Probabilistic Mechanics of Quasibrittle Structures
Strength, Lifetime, and Size Effect

This book presents an experimentally validated probabilistic strength theory of structures made of concrete, composites, ceramics and other quasibrittle materials.

Zdenek P. Bazant (Author), Jia-Liang Le (Author)

9781107151703, Cambridge University Press

Hardback, published 25 May 2017

316 pages
25.4 x 17.8 x 1.9 cm, 0.79 kg

'This new book provides a welcome addition to the very sparse collection of contemporary books that genuinely move the field of mechanics and materials forward. It does so by major steps of progress and consolidation, not just by incremental change. And its beneficial effects are not limited to mechanics and materials. … Virtually all work is supported by experimental verification. There is an unusually large, detailed and illuminating summary of past work and references. Much of it is from the senior author's voluminous and well received contributions to the research literature. As is evident, this is a research oriented book. It is not for beginners. But for those interested in the topic and determined to diligently pursue it, then this book will prove to be an invaluable and indispensable resource. The authors seem to have been committed to work on some of the very hardest problems in existence and their progress is nothing short of remarkable.' Richard M. Christensen, Meccanica

Quasibrittle (or brittle heterogeneous) materials are becoming increasingly important for modern engineering. They include concretes, rocks, fiber composites, tough ceramics, sea ice, bone, wood, stiff soils, rigid foams, glass, dental and biomaterials, as well as all brittle materials on the micro or nano scale. Their salient feature is that the fracture process zone size is non-negligible compared to the structural dimensions. This causes intricate energetic and statistical size effects and leads to size-dependent probability distribution of strength, transitional between Gaussian and Weibullian. The ensuing difficult challenges for safe design are vanquished in this book, which features a rigorous theory with detailed derivations yet no superfluous mathematical sophistication; extensive experimental verifications; and realistic approximations for design. A wide range of subjects is covered, including probabilistic fracture kinetics at nanoscale, multiscale transition, statistics of structural strength and lifetime, size effect, reliability indices, safety factors, and ramification to gate dielectrics breakdown.

1. Introduction
2. Review of classical statistical theory of structural strength and structural safety, and of classical fundamentals
3. Review of fracture mechanics and deterministic size effect in quasibrittle structures
4. Failure statistics of nanoscale structures
5. Nano-macro scale bridging of probability distributions of static and fatigue strengths
6. Multiscale modeling of fracture kinetics and size effect under static and cyclic fatigue
7. Size effect on probability distributions of strength and lifetime of quasibrittle structures
8. Computation of probability distributions of structural strength and lifetime
9. Indirect determination of strength statistics of quasibrittle structures
10. Statistical distribution and size effect on residual strength after sustained load
11. Size effect on reliability indices and safety factors
12. Crack length effect on scaling of structural strength and type 1 to 2 transition
13. Effect of stress singularities on scaling of structural strength
14. Lifetime of high-k gate dielectrics and its analogy with failure statistics of quasibrittle structures.

Subject Areas: Other technologies & applied sciences [TT], Mechanical engineering & materials [TG], Technology: general issues [TB]