Numerical Homogenization of Single-Walled Corrugated Board with Imperfections

Numerical homogenization is an excellent tool for the quick simplification of complex structures with a model that is much simpler and, at the same time, accurately reflects the mechanical behavior of the original model. Corrugated cardboard modeling, with all geometrical nuances preserved, is a complicated and time-consuming process. The transfer of a full 3D model of corrugated board composed of two flat layers and a corrugated middle layer to one layer only, with substitute elastic parameters, greatly simplifies this process. Because the individual layers of corrugated cardboard are made of paper with a grammage in the range of 80–200 g/m2, i.e., very thin plates, they are slightly buckled even in the initial configuration. These imperfections affect the equivalent parameters that are obtained in the homogenization process. This paper presents an approach of taking into account these imperfections when creating a simplified model. The numerical homogenization method based on the equivalence of elastic energy between a representative volumetric element (i.e., a part of a full 3D model) and an equivalent plate were applied. Different shapes of imperfections were analyzed in order to account for the buckling modes, notably for a specific unit deformation and curvature. Finally, one form of initial imperfections was proposed, which most accurately reflects the decrease in all plate stiffnesses.