A scale-invariant cohesive crack model for quasi-brittle materials

Abstract

The fictitious crack model by Hillerborg is the most widely used model to simulate damage and fracture in concrete structures. Its peculiar capability to capture the evolution of the cracking process is accompanied by its simplicity. However, some aspects of the phenomenon are not considered in the model, for instance the size-dependence of the nominal quantities involved in the cohesive law. This affects the predictive capabilities of the model, when it is used to extrapolate results from small laboratory specimens to full-scale structures. In this paper, a scale-independent cohesive law is put forward, which overcomes these drawbacks and permits to obtain a unique constitutive relationship for softening in concrete. By assuming damage occurring in a fractal band inside the specimen, nominal stress, crack opening displacement and nominal fracture energy become scale dependent. Hence they should be substituted by fractal quantities, which are the true material constants. A mutual relation among their fractal physical dimensions puts a strong restriction to disorder. By varying the scaling exponents of the kinematical quantities, a clear transition from discrete to smeared cracking can be obtained. The fractal cohesive law is eventually applied to some tensile test data, showing perfect agreement between theory and experiments.