Cohesive crack model description of ductile to brittle size-scale transition: dimensional analysis vs. renormalization group theory

Abstract

The present paper is a review of the research works carried out on the cohesive crack model and its applications at the Politecnico di Torino during the last decade. The topic encompasses experimental, numerical and theoretical aspects of the cohesive crack model. The research work followed two main directions. The early work concerns the development and the implementation of the cohesive crack model, which has been shown to be able to simulate experiments on concrete specimens and structures. It is referred to as the dimensional analysis approach, since it succeeds in capturing the ductile-to-brittle transition by increasing the structural size owing to the different physical dimensions of two material parameters: the tensile strength and the fracture energy. On the other hand, the later research direction aims at extending the classical cohesive model to quasi-brittle materials showing (as they often do) fractal patterns in the failure process. This approach is referred to as the renormalization group (or fractal) approach and leads to a scale-invariant cohesive crack model. This model is able to predict the size effects even in tests where the classical approach fails, e.g. the direct tension test. The two research paths, therefore, complete each other, allowing a deeper insight into the ductile-to-brittle transition usually detected when testing quasi-brittle material specimens or structures at different size-scales.