Fishnet Statistics for Design of Quasibrittle and Biomimetic Materials and Structures for Failure Probability <10-6
Zdeněk P. Bažant, PhD
McCormick Institute Professor, Walter P. Murphy Professor of Civil and Environmental Engineering, Mechanical Engineering and Material Science and Engineering at Northwestern University in Evanston, Illinois
Member of the National Academy of Sciences, National Academy of Engineering and American Academy of Arts & Sciences
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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.
Zdeněk P. Bažant was born and educated in Prague (PhD 1963), he 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 (1981-1987). He was inducted to National Academy of Sciences, National Academy of Engineering and American Academy of Arts & Sciences, as well as Italian National Academy, Austrian Academy of Sciences, Czech Academy of Engineering, Spanish Royal Academy of Engineering, European Academy of Sciences & Arts and Istituto Lombardo. He received seven honorary doctorates, Austrian Cross of Honor for Science and Art from President of Austria, the ASME Medal, the ASME Timoshenko, Nadai and Warner Medals, the American Society of Civil Engineering (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 and the Torroja Medal. He authored eight books. With H-index 129 and more than 67,000 citations and i10 index of 614. In 2015, ASCE established the ZP Bažant Medal for Failure and Damage Prevention. He is one of the original top 100 ISI Highly Cited Scientists in engineering. His 1959 mass-produced patent of safety ski binding is exhibited in New England Ski Museum.