Mecânica do dano concentrado para meios bidimensionais: formulação para modo I com lei de dano não linear - Teles, Daniel Victor da Cunha (2022)
Description of nonlinear behaviour of structural elements is of fundamental importance in engineering. Mathematical models using computational tools that are able to simulate phenomena observed in reality make this description. Currently, the main models used are based on concepts of plasticity, fracture and damage mechanics. The first presents important remarks about nonlinear phenomena after the elastic regime. Second describes the deterioration process through a small number of discrete cracks. On the other hand, the damage mechanics incorporate a new internal variable responsible for material deterioration. Despite the great contributions provided by these theories, the practical application in civil engineering situations presents some problems, such as the failure to reproduce through plasticity the nonlinear behaviour close to collapse, the need to consider initial cracks in fracture mechanics and the infinity of solutions when trying to analyse the phenomenon of strain localization by classic damage mechanics. The aforementioned phenomenon is physically characterized by the concentration of deformations in narrow bands of materials, which can drastically accelerate structural failure. A more recent theory has been successfully in analysing this phenomenon, the lumped damage mechanics. This theory uses key concepts of fracture and mechanics in inelastic hinges. Later, the lumped damage mechanics was extended to the analysis of twodimensional problems, initialling the so-called Expanded Lumped Damage Mechanics (XLDM). In this sense, the inelastic hinge become localization bands, and, therefore, the element is composed by inelastic lines that concentrate non-linear phenomena while all the rest of the element remains elastic. The target finite element of this work was initially proposed by Amorim (2016) to analyse plates with failure mode I. This element has four localization bands on the faces of a quadrilateral element with four nodes. The objective of this study is to continue the advances obtained so far in MDCX, introducing a nonlinear damage law on the element proposed by Amorim (2016) in order to improve the behaviour of the material after the elastic regime. The results show that the modification presents promising results, solution objectivity and ability to locate the zone failure in academic and experimental examples.