Adaptable materials via retraining

Abstract

Elastic metamaterials are often designed for a single permanent function. We explore the possibility of altering a material's function repeatedly through a self-organization, "training" process, controlled by applied strains. We show that the elastic function can be altered numerous times, though each new trained task imprints a memory. This ultimately leads to material degradation through the gradual reduction of the frequency gap in the density of states. We also show that retraining adapts previously trained low energy modes to a new function. As a result consecutive trained responses are realized similarly. We show how retraining can be exploited to attain a response that would otherwise be difficult.

Loss of material trainability through an unusual transition

“…Therefore to realize a given response one must train the system until the stiffness along the valley falls below the stiffness of all remaining modes. A similar scenario has been suggested when a material is retrained over and over [29].…”

“…We find a substantial increase in the low frequency spectrum as complexity is increased. The trained response can be associated with a single low frequency mode that is separated from the remaining of the spectrum [29]. Here, failure is accompanied with a proliferation of low frequency modes that presumably compete with the desired response.…”

“…To this end, we compute the Hessian, H, defined by the matrix of second derivatives, and diagonalize it to find its spectrum. Previously it was found, that training creates a single low energy modes separated from the remaining of the spectrum [29].…”

“…With increased difficulty, there is also an increase in degradation, marked by the enhanced low frequency spectrum. This could affect robustness of the response as well as the number of times the system can be retrained [29]. It is interesting to ask how universal this type of transition is, and whether it applies to other forms of training.…”

The Physical Effects of Learning

“…Some folded proteins, often modeled as mechanical networks [29,30], have evolved allosteric function, where binding of a regulatory molecule at a "source" site triggers a conformational change in the protein that either enables or inhibits binding of another molecule at a distant "target" site. Model networks, as well as networks derived from folded proteins, that display allosteric behavior have been shown to exhibit low-dimensional responses to strains applied at the source [31][32][33][34][35][36][37][38][39][40]. In particular, the allosteric response is well-captured by lowenergy (soft) normal modes of vibration [36,37,41,42].…”