Analytic Simulations of Packaging Cardboards with Non-Rigid Adhesives

Abstract

The understanding of the cardboard performance is necessary to the design of packaging containers and the protection of their contents for safe deliveries. The use of adhesives is unavoidable in the manufacturing of the cardboards. Like all materials, the adhesives have finite stiffness but when used in the literature, they are assumed perfectly rigid. This study changes this assumption by using the real properties of adhesives. A closed-form solution for cardboard panelsassembled withnon-rigid adhesives, and subjected to edgewise loading is presented. The solution satisfies the equilibrium equations of the layers, the compatibility equations of stresses and strains at the interfaces, and the boundary conditions. To investigate the effects of the finite values of adhesivestiffness on the responses, numerical evaluations are conducted. The results obtained have shown that the adhesive stiffness has a strong effect on the performance. Beyond a certain level of stiffness, the usual assumption of perfect bonding used in classical theories is acceptable. This could provide an answer to what constitutes perfect bonding in terms of the ratio of the fluted layer, or simply flute, stiffness to the bonding stiffness.