Computation of probability distribution of strength of quasibrittle structures failing at macrocrack initiation / Jia-Liang Le in Journal of engineering mechanics, Vol. 138 N° 7 (Juillet 2012)  

Public ISBD [article]  inJournal of engineering mechanics > Vol. 138 N° 7 (Juillet 2012) . - pp.888–899. Titre : Computation of probability distribution of strength of quasibrittle structures failing at macrocrack initiation Type de document : texte imprimé Auteurs : Jia-Liang Le, Auteur ; Jan Elias, Auteur ; Zdenek P. Bazant, Auteur Année de publication : 2012 Article en page(s) : pp.888–899. Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Finite weakest link model Strength statistics Representative volume element Structural safety Fracture Concrete structures Composites Résumé : Engineering structures must be designed for an extremely low failure probability, Pf<10−6. To determine the corresponding structural strength, a mechanics-based probability distribution model is required. Recent studies have shown that quasibrittle structures that fail at the macrocrack initiation from a single representative volume element (RVE) can be statistically modeled as a finite chain of RVEs. It has further been demonstrated that, based on atomistic fracture mechanics and a statistical multiscale transition model, the strength distribution of each RVE can be approximately described by a Gaussian distribution, onto which a Weibull tail is grafted at a point of the probability about 10−4 to 10−3. The model implies that the strength distribution of quasibrittle structures depends on the structure size, varying gradually from the Gaussian distribution modified by a far-left Weibull tail applicable for small-size structures, to the Weibull distribution applicable for large-size structures. Compared with the classical Weibull strength distribution, which is limited to perfectly brittle structures, the grafted Weibull-Gaussian distribution of the RVE strength makes the computation of the strength distribution of quasibrittle structures inevitably more complicated. This paper presents two methods to facilitate this computation: (1) for structures with a simple stress field, an approximate closed-form expression for the strength distribution based on the Taylor series expansion of the grafted Weibull-Gaussian distribution; and (2) for structures with a complex stress field, a random RVE placing method based on the centroidal Voronoi tessellation. Numerical examples including three-point and four-point bend beams, and a two-dimensional analysis of the ill-fated Malpasset dam, show that Method 1 agrees well with Method 2 as well as with the previously proposed nonlocal boundary method. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000396 [article] Computation of probability distribution of strength of quasibrittle structures failing at macrocrack initiation [texte imprimé] / Jia-Liang Le, Auteur ; Jan Elias, Auteur ; Zdenek P. Bazant, Auteur . - 2012 . - pp.888–899. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 138 N° 7 (Juillet 2012) . - pp.888–899. Mots-clés : Finite weakest link model Strength statistics Representative volume element Structural safety Fracture Concrete structures Composites Résumé : Engineering structures must be designed for an extremely low failure probability, Pf<10−6. To determine the corresponding structural strength, a mechanics-based probability distribution model is required. Recent studies have shown that quasibrittle structures that fail at the macrocrack initiation from a single representative volume element (RVE) can be statistically modeled as a finite chain of RVEs. It has further been demonstrated that, based on atomistic fracture mechanics and a statistical multiscale transition model, the strength distribution of each RVE can be approximately described by a Gaussian distribution, onto which a Weibull tail is grafted at a point of the probability about 10−4 to 10−3. The model implies that the strength distribution of quasibrittle structures depends on the structure size, varying gradually from the Gaussian distribution modified by a far-left Weibull tail applicable for small-size structures, to the Weibull distribution applicable for large-size structures. Compared with the classical Weibull strength distribution, which is limited to perfectly brittle structures, the grafted Weibull-Gaussian distribution of the RVE strength makes the computation of the strength distribution of quasibrittle structures inevitably more complicated. This paper presents two methods to facilitate this computation: (1) for structures with a simple stress field, an approximate closed-form expression for the strength distribution based on the Taylor series expansion of the grafted Weibull-Gaussian distribution; and (2) for structures with a complex stress field, a random RVE placing method based on the centroidal Voronoi tessellation. Numerical examples including three-point and four-point bend beams, and a two-dimensional analysis of the ill-fated Malpasset dam, show that Method 1 agrees well with Method 2 as well as with the previously proposed nonlocal boundary method. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000396

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