no. 6
Analysis of cell size effects in atomistic crack propagation
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 6, pp. 1821-1847

We consider crack propagation in a crystalline material in terms of bifurcation analysis. We provide evidence that the stress intensity factor is a natural bifurcation parameter, and that the resulting bifurcation diagram is a periodic “snaking curve”. We then prove qualitative properties of the equilibria and convergence rates of finite-cell approximations to the “exact” bifurcation diagram.

DOI : 10.1051/m2an/2020005
Classification : 65L20, 70C20, 74A45, 74G20, 74G40, 74G60, 74G65
Keywords: Crystal lattices, defects, crack propagation, regularity, bifurcation theory, convergence rates 
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     title = {Analysis of cell size effects in atomistic crack propagation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1821--1847},
     year = {2020},
     publisher = {EDP Sciences},
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     number = {6},
     doi = {10.1051/m2an/2020005},
     mrnumber = {4129381},
     zbl = {07357913},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/m2an/2020005/}
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Buze, Maciej; Hudson, Thomas; Ortner, Christoph. Analysis of cell size effects in atomistic crack propagation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 6, pp. 1821-1847. doi: 10.1051/m2an/2020005

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