In the transportation and distribution of goods, cardboard boxes are often subjected to mechanical impacts such as shocks and random vibrations, which can cause damage to the goods. In this study, static and dynamic tests on cardboard boxes were designed and conducted to determine the compression strength, natural frequencies, and modal characteristics of the boxes. A finite element model of cardboard boxes considering the in-plane orthotropic elastic–plastic behavior of the cardboard was implemented in the Abaqus software through a VUMAT subroutine to perform numerical simulations under compression and random vibrations. The parameters of the model were determined through an inverse identification process. As a first result, the predicted force–displacement curves show good agreement with the measured curves. Furthermore, the power spectral density (PSD) response of the mass/box system under random vibrations obtained through numerical simulations is consistent with the responses obtained from experimental measurements.

In the transportation and distribution of goods, cardboard boxes are often subjected to mechanical impacts such as shocks and random vibrations, which can cause damage to the goods. Many studies have focused on the durability of corrugated cardboard boxes. However, there is very limited research on compact cardboard boxes, especially in the case of exposure to random vibrations. In this study, static and dynamic tests on cardboard boxes were designed and conducted to determine compression strength, natural frequencies, and modal characteristics of the boxes. Subsequently, a finite element model of cardboard boxes taking into account the effects of the box manufacturing process on the mechanical properties of the cardboard, was developed to perform numerical simulations under compression and random vibrations. In this context, the in-plane orthotropic elastic-plastic behavior model of rigid cardboard was implemented in the Abaqus software through a VUMAT subroutine. Additionally, the parameters of the model were determined through an inverse identification process. Finally, numerical simulations of compression and random vibration tests were carried out to validate the experimental results. The comparison results show that the power spectral density (PSD) response of the mass/box system under random vibrations obtained through numerical simulations is consistent with the responses obtained from experimental measurements. Furthermore, the predicted force-displacement curves demonstrate good agreement with the measured curves.

The study aims to build an equivalent 2D model as an alternative to the 3D model of sandwich panel structures. This model enables for reducing model building time and calculation time in the design calculation of this sandwich structure. The research object in this study is corrugated core cardboard. First, the isotropic plasticity equivalent (IPE) model for the paper material is implemented in the Abaqus software, using the VUMAT user subroutine. Subsequently, the homogenization method is proposed as an equivalent elastic-plastic finite element model. This model is implemented in Abaqus using the UGENS subroutine. Finally, numerical simulations of different load cases between the 3D model and the equivalent 2D model are performed to confirm the accuracy of the proposed model. The comparison results indicate that the equivalent model ensures exceptional accuracy compared to the 3D model but significantly reduces model building time and CPU time.