Effect of stress-softening on the ballooning motion of hyperelastic strings

This work concerns nonlinear dynamic response of a stress-softened neo-Hookean rubber cord fixed at one boundary and undergoing constant speed circular motion at the other giving rise to ballooning motions. The steady state results are compared with that for the elastic string. The effect of material nonlinearity shows difference in these results for the single loop balloon even though the stretching deformation is not significantly high. This difference grows if the speed of rotation is increased further. Linear stability analysis shows that the single loop balloons are always stable, whereas, the stability of multi-loop balloons depends on the maximum preconditioning stretch. In usual case, one and half loop balloons are divergent unstable. Flutter instability of two loop balloons are also observed. It is shown that for certain precondition stretch, one and half loop and two loop balloons can be made completely stable. This result is in contrast to that of a linear elastic string. Thus preconditioned stretch of the rubber cord serves as a passive control parameter for stabilization of multi-loop balloons. Finally, experiments are conducted for both virgin and stress-softened rubber cords to verify the steady state and the stability results. (C) 2015 Elsevier Ltd. All rights reserved.