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Z. P. Bazant and V. S. Gopalaratnam, “Fracture Mechanics of Concrete: An Apercu of Basic Concepts and Models,” Proceedings of the First International Conference on Fracture Mechanics of Concrete Structures, Breckenridge, Colorado, 1-5 June 1992, pp. 145-154.

has been cited by the following article:

• TITLE: Fracture Response of Reinforced Concrete Deep Beams Finite Element Investigation of Strength and Beam Size

  AUTHORS: Guillermo A. Riveros, Vellore Gopalaratnam

  KEYWORDS: Automatic Remeshing; Bond Slip; Concrete; Discrete Crack; Finite Element; Fracture Mechanics; Size Effects; Tensile Softening

  JOURNAL NAME: Applied Mathematics, Vol.4 No.11, November 5, 2013

  ABSTRACT: This article presents a finite element analysis of reinforced concrete deep beams using nonlinear fracture mechanics. The article describes the development of a numerical model that includes several nonlinear processes such as compression and tension softening of concrete, bond slip between concrete and reinforcement, and the yielding of the longitudinal steel reinforcement. The development also incorporates the Delaunay refinement algorithm to create a triangular topology that is then transformed into a quadrilateral mesh by the quad-morphing algorithm. These two techniques allow automatic remeshing using the discrete crack approach. Nonlinear fracture mechanics is incorporated using the fictitious crack model and the principal tensile strength for crack initiation and propagation. The model has been successful in reproducing the load deflections, cracking patterns and size effects observed in experiments of normal and high-strength concrete deep beams with and without stirrup reinforcement.