Eshelby-like forces acting on elastic structures: Theoretical and experimental proof

Abstract

The Eshelbian (or configurational) force is the main concept of a celebrated theoretical framework associated with the motion of dislocations and, more in general, defects in solids. In a similar vein, in an elastic structure where a (smooth and bilateral) constraint can move and release energy, a force driving the configuration is generated, which therefore is called by analogy 'Eshelby-like' or 'configurational'. This force (generated by a specific movable constraint) is derived both via variational calculus and, independently, through an asymptotic approach. Its action on the elastic structure is counterintuitive, but is fully substantiated and experimentally measured on a model structure that has been designed, realized and tested. These findings open a totally new perspective in the mechanics of deformable mechanisms, with possible broad applications, even at the nanoscale.

Serpentine locomotion through elastic energy release

“…These counter-intuitive reactions are strictly related to the deformability of the constrained rod and to the non-rectilinearity of the channel and have been found in other ‘non-classical’ situations [26,28,31]. …”

Chain paradoxes

“…15 Problem (b) is perhaps the most controversial of the three considered here. If, as we learned above, Love [30, p. 261] assumed that the chain's arm with a free end falls freely, 16 Hamel [39, 12 The tension is indeed an important player in the dynamics of chains, at least as important as the equation of motion, especially at the points where it is discontinuous. These latter are admirably described by Love [30, p. 259]: 'It often happens that two parts of a chain move in different ways and that portions of the chain are continually transferred from the part that is moving in one way to the part that is moving in the other way.…”

New phenomena in nonlinear elastic structures: from tensile buckling to configurational forces

“…Following Bigoni et al (2015), an inextensible elastic rod (straight in its unloaded configuration, with bending stiffness B and total lengthl) is considered now in a more general setting. In particular, the rod is constrained Figure 30.…”

“…so that the axial force S at the end of the sliding sleeve (which has been experimentally measured through a load cell by Bigoni et al (2015)) is given by…”

“…'Expulsion' of the elastic rod is consequent to a value of the Eshelby-like force exceeding the axial component of P , namely, P cos α. Quantitative experiments are reported in Bigoni et al (2015), whereas movies of the experiments can be found at http://ssmg.unitn.it/eshelbylikeforce.html. The purpose is now to analyze the effects of Eshelby-like force on bifurcation and instability of structures.…”