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Linear elastic fracture mechanics predicts the failure strain of a centre-cracked panel to scale as χ^−0.5 with relative crack size; a power-law fit to the simulations gives an exponent of −0.0362, so LEFM fails to describe the alpha-helix network.
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Notation basis: Both exponents are in the text; the LEFM expression itself (eq. 1–2) is an image not in the vendored text. The χ^−1/2 form follows from Griffith's σ_f = sqrt(2Eγ/(πξ)) with ε = σ/E.
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Griffith scaling predicts χ^−0.5; the network's failure strain scales as χ^−0.036
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\varepsilon_f^{\mathrm{LEFM}} \propto \chi^{-1/2} \quad \text{vs} \quad \varepsilon_f^{\mathrm{sim}} \propto \chi^{-0.0362}
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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: Centre-cracked alpha-helix network under mode I tension
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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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This analysis reveals that the scaling parameter a of versus χ are much different (−0.0362 vs. −0.5), and that the conventional LEFM model fails to describe the failure behavior of this system.
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Theodor Ackbarow et al. 2009 claim: Griffith scaling predicts χ^−0.5; the network's failure strain scales as χ^−0.036
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