Mecânica do dano concentrado para análise de placas, lajes e cascas delgadas

Abstract

The search for a better understanding and precise mathematical description of the behaviour of structural behaviour is of fundamental importance in structural engineering. For an accurate representation, mathematical models must account for the physical non-linear behaviour of materials. The main theories that account for nonlinear effects include the theory of plasticity and the mechanics of continuous damage. These theories have significantly contributed to structural engineering, they also face limitations associated with nonlinear solutions. Challenges include describing post-peak non-linear behaviour or encountering infinite solutions when analysing strain localization problems. To address these issues, various alternative theories have been proposed, such as fracture mechanics, modern damage mechanics, phase field models, and lumped damage mechanics (CDM). Initially developed for frame elements, CDM was later extended to two-dimensional media (e.g., membrane finite elements). It has demonstrated the capability to perform non-linear analyses, avoiding the problem of strain localization without relying on regularization techniques. This study aims to contribute to the development of analyses using CDM by proposing new models for the analysis of thin plates, slabs, and thin shells. The study selected the Discrete Kirchhoff Triangle (DKT) finite element for plate analysis, and the Constant Moment Triangle (CMT) was chosen for the analysis of slabs, plates, and shells. Additionally, the Constant Strain Triangle (CST) element was employed for shell analysis. All the elements were reformulated to modify their kinematic variables, enabling the incorporation of CDM considerations. For plate elements, a nonlinear damage evolution law with exponential softening behaviour was adopted. This study also developed an experimental campaign involving the casting of fibre-reinforced concrete plates. The plate elements were tested against a series of experimental tests found in the literature as well as the experimental tests conducted in this study. The results demonstrated accurate performance in terms of force-displacement relationships, crack distribution, and crack opening. Based on the plate element using the CMT, this study proposes a new model for evaluating reinforced concrete plates (slabs). Within this model, inelastic variables, defined as damage and plastic rotations, are associated with the behaviour of reinforced concrete (cracking and reinforcement yielding). Accordingly, this study introduces different laws governing the evolution of damage and plastic rotation. The proposed model was tested against series of experimental tests from the literature, yielding results with high accuracy compared to experimental data, in terms of Force vs. Displacement and the initiation and propagation of complex networks of cracks. Finally, a flat shell model for application in reinforced concrete shells is proposed. Axial effects are described using the CST finite element, assumed to exhibit a linear-elastic response, while bending effects are modelled using the proposed slab element. The model was validated against various experimental examples from the literature, delivering accurate predictions of force-displacement responses and cracking behaviour, consistent with both an arch model and experimental results.