An action for nonlinear dislocation dynamics

TL;DR

This paper develops an action functional for nonlinear dislocation dynamics, aiming to bridge continuum mechanics, material science, and effective field theories to better understand plasticity in crystalline solids.

Contribution

It introduces a variational principle for nonlinear dislocation dynamics, connecting physics-based field theories with defect mechanics in solids.

Findings

Established a new action functional for nonlinear dislocation systems

Linked dislocation dynamics with effective field theory and fracton tensor gauge theories

Demonstrated the generality of the variational scheme for nonlinear PDEs

Abstract

An action functional is developed for nonlinear dislocation dynamics. This serves as a first step towards the application of effective field theory in physics to evaluate its potential in obtaining a macroscopic description of dislocation dynamics describing the plasticity of crystalline solids. Connections arise between the continuum mechanics and material science of defects in solids, effective field theory techniques in physics, and fracton tensor gauge theories. The scheme that emerges from this work for generating a variational principle for a nonlinear pde system is general, as is demonstrated by doing so for nonlinear elastostatics involving a stress response function that is not necessarily hyperelastic.