Multiscale GFEM with superposition of crack enrichment functions driven by finite fracture mechanics: Theory, first computation and open problems

This work presents a direct extension of the multiscale GFEM (MS-GFEM) where damage and fracture mechanisms are now taken into account. Using a pattern-based description of the microscale, the construction of the model falls into two main parts: the modeling of a multiphase composite yarn, and the modeling of crack events inside the microstructure. The classical difficulties associated with the implementation and computation cost of the GFEM are dealt through a multiscale approach based on the Saint-Venant principle. This multiscale vision enables the microstructure and the microkinematics to be handled on the scale of the pattern independently of the macroscale discretization. Additionally, numerical enrichment functions are superimposed between the existing enrichment functions in a local computational domain. These enrichment functions deliver accurate solutions of crack interactions among local features, like inclusions, voids, etc, and are specifically appealing to evolution type problems like the crack events defined under the finite fracture mechanics framework. Different crack patterns can be introduced at different positions in the global domain when certain fracture criteria are met. The multiscale approach is implemented inside the finite element software Cast3M in order to use the existing infrastructure of the object oriented code for the development of MS-GFEM.