An action for nonlinear dislocation dynamics

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.