Comparison of Postbuckling Model and Finite Element Model with Compression Strength of Corrugated Boxes

Conventional compression strength formulas for corrugated fiberboard boxes are limited to geometry and material that produce an elastic postbuckling failure. Inelastic postbuckling can occur in squatty boxes and trays, but a mechanistic rationale for unifying observed strength data is lacking. This study employs a finite element model, instead of actual experiments, to generate experimentally designed data and a smoothed model. Results lead to a better understanding of how to unify elastic and inelastic failure data and form a more general box strength formula. The objective of this study is to determine if the postbuckling formula advocated in a previous review of some historical data on box compression, including subsets of elastic and inelastic buckling, is supported by more pertinent experiments and can thus constitute a mechanistically rational more general box compression formula. The review revealed that a combination of elastic and inelastic postbuckling theory can be universally applied to the data, with different constants for each data source, provided that nonlinear material characterization is introduced and that an empirical correction is applied to panel stiffness. Thorough experimental replication and inclusion of all geometry and material variables would be prohibitively expensive. Therefire, our approach is to numerically generate postbuckling data with finite element analysis (FEA) of buckling stress and then apply the previous formula. We it makes some sense to terminate the analysis with the FEA predictions, having a simpler, yet mechanistic, strength formula can provide the basis for actual experimental confirmation and practitioner use. Various smoothed models were fit to the finite element predictions. An empirical correction for panel stiffness input to a broadened form of an elastic-inelastic postbuckling model gave the best results. The finite element predictions corroborate previous experiments, and results are applicable to box geometry beyond the range of what has previously been investigated. Objective and Scope The objective of this study is to determine if the postbuckling formula advocated in previous work (Urbanik 1996) for combined elastic and inelastic failure is supported by more pertinent experiments and can thus constitute a mechanistically rational basis for a more general box compression formula. In the previous study (Urbanik 1996), the best model of box strength was obtained with each panel characterized by the following two-part formula: