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SEMINAR: Fishnet Statistics for Design of Quasibrittle and Biomimetic Materials and Structures for Failure Probability <10-6
October 4 @ 10:00 am - 11:00 am
The failure probability of engineering structures such as bridges, airframes and MEMS ought to be <10-6. This is a challenge. For perfectly brittle and ductile materials obeying the Weibull or Gaussian distributions with the same coefficient of variation, the distances from the mean strength to 10-6 differ by cca 2:1. For quasibrittle or architectured materials such as concrete, composites, tough ceramics, rocks, ice, foams, bone or nacre, this distance can be anywhere in-between. This necessitates a new theory of strength probability distribution. The recent formulation of Gauss-Weibull statistics derived from analytical scale transitions and frequency of activation-energy controlled interatomic bond ruptures is reviewed. Then, motivated by imbricated lamellar architecture of nacre, a new probability model with alternating series and parallel links, resembling a diagonally-pulled fishnet, is developed. After the weakest-link and fiber-bundle models, it is the third model tractable analytically. It allows for a continuous transition between Gaussian and Weibull distributions, and is size-dependent. Comparisons with histograms and size-effect tests support the theory.
Born and educated in Prague (Ph.D. 1963), Bažant joined Northwestern in 1969, where he has been W.P. Murphy Professor since 1990 and simultaneously McCormick Institute Professor since 2002, and Director of Center for Geomaterials (1981-87). He was inducted to NAS, NAE, Am. Acad. of Arts & Sci., and Royal Soc. London; to the academies of Italy (Lincei), Austria, Spain, Czechia, Greece, India and Lombardy;Academia Europaea, Eur. Acad. of Sci. & Arts. Hon. Mem. of ASCE, ASME, ACI, RILEM; 7 honorary doctorates (Prague, Karlsruhe, Colorado-Boulder, Milan Poly, INSA Lyon, TU Vienna, Ohio State); Austrian Cross of Honor for Science and Art from President of Austria; ASME Medal, ASME Timoshenko, Nadai and Warner Medals; ASCE von Karman, Freudenthal, Newmark, Biot, Mindlin and Croes Medals, Huber Prize, TY Lin & Lifetime Achievement Awards; SES Prager Medal; RILEM L’Hermite Medal; Exner Medal (Austria); Torroja Medal (Madrid); etc; was SES President and Founding President of IA-FraMCoS and IA-ConCreep; Editor-in-Chief, J. Eng.Mech. ASCE. Authored 8 books on creep struct. effects, scaling of structural strength, inelastic analysis, fracture & size effect, stability of structures, concrete at high temperatures, creep & hygrothermal effects, and probabilistic mech. of quasibrittle mat. H-index: 124, citations: 67,000 (on Google, incl. self-cit.), i10 index: 614. In 2015, ASCE established ZP Bažant Medal for Failure and Damage Prevention. He is one of the original top 100 ISI Highly Cited Scientists in Engrg. (www.ISIhighlycited.com). His 1959 mass-produced patent of safety ski binding is exhibited in New England Ski Museum. http://cee.northwestern.edu/people/bazant/