Milan Jirásek: Smeared-Crack Modeling

At LSC-DGC of EPF Lausanne we have developed a constitutive model for smeared-crack simulation of concrete fracture. The model combines the standard rotating crack approach with scalar damage. The rotating crack performs well at the initial stage of softening and it properly reflects cracking-induced anisotropy. At later stages, the standard rotating crack model leads to stress locking (spurious stress transfer across widely open cracks), and it can also lose stability due to the presence of negative shear stiffness coefficients. Both problems are remedied by transition to a scalar damage approach. The (already anisotropic) secant material stiffness matrix at the moment of transition is multiplied by a scalar factor that decreases from one to zero. Mesh-induced directional bias (sensitivity of the crack propagation direction to the orientation of the finite element mesh) is alleviated by a nonlocal formulation. For more information please check the following papers.

M. Jirásek and T. Zimmermann:
Analysis of the rotating crack model
Journal of Engineering Mechanics ASCE, 124 (1998), 842-851.

M. Jirásek and T. Zimmermann:
Rotating crack model with transition to scalar damage
Journal of Engineering Mechanics ASCE, 124 (1998), 277-284.

M. Jirásek:
Nonlocal models for damage and fracture: Comparison of approaches
International Journal of Solids and Structures, 35 (1998), 4133-4145.

There exists also an internal report that contains unpublished details on the mesh-adaptive procedure. The meshes have been generated using Targe2, a mesh generator based on the advancing front technique and created by Petr Krysl.

Application Examples

Plane strain analysis of a gravity dam (Koyna Dam) with a preexisting crack loaded by full reservoir water pressure plus additional pressure due to overflow:


Click on the left figure if you want see a sequence of meshes generated by a pseudo-adaptive procedure. By clicking on the right figure you can start a crack propagation video.

Plane-stress analysis of a double-edge notched specimen loaded by a combination of tension and shear:

Three-dimensional analysis of an unnotched beam subjected to three-point bending. This simulation has been run on a mesh consisting of 13,000 tetrahedral elements using the nonlocal version of the RC-SD model.

The figures below illustrate the transition from the initial diffuse damage pattern to the final highly localized one. Black lines correspond to opening cracks and white lines to closing cracks. Colors indicate various levels of cracking strain. You may also look at an animated sequence.
  Initial diffuse crack pattern 
  Onset of localization 
  Growth of the localized zone 
  Final localized crack pattern 

To the home page of Milan Jirásek.

EPFL / 29 August 1997 /