The large strain snap-through effect in free torsion of highly elastic soft thin-walled tubes with exact closed-form solutions

It is found for the first time that, as the applied torque attains a critical value, a freely twisted highly elastic tube may jump from one to another state over large strain range. Unlike usual approximate buckling analyses of thin shell structures with Hooke’s law for small strain, such large strain snap-through effect needs to be studied with a large strain model that can accurately simulate nonlinear elastic behaviors of soft materials. As such, nonlinear coupling issues have to be treated both in large strain kinematics and in hyper-elastic constitutive formulation.It appears that exact results would be rare even for buckling analyses with small strain but large deflections. Here, the above coupling issues are treated with a novel and decoupled approach. To this end, explicit and decoupled forms of the dual potentials for hyper-elastic stress–strain and strain-stress relationships are constructed with well-designed invariants of the Hencky strain and the deviatoric Cauchy stress and, hence, multiple data sets from benchmark tests are accurately matched with these forms in a decoupled sense. It is then shown that the nonlinear coupling equations for large torsion of elastic thin tubes can be worked out to produce exact closed-form solutions for the average radius ratio, the axial length ratio and the thickness ratio as well as the applied torque. With these solutions, the large strain snap-through effect is disclosed with an explicit criterion. Furthermore, numerical examples are provided with comparison to test data and, in particular, the large torsion response features with the snap-through effect are discussed with reference to possible correlations to certain symptoms in vascular abnormalities of blood vessels, etc.