Gradient flows as a selection procedure for equilibria of nonconvex energies

Journal article

For atomistic material models, global minimization gives the wrong qualitative behavior; a theory of equilibrium solutions needs to be defined in different terms. In this paper, a concept based on gradient flow evolutions, to describe local minimization for simple atomistic models based on the Lennard-Jones potential, is presented. As an application of this technique, 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 elastic deformation and a simple damaged state. © 2006 Society for Industrial and Applied Mathematics.

Authors: Ortner, C

• Publication status: Published
• Journal: SIAM JOURNAL ON MATHEMATICAL ANALYSIS
• Volume: 38
• Issue: 4
• Pages: 1214-1234
• Publication date: 2006-01-01
• DOI: 10.1137/050643982
• EISSN: 1095-7154
• ISSN: 0036-1410
• Language: English
• Keywords: gradient flows; continuum limit; atomistic models; lambda-convexity