Necking localization under quasi–static uniaxial tension is experimentally observed in
ductile thin-walled cylindrical tubes, made up of soft polypropylene. Necking nucleates in multiple locations of the tube and spreads throughout it, involving also the occurrence of higher–order modes, evidencing trefoil and fourth–foiled (but rarely even fifth–foiled) shaped cross sections. No evidences in other ductile materials of such a complicated necking occurrence and growth were found for thin–walled cylinders under quasi–static loading. With the aim of modelling this phenomenon, as well as all other possible bifurcations, a two–dimensional formulation is introduced, in which only the mean surface of the tube is considered, paralleling the celebrated Flügge’s treatment of axially compressed cylindrical shells. That treatment is extended to include tension and a broad class of nonlinear–hyperplastic constitutive law for the material, which is also assumed to be incompressible. The theoretical framework leads to a number of new results, including closed-form formulae for wrinkling (showing that a direct application of the Flügge equation can be incorrect), for Euler buckling, and for necking. Finally, it is shown that the J2 –deformation theory of plasticity captures multiple necking and occurrence of higher–order modes, so that experiments are explained. The presented results are important for several applications, ranging from aerospace and automotive engineering to the vascular mechanobiology, where a thin–walled tube (for instance an artery, or a catheter, or a stent) may become unstable not only in compression, but also in tension.
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