Effect of Stress-Strain Relations on the Nonlinear Behavior of Quasi-Brittle Structures

Abstract

The fracture of quasi-brittle structures is modeled with two-dimensional finite elements with inclusion of special elements along a predefined crack. These special elements are rod elements with a nonlinear stress-strain diagram which allow for softening behavior, providing for gradual reduction of stress in the crack opening process. The fracture energy per unit of area, specified for the material, corresponds to the work performed in the rod elements. A general purpose finite element code with nonlinear analysis capability is used. Results for standard three-point beam tests are obtained with use of nonlinear analysis with generalized displacement control, aiming to reproduce test results with use of a clip gage or similar device for the measuring of the crack mouth opening displacement (CMOD). Four beams of different sizes, with the same height/length ratio are analyzed with various levels of mesh refinement. An edge notch at mid span warrants the formation of a single crack normal to the beam axis. Linear and bilinear softening diagrams are considered, with different fracture energies, applicable to concrete. The examples demonstrate the influence of the fracture energy and the shape of the stress-strain diagram on the representative features of structure behavior, such as maximum load, load-displacement curve and size effect.