An action functional for nonlinear dislocation dynamicsMI 03.04.011 (Boltzmannstr. 3, 85748 Garching)

Dislocations are the physical defects whose motion and interaction are responsible for the plasticity of crystalline solids. The physics can be characterized by a system of nonlinear PDE which does not naturally emanate from a variational principle. We describe the development of a family of dual variational principles for this primal system with the property that the Euler-Lagrange system of each of its members is the primal system in a well-defined sense. We illustrate the main idea of the scheme and its viability by applying it to compute approximate solutions to the linear heat, and first-order, scalar wave equations, and 1-d, nonconvex elastostatics.