Regensburg 2013 – wissenschaftliches Programm

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MM: Fachverband Metall- und Materialphysik

MM 62: Topical Session: Fundamentals of Fracture - Stochastic Aspects

MM 62.1: Topical Talk

Donnerstag, 14. März 2013, 17:15–17:45, H4

Elasticity and disorder for fracture size effects — •Stefano Zapperi — IENI-CNR, Milano, Italy — ISI foundation, Torino,Italy

I will discuss the asymptotic properties of fracture strength distributions of disordered elastic media studied by combination of renormalization group, extreme value theory, and numerical simulation. We investigate the validity of the weakest-link hypothesis in the presence of realistic long-ranged interactions in the random fuse model. Numerical simulations indicate that the fracture strength is well-described by the Duxbury-Leath-Beale (DLB) distribution which is shown to flow asymptotically to the Gumbel distribution. We explore the relation between the extreme value distributions and the DLB-type asymptotic distributions and show that the universal extreme value forms may not be appropriate to describe the nonuniversal low-strength tail. Finally, we confirm numerically that the Weibull distribution, widely used in the past to fit failure statistics from experiments, only arises when the distribution of pre-existing disorder has a power law tail and is otherwise unstable due to interactions.