Sectional homogenization with a general nonlinear constitutive law for corrugated board analysis

Corrugated board is widely used in packaging applications due to its favorable mechanical properties and cost-effectiveness. This study proposes a two-step, multiscale, sectional homogenization approach to determine the effective elastic parameters and predict the mechanical behavior of cardboard under various loading conditions. In the first step, a representative 3D periodic model of corrugated board is developed to extract its effective elastic properties. This homogenization process reduces the complex 3D structure to a simplified 2D shell model. The second step focuses on computing deformations, strains, and stresses in cardboard structures. Instead of using a conventional plastic constitutive model, the 3D Representative Volume Element (RVE) model is employed. Strains from the 2D model are applied as boundary conditions to the 3D RVE, where corresponding stresses are determined based on pre-calibrated strain-stress relationships obtained from uniaxial tests. Stiffness degradation is captured, from a computational viewpoint, at Gauss points in the 2D model. The results demonstrate that the proposed approach accurately reproduces the real mechanical behavior of cardboard while utilizing a simplified 2D model.