Onset of fracture in random heterogeneous particle chains

  • Laura Lauerbach

    University of Kassel, Germany
  • Stefan Neukamm

    Technische Universität Dresden, Germany
  • Mathias Schäffner

    Martin Luther University Halle-Wittenberg, Germany
  • Anja Schlömerkemper

    University of Würzburg, Germany
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In mechanical systems, it is of interest to know the onset of fracture in dependence of the boundary conditions. Here we study a one-dimensional model which allows for an underlying heterogeneous structure in the discrete setting. Such models have recently been studied in the passage to the continuum by means of variational convergence (-convergence). The -limit results determine thresholds of the boundary condition, which mark a transition from purely elastic behavior to the occurrence of a crack. In this article, we provide a notion of fracture in the discrete setting and show that its continuum limit yields the same threshold as that obtained from the -limit. Since the calculation of the fracture threshold is much easier with the new method, we see a good chance that this new approach will turn out useful in applications.