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Passages from discrete to continuous systems allowing for fracture, external forces and heterogeneities

Presented by: 
Anja Schlömerkemper Julius-Maximilians-Universität Würzburg
Date: 
Wednesday 3rd April 2019 - 14:30 to 15:10
Venue: 
INI Seminar Room 2
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.





University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons