Mecânica do dano concentrado expandida para meios bidimensionais: elemento finito para problemas de localização de deformações em chapas - Oliveira, João Marcos de Jesus (2020)
In engineering, the representation of structures using mathematical models has a fundamental importance. Through them, together with computational tools, it is possible to simulate the behaviour of structural elements, allowing for various analyses. Thus, the development of increasingly precise models that includes a greater number of phenomena observed in reality becomes crucial. The main current models are based on plasticity theory, damage mechanics and fracture mechanics. As it is well known, upon reaching the softening zone, classic damage models lead to mesh dependency in a finite element analysis whenever a localized solution is chosen. The so-called phenomenon of localization in these models leads to infinite possible solutions and obviously needs some regularization criteria to obtain the correct solution. This paper presents a new finite element formulation for the analysis of a tensile plate regarding strain localization problems, based mainly on the previous work by Amorim et al. (2018). The new model is not based on modern approaches to damage mechanics that use nonlocal or gradient models to circumvent the localization problem. It is an expansion of Concentrated Damage Mechanics, or MDC, into two-dimensional continuum. This more general formulation of the theory is here referred to as Expanded Concentrated Damage Mechanics, or MDCX. MDC uses key ideas of fracture mechanics and damage mechanics in conjunction with the concept of plastic hinges. Until then, in terms of concrete applicability, the MDC models were limited to analysis of frames and arches, demonstrating objective results for these cases. For these models, the finite element is given by combining an elastic bar element with two inelastic hinges at the ends. In the case of a two-dimensional medium, such as plate elements, inelastic hinges become localization bands. The finite element proposed in this work consists of joining a four-node elastic element with a set of locating bands on the sides and also within the element. Damage evolution laws that describe the behaviour of each location band are introduced in the model formulation and the proposed element is then implemented in a finite element analysis program. The convergence of numerical results to a single solution as the mesh is refined is demonstrated through examples and related problems are discussed. The results are presented graphically along with the final configuration of the problem structure, highlighting the formation of the localization bands.