Incorporating Transverse Normal Strain in the Homogenization of Corrugated Cardboards

Homogenization researches for corrugated cardboard are predominantly based on plate theories assuming constant thickness, such as the Reissner–Mindlin plate. However, corrugated cardboard is prone to significant deformation in the thickness direction. To address this limitation, the present work proposes an improved plate element designed by expanding the deflection function to the quadratic term of the thickness coordinate, enabling a linearly varied transverse normal strain. Furthermore, an extension of the established homogenization method is developed to derive the constitutive matrix. The element is implemented via the Abaqus user subroutine UEL. Validation demonstrates that the proposed element effectively characterizes a linearly varied transverse normal strain and stress. Simulation results from the homogenized model applying the proposed element and extended homogenization method are compared with those from detailed models. The comparisons confirm the efficiency and accuracy of the proposed approach.