Multiscale strategy for the analysis of softening media using the generalized finite element method
Humberto Alves da Silveira Monteiro1; Roque Luiz da Silva Pitangueira1; Felício Bruzzi Barros1
1 Universidade Federal de Minas Gerais
doi:10.20906/CPS/CILAMCE2017-0253
Resumo
In structural analysis, it is usual to adopt single-scale models, representing the structural or macroscopic level, in which one would examine the overall response of the studied domain. In these models, the material is homogeneous and it is required the use of appropriate phenomenological constitutive relations to reflect the behavior of the underlying scales. However, all the materials are heterogeneous in some sufficiently small length scale and in the case of quasi-brittle media it is exactly the inhomogeneous nature of the continuum that accounts for many of the phenomena captured in structural level, especially the prominent non-linear mechanical behavior. Thus, the investigation of the material in different length scales is critical to its proper modeling. In this sense, this work proposes the adoption of the Generalized Finite Element Method associated with the Global-Local methodology (GFEM-GL) to build a different multiscale strategy able to model general strain softening materials, especially quasi-brittle media and its main archetypical specimen, the concrete. In an incremental-iterative scheme, the solution of an initial global boundary value problem (macroscale) generates boundary conditions to local domains (mesoscale). Then the solution of the inhomogeneous local problems numerically generates enrichment functions for the global domain and the constitutive response of the non-linear material. Lastly, the enriched global problem is processed again. Hence, in that sense, one could say that the method relies on two main mechanisms: the downscaling and the upscaling. The first one consists in the generation of boundary conditions to local domains by a weak coupling between macro and meso meshes. The second one handles a simple homogenization procedure, which accounts for the volume equivalence between the global and local domains, followed by the enrichment of the global partition of unity. At the current stage, the material morphology has been modeled using a stochastic-heuristic algorithm and numeri
Palavras-chave: Generalized Finite Element Method; Multiscale Analysis; Mesostructure; Softening; Quasi-Brittle Media; Non Linear Analysis