Descrição do fenômeno de fraturamento do concreto: uma abordagem estocástica baseada em modelos contínuos-descontínuos de dano e phase-field

Abstract

This thesis proposes a complete description of the concrete degradation process based on the development of a continuous-discontinuous approach, whose transition criterion is the phase-field variable. Although the search for constitutive models and numerical methods able to represent the behavior of quasi-brittle materials has aroused the interest of researchers since the beginning of the 20th century, this is a challenge that endures in Structural Engineering. Continuous and discontinuous approaches embrace, respectively, the initial stage of concrete degradation, characterized by the nucleation of microcracks, and the final stage, when macroscopic cracks emerge. However, a representative model of the material media deterioration must comprise it entirely. To aim at this purpose, it is necessary to associate both theories. The literature reports some works that discuss the theme. Nevertheless, they present limitations to complex fracture standards, and there are gaps in the procedure for transitioning between continuous and discontinuous. In this context, the present study intends to develop an approach that associates continuous nonlocal damage models with introducing discrete cracks into the finite element mesh using nodal duplication. The option for the phase-field variable as the transition criteria between smeared damage and discrete fracture is justified by its characteristic of relating damage mechanics and fracture mechanics, besides its capability to indicate the nucleation, propagation, and coalescence of cracks. Additionally, to incorporate the randomness inherent in the material and the fracturing process into the numerical simulations, a stochastic parameterization strategy based on the Monte Carlo method is presented. A series of numerical simulations were performed to validate the proposed constitutive model, and the results indicated the effectiveness of the developed formulation in reproducing concrete degradation, from incipient stages to imminent collapse.