Probabilistic Mechanics of Quasibrittle Structures

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

This book presents a mathematical exposition of the strength and lifetime statistics of structures made of brittle heterogeneous materials. This subject is of paramount importance for analysis and design of many man-made structures with applications to civil, mechanical, aerospace, geotechnical, ocean, offshore, petroleum, naval, nuclear, mining, biomedical and materials engineering.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.