Folded states of thin walled tubes as energy minimizers

Buckling deformations of hollow cylinders whose buckled configurations consist of inextensional deformations (folding) of their middle surface can be described as minimal states in a free gradient discontinuity problem. In the contribution this general idea is applied to a far simpler context namely the case in which the shape of the folding pattern is somehow known, that is depends on a small number of discrete or continuous parameters. The example we consider is the axial compression of a tube of rectangular hollow section. If the tube is short and thin, in a sense that can be made precise in terms of the ratio between the yield stress and the Young modulus of the material, it exhibits local buckling in the form of a rather typical pattern controlled by at most three parameters. Such parameters are identified by minimizing the total potential energy and the results are compared with test results for aluminum alloy specimens