Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation

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