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Assuming a linear geometric transformation of the crack and a crack-propagation condition at the flawless network's strength, the failure stress follows a scaling law in χ like LEFM's but with one parameter C describing tip blunting; a least-squares fit gives C = 1.102 and matches the simulations far better than LEFM.
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Notation basis: Equations (4)–(6) are images absent from the vendored text; only the structure (LEFM-like scaling in χ with one blunting parameter), the propagation condition and the fitted C are stated in prose. The explicit f must be taken from the PDF.
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A one-parameter blunting law (C = 1.102) predicts failure stress versus crack size
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\sigma_f(\chi) = \sigma_f^{0}\, f(\chi; C),\quad C = 1.102
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Theodor Ackbarow et al., “Alpha-Helical Protein Networks Are Self-Protective and Flaw-Tolerant”, PLoS ONE 4, e6015 (2009), doi:10.1371/journal.pone.0006015; Results and Discussion. Scope: Alpha-helix network model, cracks from 10% to 80% of width
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Theodor Ackbarow, Dipanjan Sen, Christian Thaulow, Markus J. Buehler. Alpha-Helical Protein Networks Are Self-Protective and Flaw-Tolerant. PLoS ONE 4, e6015 (2009). doi:10.1371/journal.pone.0006015
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Alpha-Helical Protein Networks Are Self-Protective and Flaw-Tolerant
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Quoted from the full text (cc by licence), paragraph 25–26 of 2009-helical-networks.txt (sha256 d35d9ea109c79b04ca4f44608c823ee0ab4e43a642147772bb6b89e3fe2d734f), vendored from Europe PMC PMC2696088 by build/resolve.py and checked by build/check.py.
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Equation (6) is a similar scaling law as proposed in eq. (2), but features an unknown parameter C that effectively describes the geometric change of the blunted crack tip under elastic deformation. This parameter can be identified by carrying out a least-squares curve fit for C to the range of geometries considered in our computational experiments, leading to C = 1.102.
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Theodor Ackbarow et al. 2009 claim: A one-parameter blunting law (C = 1.102) predicts failure stress versus crack size
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