Numerical Analysis of Mixed-Mode Fracture in Concrete Using Extended Fictitious Crack Model

Abstract

A numerical formulation of the mixed-mode (mode-I and mode-II) fracture in concrete based on the extended fictitious crack model is presented. For crack propagation, the maximum principal stress criterion is used, assuming that the mode-I condition is dominant at the tip of a mixed-mode crack. A main feature of this study is that normal and tangential tractions are applied directly to the crack surface, following specific tension-softening and shear-transfer laws. To verify the approach, two well-known experimental problems are solved. The first is the single-notched shear beam test by Arrea and Ingraffea, and the second is the scale-model test of gravity dams by Carpinteri et al. Varying the shear-transfer characteristics on the crack surface, the numerical model predicts distinct transitions from the mode-I fracture to the mixed-mode fracture in the structural response and the crack path, which both show reasonable agreement with experimental observations. The issue of stress singularity in finite-element computations of tip tensile forces is also addressed.