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Research Papers

# A Probabilistic Crack Band Model for Quasibrittle Fracture

[+] Author and Article Information
Jia-Liang Le

Department of Civil, Environmental,
and Geo-Engineering,
University of Minnesota,
Minneapolis, MN 55455
e-mail: jle@umn.edu

Jan Eliáš

Institute of Structural Mechanics,
Faculty of Civil Engineering,
Brno University of Technology,
Brno, Czech Republic
e-mail: elias.j@fce.vutbr.cz

1Corresponding author.

Manuscript received January 26, 2016; final manuscript received February 5, 2016; published online February 23, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(5), 051005 (Feb 23, 2016) (7 pages) Paper No: JAM-16-1053; doi: 10.1115/1.4032692 History: Received January 26, 2016; Revised February 05, 2016

## Abstract

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.

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## Figures

Fig. 1

Damage localization in one material element

Fig. 2

Determination of localization level using information of neighboring Gauss points

Fig. 6

Loading configurations of three specimens: (a) uniaxial tension, (b) pure bending, and (c) three-point bending

Fig. 3

Regularization of fracture energy based on localization parameter κc

Fig. 5

Dependence of the number of potential crack bands on the localization parameter κw

Fig. 4

Propagation of localized damage

Fig. 7

Simulated strength distributions of three specimens with different mesh sizes

Fig. 8

Distribution of localization parameter κw at the peak load

Fig. 9

Deterministic calculations of the nominal structural strengths

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