An Energy Model for Bifurcation Analysis of a Double-Notched Concrete Panel: Simplified Model

Abstract

The uni-axial tension of a double-notched concrete panel is analyzed. The unsymmetrical crack propagation is treated as a bifurcation problem. The concept of minimization of the second-order energy is used as the criterion for the bifurcation from symmetrical crack propagation to unsymmetrical crack propagation. In order to study the decisive factors affecting bifurcation, a simplified softening model is adopted where the cracked material is represented by softening rods, and un-cracked material by elastic rods. The influences on bifurcation of the crack plane dimension, the material cohesiveness, and the local constitutive law are analyzed. The analysis shows that the unsymmetrical crack propagation (i.e. strains localizing on one side of the specimen) may occur either before or after the peak load. Whether the unsymmetrical crack propagation occurs before the peak load or not depends on the ratio of the cracked length to un-cracked ligament. Shear stiffness does not have a significant influence on crack propagation before the peak load; however, it does determine whether the unsymmetrical crack propagation arises after the peak load.