Abstract
This work presents one and two-dimensional numerical analyses using isotropic and anisotropic damage models for the concrete in order to discuss the advantages of these modeling. Initially, it is shortly described the damage model proposed by Mazars. This constitutive model assumes the concrete as isotropic and elastic material, where locally the damage is due to extensions. On the other hand, the damage model proposed by Pituba, the material is assumed as initial elastic isotropic medium presenting anisotropy, plastic strains and bimodular response (distinct elastic responses whether tension or compression stress states prevail) induced by the damage. To take into account for bimodularity two damage tensors governing the rigidity in tension and compression regimes, respectively, are introduced. Damage activation is expressed by two criteria indicating the initial and further evolution of damage. Soon after, the models are used in numerical analyses of the mechanical behavior of reinforced concrete structures. Accordingly with comparison of the obtained responses, considerations about the application of the isotropic and anisotropic damage models are presented for 1D and 2D reinforced concrete structures modeling as well as the potentialities of the simplified versions of damage models applied in situations of structural engineering.
Highlights
In the Continuum Damage Mechanics (CDM), the damage effects are evidenced in the stiffness constitutive tensor
It is important to observe that the proposal and parametric identification of evolution laws for damage variables D4 and D5 must increase the accuracy of the anisotropic model
These cracking processes related to shear behavior of the concrete are significant contributions to the released energy. This feature has been studied by Pituba [20] and a theoretical analysis has shown that the anisotropic model has advantage upon constitutive models that use the so called “shear retention factor”
Summary
In the Continuum Damage Mechanics (CDM), the damage effects are evidenced in the stiffness constitutive tensor. In the last decades anisotropic models which can modify both the direction and the number of the material symmetry planes have been proposed (Brünig [5], Pituba [6], Pietruszczak [7], Ibrahimbegovic [8] and Dragon [9]) Another important characteristic presented by many fiberreinforced composite materials is the intrinsic bimodularity, i.e., distinct responses in tension and compression prevailing states. To compute the aT and aC values defined in Eq(4), we have to obtain, initially, the deformations eT and eC associated, respectively, to tension and compression states as follows: and compression when damaged This model has been proposed by Pituba [6] and it follows the from the formalism presented in Pituba [11].
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