Finite Element Analyses of mesh-objectivity for Smeared, Damage and Discrete models applied to concrete cracking

Resumo

This paper will address the issue of mesh objectivity regarding Smeared, Damage and Discrete models
applied to concrete cracking in the framework of the Finite Element Method. It will be shown that assigning the
same stress-strain relationship with softening for all elements regardless their size and shape will lead to spurious
results. This will make the fracture energy decrease as the mesh is refined, sometimes even converging zero which
is completely unacceptable. This problem is related to the negative slope of the tangent stiffness tensor, that is, the
increase in strain with decreasing stress which will make a small portion of the body experience softening while
the rest of it unloads elastically. In order to circumvent this issue, it must be employed a regularization technique,
also known as localization limiter. The first localization limiter that this study will adopt is the Crackband
technique applied to both Smeared and an isotropic scalar Damage models. It is easily implemented in an existing
Finite Element code and its main feature is the assumption of a bandwidth where the crack is supposed to
propagate. It will be presented that the Crackband technique is the simplest but crudest approach. Nevertheless, it
will assure the convergence of the results but its accuracy hinges on choosing the bandwidth properly. The second
localization limiter adopted in this paper is the Nonlocal integral-type technique which recovers the objectivity by
taking the weighted average of a variable that controls cracking. This technique will be used in the isotropic scalar
Damage model. Finally, it will be discussed the Discrete crack approach through interface elements with
vanishingly thickness. This technique won’t need any regularization since the constitutive relationship is already
written in terms of Stress-Displacement. The three approaches will be employed in the simulation of a notched
fiber-reinforced concrete beam and compared with its experimental data. In order to show the feasibility of each
methodology, these analyses will debate their convergence properties which is the main focus of the present study
and features such as computational effort, crackpath and assessment of input parameters.