Confinement-shear lattice CSL model for fracture propagation in concrete

Gianluca Cusatis*, Zdeněk P. Bažant, Luigi Cedolin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

143 Scopus citations


A previously developed lattice model is improved and then applied to simulations of mixed-mode crack propagation in concrete. The concrete meso-structure is simulated by a three-dimensional lattice system connecting nodes which represent the centers of aggregate particles. These nodes are generated randomly according to the given grain size distribution. Only coarse aggregates are taken into account. Three-dimensional Delaunay triangulation is used to determine the lattice connections. The effective cross-section areas of connecting struts are defined by performing a three-dimensional domain tessellation partly similar to Voronoi tessellation. The deformations of each link connecting two adjacent aggregate pieces are defined in the classical manner of Zubelewicz and Bažant in which rigid body kinematics is assumed to characterize the displacement and rotation vectors at the lattice nodes. Each strut connecting adjacent particles can transmit both axial and shear forces. The adopted constitutive law simulates fracture, friction and cohesion at the meso-level. The behavior in tension and shear is made dependent on the transversal confining strain, which is computed assuming a linear displacement field within each tetrahedron of Delaunay triangulation, and neglecting the effect of the particle rotations. A mid-point explicit scheme is used to integrate the governing equations of the problems. General procedures to handle the boundary conditions and to couple the lattice mesh to the usual elastic finite element mesh are also formulated. Numerical simulations of mixed-mode fracture test data are used to demonstrate that the model is capable of accurately predicting complex crack paths and the corresponding load-deflection responses observed in experiments.

Original languageEnglish (US)
Pages (from-to)7154-7171
Number of pages18
JournalComputer Methods in Applied Mechanics and Engineering
Issue number52
StatePublished - Nov 1 2006


  • Concrete
  • Delaunay triangulation
  • Explicit scheme
  • Fracture propagation
  • Lattice model
  • Meso-structure
  • Particle model
  • Voronoi tesselation

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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