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

TL;DR

This paper introduces and experimentally verifies the concept of Eshelby-like forces in elastic structures, demonstrating their theoretical derivation and measurable effects, which could impact the understanding of deformable mechanisms at various scales.

Contribution

It provides the first experimental proof of Eshelby-like forces acting on elastic structures, supported by theoretical derivation and experimental validation.

Findings

Theoretical derivation of Eshelby-like forces via variational calculus and asymptotic methods.

Experimental measurement of these forces on a custom-designed elastic model.

Potential applications in deformable mechanisms and nanoscale systems.

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 we have 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.