This book chapter is published open access.
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.