Gradient flows as a selection criterion for equilibria of non-convex material models.

24 October 2005
17:00
Christoph Ortner
Abstract
For atomistic (and related) material models, global minimization gives the wrong qualitative behaviour; a theory of equilibrium solutions needs to be defined in different terms. In this talk, a process based on gradient flow evolutions is presented, to describe local minimization for simple atomistic models based on the Lennard- Jones potential. As an application, it is shown that an atomistic gradient flow evolution converges to a gradient flow of a continuum energy, as the spacing between the atoms tends to zero. In addition, the convergence of the resulting equilibria is investigated, in the case of both elastic deformation and fracture.
  • Applied Analysis and Mechanics Seminar