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.

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.

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.

To measure the sensitivity and specificity of differences cut-off values for isokinetic H_con/Q_con ratio in order to improve the capacity to evaluate (retrospectively) the injury of hamstring muscles in professional soccer screened with knee isokinetic tests. Retrospective study. Medical and biomechanical data of professional football players playing for the same team for at least one season between 2010 and 2016 were analysed. Hamstring strain injury cases and the reports generated via isokinetic testing were investigated. Isokinetic concentric(con) hamstring(H) and quadriceps(Q) absolute strength in addition with H_con/Q_con ratio were examined for the injured versus uninjured limbs among injured players, and for the injured and non-injured players. 2 x 2 contingency table was used for comparing variables: predicted injured or predicted uninjured with actual injured or actual uninjured. Sensitivity, specificity, accuracy, positive and negative predictive values, and positive and negative likelihood ratio were calculated for three different cut-off values (0.47 vs. 0.6 vs. 0.658) to compare the discriminative power of an isokinetic test, whilst examining the key value of H_con/Q_con ratio which may indicate the highest level of ability to predispose a player to injury. McNemar’s chi² test with Yates’s correction was used to determine agreement between the tests. PQStat software was used for all statistical analysis, and an alpha level of p <0.05 was used for all statistical comparisons. 340 isokinetic test reports on both limbs of 66 professional soccer players were analysed. Eleven players suffered hamstring injuries during the analysed period. None of these players sustained recurrence of hamstring injury. One player sustained hamstring strain injury on both legs, thus the total number of injuries was 12. Application of different cut-off values for H_con/Q_con significantly affected the sensitivity and specificity of isokinetic test used as a tool for muscle injury detection. The use of 0.47 of H_con/Q_con as a discriminate value resulted in significantly lower sensitivity when compared to 0.658 threshold (sensitivity of 16.7% vs. 91.7%, respectively; t = 6.125,p = 0.0133). Calculated values of specificity (when three different cut-off were applied) were also significantly different. Threshold of 0.6 of H_con/Q_con resulted with significantly lower specificity compared to 0.47 value (specificity of 46.9% vs. 94.5%, respectively; t = 153.0,p<0.0001), and significantly higher specificity when compared to 0.658 (specificity of 46.9% vs. 24.1%, respectively; t = 229.0, p<0.0001). The use of different cut-off values for H_con/Q_con significantly affected the sensitivity and specificity of isokinetic testing. The interpretation of usefulness of isokinetic test as a screening tool in a group of male professional football players to predict hamstring injury occurrence within the next 12 months might be therefore significantly biased due to the different threshold values of H_con/Q_con. Using one “normative” value as a cut-off (e.g. 0.47 or 0.60, or 0.658) to quantify soccer players (or not) to the group with a higher risk of knee injury might result in biased outcomes due to the natural strength asymmetry that is observed within the group of soccer players.

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.