Stochastic computational mechanics of quasibrittle structures

habilitation thesis

English

Quasibrittle materials such as concrete, fiber composites, rocks, tough ceramics, sea ice, dry snow slabs, wood and some biomaterials, fail at different nominal strengths with respect to their structural size. Smaller structures fail in a ductile manner which usually involves distributed cracking with strain-softening. The stress redistribution that is caused by fracture and distributed cracking engenders an energetic size effect, i.e., decrease of the nominal strength of structures with increasing structure size. A structure far larger than the fracture process zone (FPZ) fails in an almost perfectly brittle manner and, if the failure occurs right at the crack initiation, the failure load is governed by the statistically weakest point in the structure, which gives a basis to the statistical size effect. Strategies for capturing the statistical size effect using the stochastic finite element method in the sense of extreme value statistics are presented. They combine feasible types of Monte Carlo simulation based on nonlinear fracture mechanics. This is exemplified by various cases of size effect in plain concrete structures. A special attention is devoted to size effects of concrete reinforcement in the form of yarns made of glass fibers (a new composite material called textile reinforced concrete). The rational treatment of uncertainties in computational mechanics receives particularly in recent years increasing attention. Loading conditions, material properties, geometry and various other parameters show in some cases considerable variations. Observations and measurements of physical processes as well as parameters clearly show their random characteristics. Hence statistical and probabilistic procedures provide a sound framework for a rational basis for processing these uncertainties. In the present thesis, conceptual and computational aspects of uncertainty processing and assessment are be discussed. It is for the highly developed computational means that the traditional intuitive treatment of uncertainties may be replaced already in the not too distant future by this rational approach. Problems in structural mechanics are addressed. The interdisciplinary field of stochastic fracture mechanics is accessed by utilizing new advanced software developments which progress beyond the traditional approach and attempt to treat in a combined manner the reliability theory with fracture nonlinearity. This approach automatically yields not only the statistical part of size effect at crack initiation, but also the energetic part of size effect. Examples of statistical simulations of size effect with nonlinear fracture mechanics software ATENA combined with probabilistic software FReET are presented. Capturing the statistical size effect is made possible by (1) incorporating the analytical results of extreme value statistics into the stochastic finite element calculations, (2) implementing an efficient random field generation, and (3) exploiting small-sample Monte-Carlo type simulation called Latin Hypercube Sampling. The necessary steps towards the results were the development of mathematical tools and algorithms (with their theoretical and numerical validation) and finally software development (FReET). Next, the applications of the methods and software follow aiming at study of size effects in various materials and loading conditions.

probabilistic-based assessment, failure probability, reliability, statistical analysis, sensitivity analysis, reliability analysis reliability software, software design, design of experiments, adaptive sampling refinement, sampling, Monte Carlo simulation, Latin Hypercube Sampling, random vectors, random fields, theory of extreme values, dependence, copula, correlation, autocorrelation, cross correlation, multivariate random field, combinatorial optimization, simulated annealing, stochastic finite element method

VOŘECHOVSKÝ, M.

15. 8. 2007

Brno: VUTIUM

Brno, Czech Republic

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