Alexander revisited—A two folding elements model of progressive crushing of tubes

Abstract A new model of the progressive crushing of circular tubes is developed in which an active zone of plastic deformations contains two folds or buckles. The model captures, with great realism, several features of the crushing process which were unaccounted for in all previous computational models of progressive folding. These include : finite values of the load peaks, alternating heights of the peaks, unequal distances between peaks, reduced crush distance, realistic final shape of crushed tubes and a longer distance between the two first peaks. Closed-form solutions, derived for the length of the plastic folding wave and the mean crushing force, show very good agreement with experimental results. The history of the crushing force is shown to depend on the eccentricity parameter, i.e. on the way the lube material folds with respect to the original tube radius. However, the mean crushing force is found to be independent of the eccentricity parameter.