Uma nova abordagem para análise estática em duas escalas : método dos elementos finitos generalizados/estendidos, estratégia global-local e modelos de degradação elástica no estudo de meios não lineares, parcialmente frágeis e heterogêneos

Abstract

In structural analysis it is usual to adopt single-scale models, representing the structural or macroscopic level, in which one would investigate the overall behaviour of the studied domain. In those models, the material is homogeneous, and it is necessary to use some appropriate phenomenological constitutive relations to reflect the behavior of the underlying scales. However, all the materials are heterogeneous in some small length scale and with quasi-brittle media, it is that inhomogeneous nature of the continuum that accounts for many of the phenomena captured in structural level, notably the prominent nonlinear mechanical behavior. Thus, examine the material in different length scales is critical to its proper modeling. In this sense, this work proposes a new nonlinear strategy associated to the Generalized/Extended Finite Element Method with Global-Local enrichment for modeling heterogeneous quasi-brittle structures in two scales by a modified incremental-iterative scheme, in which global (macroscale) and local (mesoscale) boundary value problems, in weak coupling, are concurrently solved. Different material compositions were prescribed in each scale and proper descending and ascending communication techniques were investigated. The proposed method could capture the fine-scale behavior, and its effect on the structural problem. The strategy developed here works not only as a traditional and versatile refinement mechanism that allows coupling of nonconforming meshes, in a hybrid hp refinement fashion, but also, it can introduce in the numerical model, through the local scale, several characteristics or modifications without major compromise of global/structural hypotheses.