Instability of a penetrating blade

Application of a dead compressive load at the free end of an elastic rod (the ‘blade’) induces its penetration into a sliding sleeve ending with a linear elastic spring. Bifurcation and stability analysis of this simple elastic system shows a variety of unexpected behaviours: (i.) an increase of buckling load at decreasing of elastic stiffness; (ii.) a finite number of buckling loads for a system with infinite degrees of freedom (leading to a non-standard Sturm-Liouville problem); (iii.) more than one bifurcation loads associated to each bifurcatio mode; (iv.) a restabilization of the straight configuration after the second bifurcation load associated to the first instability mode; (v.) the presence of an Eshelby-like (or configurational) force, deeply influencing stability. Only the first of these behaviours was previously known, the second and third ones disprove common beliefs, the fourth highlights a sort of ‘island of instability’, and the last one shows surprising phenomena and effects on stability.



Related papers:

• Bigoni, D., Bosi, F., Dal Corso, F. and Misseroni, D. (2014).
  Instability of a penetrating blade.
  Journal of the Mechanics and Physics of Solids, 64, 411-425.
  doi: http://dx.doi.org/10.1016/j.jmps.2013.12.008

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