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.

The concept of a 'deformable arm scale' (completely different from a traditional rigid arm balance) is theoretically introduced and experimentally validated. The idea is not intuitive, but is the result of nonlinear equilibrium kinematics of rods inducing configurational forces, so that deflection of the arms becomes necessary for equilibrium, which would be impossible for a rigid system. In particular, the rigid arms of usual scales are replaced by a flexible elastic lamina, free to slide in a frictionless and inclined sliding sleeve, which can reach a unique equilibrium configuration when two vertical dead loads are applied. Prototypes designed to demonstrate the feasibility of the system show a high accuracy in the measurement of load within a certain range of use. Finally, we show that the presented results are strongly related to snaking of confined beams, with implications for locomotion of serpents, plumbing and smart oil drilling.

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 bifurcation 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.

One edge of an elastic rod is inserted into a friction-less and fitting socket head, whereas the other edge is subjected to a torque, generating a uniform twisting moment. It is theoretically shown and experimentally proved that, although perfectly smooth, the constraint realizes an expulsive axial force on the elastic rod, which amount is independent of the shape of the socket head. The axial force explains why screwdrivers at high torque have the tendency to disengage from screw heads and demonstrates torsional locomotion along a perfectly smooth channel. This new type of locomotion finds direct evidence in the realization of a ‘torsional gun’, capable of transforming torque into propulsive force.

The dynamic behavior of the class of periodic waveguides whose unit cells are generated through a quasicrystalline sequence can be interpreted geometrically in terms of a trace map that embodies the recursive rule obeyed by traces of the transmission matrices. We introduce the concept of canonical quasicrystalline waveguides, for which the orbits predicted by the trace map at specific frequencies, called canonical frequencies, are periodic. In particular, there exists three families of canonical waveguides. The theory reveals that, for those: (i) the frequency spectra are periodic and the periodicity depends on the canonical frequencies, (ii) a set of multiple periodic orbits exists at frequencies that differ from the canonical ones, and (iii) perturbation of the periodic orbit and linearization of the trace map define a scaling parameter, linked to the golden ratio, which governs the self-similar structure of the spectra. The periodicity of the waveguide responses is experimentally verified on finite specimens composed of selected canonical unit cells.