A perturbative method is introduced to analyze shear bands formation and
development in ductile solids subject to large strain.
Experiments on discrete systems made up of highly-deformable elements [1]
confirm the validity of the method and suggest that an elastic structure
can be realized buckling for dead, tensile loads. This structure has been
calculated, realized and tested and provides the first example of an
elastic structure buckling without elements subject to compression [2].
The perturbative method introduced for the analysis of shear bands can be
successfuly employed to investigate other material instabilities, such as
for instance flutter in a frictional, continuum medium [3]. In this
context, an experiment on an elastic structure subject to a frictional
contact shows for the first time that a follower load can be generated
using dry friction and that this load can induce flutter instability [4].
The perturbative approach may be used to investigate the strain state near
a dislocation nucleated in a metal subject to a high stress level [5].
Eshelby forces, similar to those driving dislocations in solids, are
analyzed on elastic structures designed to produce an energy release and
therefore to evidence configurational forces. These structures have been
realized and they have shown unexpected behaviours, which opens new
perspectives in the design of flexible mechanisms, like for instance, the
realization of an elastic deformable scale [6].
[1] D. Bigoni, Nonlinear Solid Mechanics Bifurcation Theory and Material
Instability. Cambridge Univ. Press, 2012, ISBN:9781107025417.
[2] D. Zaccaria, D. Bigoni, G. Noselli and D. Misseroni Structures
buckling under tensile dead load. Proc. Roy. Soc. A, 2011, 467, 1686.
[3] A. Piccolroaz, D. Bigoni, and J.R. Willis, A dynamical interpretation
of flutter instability in a continuous medium. J. Mech. Phys. Solids,
2006, 54, 2391.
[4] D. Bigoni and G. Noselli Experimental evidence of flutter and
divergence instabilities induced by dry friction. J. Mech. Phys.
Solids,2011,59,2208.
[5] L. Argani, D. Bigoni, G. Mishuris Dislocations and inclusions in
prestressed metals. Proc. Roy. Soc. A, 2013, 469, 2154 20120752.
[6] D. Bigoni, F. Bosi, F. Dal Corso and D. Misseroni, Instability of a
penetrating blade. J. Mech. Phys. Solids, 2014, in press.