A Geometrically Nonlinear Three Dimensional Cohesive Crack Method for Reinforced Concrete Structures

Goangseup Zi

Assistant professor, Department of Civil, Environmental & Architectural Engineering, Korea University, 5 Ga 1, An-Am Dong, Sung-Buk Gu, Seoul, 136-701, Korea; Tel.: +82-2-3290-3324

Timon Rabczuk

Senior Lecturer, Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand; Tel: +64-3-364-8836

Stéphane Bordas

Lecturer (assistant professor), Civil Engineering Department, University of Glasgow, Rankine building, G12 8LT, Glasgow, UK; Tel: +44(0)141 330 4075

Hung Nguyen-Xuan

Singapore-MIT Alliance (SMA), E4-04-10, 4 Engineering Drive 3, Singapore, 117576, National University of Singapore, 10 Kent Ridge Crescent 119260, Singapore; Tel.: +65 98604962

A three dimensional meshfree method for modeling arbitrary crack initiation and crack growth in reinforced concrete structure is presented. This meshfree method is based on a partition of unity concept and formulated for geometrically nonlinear problems. The crack kinematics are obtained by enriching the solution space in order to capture the correct crack kinematics. A cohesive zone model is used after crack initiation. The reinforcement modeled by truss or beam elements is connected by a bond model to the concrete. We applied the method to model the fracture of several reinforced concrete structures and compared the results to experimental data.

Keywords: Prestressed concrete; Reinforced concrete; Cohesive zone modelling; Crack growth; Brittle fracture

Reinforced concrete structures often undergo extensive cracking before failure. Tracking dense failure patterns by finite element methods is quite difficult. Therefore, particle methods are very attractive for this class of problems.

In this paper, we present a three-dimensional cohesive crack method for reinforced concrete structures. We model cracking in the concrete with an extended element-free Galerkin method (XEFG) that is coupled to finite elements for the reinforcement following the general formulation of geometrically nonlinear problems. The ill-posed IBVP is treated by means of cohesive surfaces in the post localization domain.

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