Oscillating elastic defects: competition and frustration

TL;DR

This paper explores how oscillating elastic defects influence strain localization, defect interactions, and pattern formation, revealing frequency-dependent behaviors and mappings to spin models that impact material frustration and transitions.

Contribution

It introduces a dynamical model of elastic defects showing frequency-dependent localization and maps defect interactions to XY spin-like models, highlighting new insights into frustration and pattern transitions.

Findings

Higher oscillation frequency leads to more localized strain fields.

Defect interactions vary from ferromagnetic to antiferromagnetic with separation and frequency.

Assemblies of defects can be modeled as XY spin systems, affecting frustration and patterns.

Abstract

We consider a dynamical generalization of the Eshelby problem: the strain profile due to an inclusion or "defect" in an isotropic elastic medium. We show that the higher the oscillation frequency of the defect, the more localized is the strain field around the defect. We then demonstrate that the qualitative nature of the interaction between two defects is strongly dependent on separation, frequency and direction, changing from "ferromagnetic" to "antiferromagnetic" like behavior. We generalize to a finite density of defects and show that the interactions in assemblies of defects can be mapped to XY spin-like models, and describe implications for frustration and frequency-driven pattern transitions.