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A dual variational principle for nonlinear dislocation dynamics

Amit Acharya

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.

A dual variational principle for nonlinear 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.
Paper Structure (5 sections, 38 equations)

This paper contains 5 sections, 38 equations.

Table of Contents

  1. Introduction
  2. The essential idea: An optimization problem for an algebraic system of equations
  3. A class of variational principles for nonlinear dislocation mechanics
  4. Linear dislocation mechanics
  5. Dual variational principle for a primal problem with initial and boundary conditions