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`Mathematical Problems in EngineeringVolume 2013, Article ID 726317, 8 pageshttp://dx.doi.org/10.1155/2013/726317`
Research Article

## Implementation of Fictitious Crack Model Using Contact Finite Element Method for the Crack Propagation in Concrete under Cyclic Load

1College of Water Conservancy and Hydropower, Hohai University, Xikang Road, Nanjing 210098, China
2School of Engineering & Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS, UK
3Changjiang Survey, Planning Design and Research Limited Liability Company, Jiefang Dadao Road, Wuhan 430010, China

Received 19 July 2013; Accepted 24 August 2013

Academic Editor: Song Cen

Copyright © 2013 Lanhao Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The mixed freedom finite element method proposed for contact problems was extended to simulate the fracture mechanics of concrete using the fictitious crack model. Pairs of contact points were set along the potential developing path of the crack. The displacement of structure was chosen as the basic variable, and the nodal contact force in contact region under local coordinate system was selected as the iteration variable to confine the nonlinear iteration process in the potential contact surface which is more numerically efficient. The contact forces and the opening of the crack were obtained explicitly enabling the softening constitutive relation for the concrete to be introduced conveniently by the fictitious crack model. According to the states of the load and the crack, the constitutive relation of concrete under cyclic load is characterized by six contact states with each contact state denoting its own displacement-stress relation. In this paper, the basic idea of the mixed freedom finite element method as well as the constitutive relation of concrete under cyclic load is presented. A numerical method was proposed to simulate crack propagation process in concrete. The accuracy and capability of the proposed method were verified by a numerical example against experiment data.