@article{LauerbachNeukammSchaeffneretal.2019,
  author    = {Lauerbach, Laura and Neukamm, Stefan and Sch{\"a}ffner, Mathias and Schl{\"o}merkemper, Anja},
  title     = {Continuum Limit and Homogenization of Stochastic and Periodic Discrete Systems - Fracture in Composite Materials},
  series = {Proceedings in Applied Mathematics \& Mechanics},
  volume    = {19},
  journal   = {Proceedings in Applied Mathematics \& Mechanics},
  number    = {1},
  doi       = {10.1002/pamm.201900070},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-211835},
  pages     = {e201900070},
  year      = {2019},
  abstract  = {The limiting behaviour of a one-dimensional discrete system is studied by means of Γ-convergence. We consider a toy model of a chain of atoms. The interaction potentials are of Lennard-Jones type and periodically or stochastically distributed. The energy of the system is considered in the discrete to continuum limit, i.e. as the number of atoms tends to infinity. During that limit, a homogenization process takes place. The limiting functional is discussed, especially with regard to fracture. Secondly, we consider a rescaled version of the problem, which yields a limiting energy of Griffith's type consisting of a quadratic integral term and a jump contribution. The periodic case can be found in [8], the stochastic case in [6,7].},
  language  = {en}
}