 70 % on different laboratory measurements was checked. Most of the typical mechanical tests were performed e.g. edge crush test, four-point bending test, shear stiffness test, torsional stiffness test, etc. on reference and crushed specimens. The residual thickness reduction of the crushed samples was also controlled. All empirical observations and performed measurements were the basis for building an analytical model of crushed corrugated board. The proven and verified model was then used to study the crushing effect of the selected corrugated board on the efficiency of simple packages with various dimensions.

Single-layer core corrugated sandwich panels generally consist of a corrugated core and two layers of panels, while multi-layer core corrugated sandwich panels are formed by stacking multiple layers of panels with multiple layers of core layers. In this study, integrated multilayer core corrugated sandwich panels with different shapes of corrugated cores (triangular, trapezoidal, and rectangular) and the different number of core layers were fabricated using 3D printing technology, and the mechanical behavior of such multilayer core corrugated sandwich panels under quasi-static three-point bending was investigated using experiments and numerical simulations. The effects of core shape and number of core layers on the bending deformation process, damage mode, load carrying capacity, and bending energy dissipation capacity of multilayer core sandwich panels are discussed. Parametric design of multilayer triangular core corrugated sandwich panels was also carried out by finite element software ABAQUS. It was found that a new multilayer corrugated sandwich panel with a multi-layer core is better than the single core shape multilayer corrugated sandwich panel in terms of bending load capacity, energy dissipation capacity and deformation capacity can be obtained through the combination design of different core shapes.

Abstract: In this study, a computational fluid dynamics (CFD) simulation was conducted to validate the CFD model with experimental data from Zimparov et.al (2012), which investigates the heat transfer performance in a spirally corrugated tube that has a twisted tape inserted. The heat transfer was then compared to a simple corrugated tube without the twisted tape and to a smooth tube with no corrugations and no twisted tape. This simulation is compared with a previous experimental study conducted by (Zimparov et al. 2012), which focuses on tubes with a height-to-diameter ratio e/Di > 0.04 and small relative pitches of the twisted tape, H/Di. The largest improvement was noticed in the tube with e/Di= 0.057 and ridge pitch-to-height ratio p/e=6.77 with a twisted tape of H/Di= 4.7. This tube is labeled 5035. Tube 5035 was found to have the most significant enhancement, hence the focus of the CFD simulation will be on this tube, and the simulation will range for Reynolds numbers, 3.5 x 103 < Re < 5.0 x 104. The focus of this simulation is the evaluation of heat transfer and friction factors; a metric was used to obtain an empirical representation of the tube’s performance. Keywords: Spirally corrugated tube; Twisted tape; Heat transfer enhancement; Friction factor; Nusselt number; Computational fluid dynamics (CFD); Star CCM+

The dynamic behaviour of a machine tool (MT) directly influences the machining performances. The adoption of lightweight structures may reduce the effects of undesired vibrations and increasing the workpiece quality. This paper aims to present and compare a set of hybrid materials that may be excellent candidate to fabricate the MT moving parts. The selected materials have high dynamic characteristics and capacity to damp mechanical vibrations. In this way, starting by the kinematic model of a milling machine that highlights the main critical factors, this study paper evaluates a number of prototypes made of Al Foam sandwiches (AFS), Al Corrugated sandwiches (ACS) and materials reinforced by carbon fibres (CFRP). A set of prototypes has been fabricated, represented the Z-axis ram of a commercial milling machine. The static and dynamical properties have been evaluated by using both FE simulations and experimental tests. The obtained results show that the proposed structures may be a valid alternative to the conventional materials of MT moving parts, increasing machining performances. In particular, the AFS prototype highlighted a damping coefficient that is 20 times greater than a conventional ram (e.g. steel). The CFRP structure is able to satisfy the machining requirements with a reduced weight of 48.5%, while the ACS prototype showed a good trade-off between stiffness and damping.