Abstract

Passages from discrete to continuous systems of particles have been the subject of research with various approaches for many years. Here we focus on one-dimensional particle systems with non-convex interaction potentials, which allow for the formation of cracks. We consider variational models and their continuum limits by means of $\Gamma$-convergence techniques.

Firstly, I will present the main ideas of a recent work with M._{Carioni and J.}Fischer which allows for external forces that may depend on the material points or on the deformed configuration, i.e._{on Lagrangian or Eulerian coordinates, and thus may be related to dead as well as live loads. Secondly, I will show homogenization results for composite materials that are modelled by either periodically or stochastically distributed non-convex interaction potentials. This is joint work with 
L.}Lauerbach, S._{Neukamm and M.}Schäffner.