Foam-Filled Grooved Tubes with Circular Cross-Section Under Axial Compression: A Theoretical Analysis

In this article, some theoretical relations are derived to predict the instantaneous folding force and the absorbed energy by the empty and polyurethane foam-filled grooved tubes with circular cross-section during the first fold formation under the axial loading. Five different modes of deformation are considered in the theoretical model of deformation: bending around two internal circular hinge lines, bending around an external circular hinge line, extensional deformation in the folding arms, axial compression of the polyurethane foam, and interaction effects between polyurethane foam and inner wall of the grooved tube. Also, based on the experiments, a semi-empirical relation is suggested to predict the effective axial displacement at the end of a complete fold creation in the polyurethane foam-filled grooved tubes. To verify the theoretical analyses, some axial compression tests were carried out on the empty and filled grooved tubes. Comparison of the theoretical predictions with the corresponding experimental results showed a good correlation.