Onset of fracture in random heterogeneous particle chains

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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 ($\Gamma$-convergence). The $\Gamma$-limit results determine thresholds of the boundary condition, which mark a transition from purely elastic behaviour 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 $\Gamma$-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.


Original languageEnglish
Title of host publicationEuropean Congress of Mathematics
PublisherEMS Publ. House
Number of pages20
ISBN (electronic)978-3-98547-551-3
ISBN (print)978-3-98547-051-8
Publication statusPublished - 14 Jul 2023

External IDs

Mendeley 403c7c20-0727-347a-8221-03ab14535468



  • math.AP