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Computational toolkit to nonlinear analysis of solid and structures by the generalized finite element method


This research project focus on new developments and improvements of numerical methods devoted to the simulation of nonlinear, discontinuous and multi-scale problems. The Generalized Finite Element Method (GFEM) and fracture/damage mechanics based approaches are combined aiming at the development of an accurate and robust numerical tool for nonlinear structural analysis accounting for multisite damage (MSD) evolution at different scales. Both computational and mathematical issues are addressed. Convergence studies, a-posteriori error analysis and adaptivity are included aiming to guarantee optimal rates of convergence while improving the computational efficiency. The option for GFEM is justified by its known ability to efficiently deal with fracture mechanics problems. Moreover, the so-called GFEM with Global-Local Enrichments (referenced here as GFEM-gl) which explores numerical solutions of local problems as enrichment functions to global analysis has recently been extended to nonlinear analysis. Both features of the GFEM-gl can be efficiently explored on multisite damage problems at different scales. The initial developments will be conduced in a two-dimensional setting, but the formulation provides a consistent extension to the three-dimensional framework. The computational toolkit to be developed will be written by using PYTHON language. This high level language supports Object Oriented Programming while allowing efficient implementations for solutions of sparse and large scale systems, as well parallel processing. (AU)

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