A probabilistic crack band model for quasibrittle fracture

Jia Liang Le, Jan Eliáš

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16 Scopus citations


This paper presents a new crack band model (CBM) for probabilistic analysis of quasibrittle fracture. The model is anchored by a probabilistic treatment of damage initiation, localization, and propagation. This model regularizes the energy dissipation of a single material element for the transition between damage initiation and localization. Meanwhile, the model also takes into account the probabilistic onset of damage localization inside the finite element (FE) for the case where the element size is larger than the crack band width. The random location of the localization band is related to the random material strength, whose statistics is described by a finite weakest link model. The present model is applied to simulate the probability distributions of the nominal strength of different quasibrittle structures. It is shown that for quasibrittle structures direct application of the conventional CBM for stochastic FE simulations would lead to mesh-sensitive results. To mitigate such mesh dependence, it is essential to incorporate the strain localization mechanism into the formulation of the sampling distribution functions of material constitutive parameters.

Original languageEnglish (US)
Article number051005
JournalJournal of Applied Mechanics, Transactions ASME
Issue number5
StatePublished - May 1 2016

Bibliographical note

Funding Information:
J.-L. Le acknowledges the support under Grant No. W911NF-15-1-0197 to the University of Minnesota from the U.S. Army Research Office. J. Elias acknowledges the support from the Czech Science Foundation under Project No. 15-19865Y.

Publisher Copyright:
Copyright © 2016 by ASME.


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