ENERGETIC-PROBABILISTIC SIZE EFFECT ON STRUCTURAL STRENGTH

ENERGETIC-PROBABILISTIC SIZE EFFECT ON

STRUCTURAL STRENGTH

Zdeněk P. Bažant

In contrast to fluid mechanics, the problems of scaling and size effect in solid mechanics have not come to the forefront of attention until late in the last century. The classical view that any observed size effect was statistical was reversed during the 1980s. As is now widely accepted, quasibrittle materials including concrete, rock, tough ceramics, sea ice, snow slabs and composites exhibit major size effects on the mean structural strength that are deterministic in nature, being caused by stress redistribution and energy release associated with stable propagation of large fractures or with formation of large zones of distributed cracking. The lecture begins by reviewing the general asymptotic properties of size effect implied by the cohesive crack model or crack band model, and highlights the use of asymptotic matching techniques as a means of obtaining scale-bridging size effect laws representing a smooth transition between two power laws. A new asymptotic matching technique combined with dimensional analysis is proposed and used to justify the size effect laws. Attention is then focused on size effects observed in fiber-polymer composites failing either by tensile fracture or by propagation of compression kink bands with fiber microbuckling. The size effects in polymeric foams and sandwich structures are
also discussed. A nonlocal model for incorporating the Weibull-type statistical size effect due to local strength randomness into the energetic size effect theory is described next, and the predictions of the combined nonlocal energetic statistical theory are compared to experimental evidence. Nonlocal probabilistic analysis of the size effect on the statistical distribution of nominal strength of structures is outlined and discussed from the viewpoint of the extreme value statistics. Implications for the design of hulls, bulkheads, decks, masts and antenna covers for very large ships, and for the design of large load-bearing aircraft fuselage panels, are pointed out. Adaptation of the stochastic finite element method to cope with extreme value statistics of energetic-statistical size effect is described, and its importance is demonstrated by analysis of some famous disasters, particularly Malpasset Dam. Finally, some problematic features of size effect in designing reinforced concrete structures against shear failures are pointed out.

References:

Bazant, Z.P. (2004). "Scaling theory for quasibrittle structural failure." Proc. National Academy of Sciences 101 (37), 13397--13399.

Bazant, Z.P. (2002). Scaling of Structural Strength. Hermes Penton Science, London (Errata: www.civil.northwestern.edu/people/bazant.html) (French transl. with updates, Hermes, Paris, 2004).

Photo by W.F. Pfeffer

Born and educated in Prague (Ph.D. 1963), Bazant joined Northwestern University in 1969, became Professor in 1973, and served as Director of Center for Geomaterials (1981-87). Since 1990 he has been W.P. Murphy Professor of Civil Eng. and Materials Science and since 2002 simultaneously McCormick School Professor. He has authored over 450 refereed journal articles and six books (Scaling of Structural Strength, Inelastic Analysis, Fracture and Size Effect, Stability of Structures, Concrete at High Temperature, and Concrete Creep). He was inducted to the National Academy of Sciences, National Academy of Engrg., Austrian Academy of Sciences, Academia di Scienze e Lettere (Italy) and Academy of Engrg. of Czech Rep. He served as Editor of ASCE J. of Engrg. Mechanics and is Regional Editor of Int. J. of Fracture; was president of Soc. of Engrg. Science, founding president of
IA-FRAMCOS and of IA-CONCREEP; Division Director in IA-SMiRT; is a member of US Nat. Comm. on Theor. & Appl. Mech.; and chaired various committees in ASCE, RILEM, ACI, SES and IA-SMiRT. He is an Illinois Registered Structural Engineer. Among his honors: 5 honorary doctorates (Colorado, Lyon, Milano, Karlsruhe, Prague); SES Prager Medal; ASME Warner Medal; ASCE Newmark Medal, Croes Medal, Huber Prize, Lin Award and Lifetime Achievement Award; RILEM L'Hermite Medal; Am. Ceramic Soc. Roy Award; Torroja Medal (Spain); Solin and Stodola Medals (Czech Rep., Slovakia); ICOSSAR Lecture Award; Medal of Merit (TU Prague); SEAOI Meritorious Paper; Best Engrg. Book of the Year (SAP); ISI Highly Cited Scientist (www.ISIhighlycited.com); and Guggenheim, Humboldt, NATO, JSPS, Kajima and Ford Fellowships.

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