| In finite element analysis of concrete structures, cracks have been represented in a discrete or smeared fashion. Although smeared crack models have been widely used in the analysis of concrete structures, they still suffer from a number of shortcomings. They seem to overestimate the stiffness and strength of structures which exhibit a shear-dominated behavior. Furthermore, they have been shown to exhibit directional bias, spurious kinematic modes, and stress locking. One objective of this study is to investigate the source of the aforementioned problems.;Despite considerable research in concrete mechanics, constitutive models for masonry are not well developed, and the finite element method has not been widely utilized to analyze masonry structures. Another objective of this study is to investigate the applicability of smeared and discrete crack models to the analysis of masonry structures. In this respect, different smeared crack models, and an interface constitutive model are developed. The interface constitutive model is capable of modeling the initiation and propagation of fracture under combined normal and shear stresses, and the experimentally observed dilatancy. It is shown that smeared crack models can model the flexural behavior of reinforced concrete masonry shear walls, but fail to capture the behavior of shear-dominated panels. A numerical approach using interface elements to model masonry joints and smeared crack elements to model masonry units is shown to be capable of simulating the behavior of unreinforced concrete masonry panels.;To circumvent the problems associated with the smeared crack models, the three-field Hu-Washizu variational statement and a four-field hybrid version of this variational statement are extended to a body with a nonlinear internal interface. The extended variational statements are then utilized to construct finite elements with internal interfaces. These elements are shown to be capable of representing fracture within an element, and are free from the deficiencies of smeared crack models. The performance of the new elements is verified with numerical examples on localized fracture. |
