Failure modeling of reinforced concrete structures using continuum damage models

Abstract

In this thesis, we develop a numerical procedure of damage in quasi-brittle material. Studying diffuse fracture processes by continuum damage mechanics can provide a good insight in prediction the failure of material. Numerical analysis is not only an easier and convenient way but also a powerful tool for giving additional information about the microstructure of the investigated system, which is not always possible in practical experiments. The thesis focuses on diffuse fracture processes of quasi-brittle material caused by tension and compression in infinitely long pre-cracked brick, three point and four point bending concrete beams. The numerical algorithm is based on the Isogeometric Analysis incorporated with Mazars damage model and enhanced gradient strain formulation. The numerical examples in this study are coded in Mathematica programming language, a computational software program used in many scientific, engineering, mathematical and computing fields, based on symbolic mathematics. We examine the reliability of the present method through three benchmark cracking problems : notched concrete beam, perfect concrete beam in the case of three point and four point bending. In the final numerical example, the four point bending problem of reinforced concrete structure is elaborated. Although the proposed method is just applied for the structural concrete beam with straight shape, it is also valuable for arbitrary shape of geometry and any other quasi-brittle materials. The numerical results show good agreement between the present approach and other published ones and also reference data. We argue that the proposed method is reliable to describe the softening behavior and diffuse fracture process of micro crack in structural concrete and reinforced concrete. In this contribution, the suitability of iso geometric finite elements for the discretization of enhancement gradient damage approximations is pointed out. The study shows that our work relied on a combination of the non-local damage approach with isogeometric finite element analysis can offer a reliable tool to predict accurately the mechanical response of reinforced concrete structures. Future work and improvement of the method are based on justification of the contact behavior on the interface between concrete and reinforced steel layer. The anisotropic model and higher order gradient formulation are also possible improvements for the presented method.