Nucleation and Crack Propagation by Generalized Finite Element Method based on a Combination of Constitutive and Kinematic Approaches
Leandro Lopes da Silva1; Roque Luiz da Silva Pitangueira1; Samuel Silva Penna1; Felício Bruzzi Barros1; Gabriel Neves Alves Ferreira1
1 Universidade Federal de Minas Gerais
doi:10.20906/CPS/COB-2015-1453
Resumo
This paper presents computational simulations of problems concerning damage and fracture mechanics in quasi-brittle materials. The physically nonlinear analysis is started using the standard Finite Element Method, where the nucleation phenomenon is assessed through constitutive methods based on elastic degradation, while crack propagation is evaluated through kinematic method that incorporates the discontinuities. Such discontinuities are represented using enriched interpolations based on Generalized Finite Element Method (GFEM). This combination of constitutive and kinematic methods has the advantage of not having to pre-set crack path or reset the mesh during analysis. The relationship between stresses and displacements in the crack path is based on the concept of cohesive or fictitious crack, in particular the Hillerborg model, in which all the inelastic deformation (occurring in the fracture process zone) are represented on a line through the cohesive forces acting on the crack, or in a fictitious crack extension. The numerical simulations are performed using an interactive graphical software that integrates mesh generator, constitutive models, nonlinear equation solvers and post-processor. Such a software results from the expansion of the project INSANE (INteractive Structural ANalysis Environment), an open source computational platform developed by the Structural Engineering Department of Federal University of Minas Gerais.
Palavras-chave: Damage and Fracture Mechanics; Quasi-Brittle Materials; Physically Nonlinear Analysis; Constitutive Method; Generalized Finite Element Method