Analysis of efficient homogenization and dynamic impact response of corrugated board considering transverse normal strain

Corrugated paperboard is prone to significant deformation in the thickness direction, and it is this characteristic that endows it with excellent energy-absorbing cushioning performance. However, most existing equivalent homogenization methods for corrugated paperboard are based on plate theories that assume constant thickness, and thus cannot accurately reflect the influence of thickness-direction deformation on the structural mechanical behavior. To overcome this limitation, this paper establishes a novel homogenization approach that can effectively replace the detailed model with complex geometric structures in finite element analysis. The proposed method introduces a displacement field assumption that accounts for thickness deformation, and accordingly derives an improved constitutive formulation. Subsequently, this formulation is numerically implemented via a user-defined element in Abaqus, and the structural maximum displacement response and peak acceleration response are analyzed under various impact loading conditions, with the results compared against those from the full detailed model. The validation results demonstrate that the proposed method can reasonably and accurately characterize the mechanical behavior of corrugated paperboard. Moreover, the analysis element developed based on this homogenization approach not only simplifies the complex pre-processing modeling operations, but also effectively reduces computation time, significantly enhancing modeling and analysis efficiency while maintaining accuracy.