| Autor: |
Lauerbach, Laura, Neukamm, Stefan, Schäffner, Mathias, Schlömerkemper, Anja |
| Rok vydání: |
2021 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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