TY - GEN
T1 - Recent progress in energetic probablistic scaling laws for quasi-brittle fracture
AU - Bažant, Zdeněk P.
AU - Le, Jia Liang
N1 - Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2009
Y1 - 2009
N2 - Rational determination of safety factors necessitates establishing the probability density function (pdf) of the structural strength. For perfectly ductile and perfectly brittle materials, the proper pdf's of the nominal strength of structure are known to be Gaussian andWeibullian, respectively, and are invariable with structure size and geometry. However, for quasibrittle materials, many of which came recently to the forefront of attention, the pdf has recently been shown to depend on structure size and geometry, varying gradually from Gaussian pdf with a remote Weibull tail at small sizes to a fully Weibull pdf at large sizes. The recent results are reviewed, and then mathematically extended in two ways: (1) to a mathematical description of structural lifetime as a function of applied (time-invariable) nominal stress, and (2) to a mathematical description of the statistical parameters of the pdf of structural strength as a function of structure size and shape. Finally, recent experimental data are analyzed and applicability of the present theory is verified.
AB - Rational determination of safety factors necessitates establishing the probability density function (pdf) of the structural strength. For perfectly ductile and perfectly brittle materials, the proper pdf's of the nominal strength of structure are known to be Gaussian andWeibullian, respectively, and are invariable with structure size and geometry. However, for quasibrittle materials, many of which came recently to the forefront of attention, the pdf has recently been shown to depend on structure size and geometry, varying gradually from Gaussian pdf with a remote Weibull tail at small sizes to a fully Weibull pdf at large sizes. The recent results are reviewed, and then mathematically extended in two ways: (1) to a mathematical description of structural lifetime as a function of applied (time-invariable) nominal stress, and (2) to a mathematical description of the statistical parameters of the pdf of structural strength as a function of structure size and shape. Finally, recent experimental data are analyzed and applicability of the present theory is verified.
KW - Cohesive fracture
KW - Extreme value statistics
KW - Probabilistic mechanics
KW - Scaling
KW - Size effect
KW - Structural strength
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U2 - 10.1007/978-1-4020-9033-2_13
DO - 10.1007/978-1-4020-9033-2_13
M3 - Conference contribution
AN - SCOPUS:84862103198
SN - 9781402090325
T3 - Solid Mechanics and its Applications
SP - 135
EP - 144
BT - IUTAM Symposium on Scaling in Solid Mechanics - Proceedings of the IUTAM Symposium
PB - Springer Verlag
T2 - IUTAM Symposium on Scaling in Solid Mechanics
Y2 - 25 June 2007 through 29 June 2007
ER -