Multiscale strategy for the analysis of softening media using the Generalized Finite Element Method

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 nonlinear mechanical behavior. In that 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 quasibrittle media and its main archetype, 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 creates enrichment functions for the global domain and the constitutive response of the non-linear material. Lastly, the enriched global problem is processed again. At the current stage, the material morphology has been modeled using a stochastic-heuristic algorithm and numerically treated by the Finite Element Method, one of the many possible options to handle the local/meso problem. The work has been carried out within the INSANE system (INteractive Structural Analysis Environment), a free software developed at the Federal University of Minas Gerais-Brazil.