A dual variational principle for nonlinear dislocation dynamics

TL;DR

This paper introduces a dual variational principle for modeling the complex nonlinear PDEs governing dislocation dynamics in elastic solids, providing a new theoretical framework for understanding these phenomena.

Contribution

It develops a novel dual variational principle applicable to nonlinear dislocation PDEs, including initial and boundary conditions, advancing the theoretical tools for dislocation modeling.

Findings

Formulation of a dual variational principle for nonlinear dislocation PDEs

Extension to include initial and boundary conditions

Provides a new theoretical approach for dislocation dynamics

Abstract

A dual variational principle is defined for the nonlinear system of PDE describing the dynamics of dislocations in elastic solids. The dual variational principle accounting for a specified set of initial and boundary conditions for a general class of PDE is also developed.