A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries

By A. Simone, Carlos Armando Duarte, E. Giessen. 2006

204 citations recorded by the source corpus.

Subfields: Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/92bf370826d478d78562f781596649039b16b99a

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In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

A robust preconditioning technique for the extended finite element method (2011, background): “polycrystals [15], multiple cracks [16], and geometric enrichment [6]).”
A review of extended/generalized finite element methods for material modeling (2009, methodology): “[90] formulated the approximation for discontinuities in the total field but only applied the approximation to problems where the tangential component is unconstrained.”
hp‐Generalized FEM and crack surface representation for non‐planar 3‐D cracks (2009, background): “In the case of contact, the non-penetration condition can be enforced using, for example, a formulation based on distributed springs with very large stiffness in the direction normal to the surfaces [49].”
Multi-phase-field modeling of anisotropic crack propagation for polycrystalline materials (2017, unknown): “There are several alternative numerical methods to study failure of polycrystalline material, such as the generalized finite elementmethod (GFEM) [44].”
A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements (2009, methodology): “Here, in both the DSDA and the GFEM, only one discontinuity is allowed in each parent finite element; however, both formulations can be extended to include multiple discontinuities (Dias-da-Costa et al. 2009; Daux et al. 2000; Simone et al. 2006).”
The extended/generalized finite element method: An overview of the method and its applications (2010, background): “These attributes are also present in some later realizations of the GFEM and PUM, see for example [196, 162].”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, unknown): “Formodelingcracks,discontinuousenrich-ment is now also adopted in the GFEM (Simone et al. 2006; Duarte and Kim 2008), and hence for fracture problems, the X-FEM and the GFEM are practically indistinguishable.”
Stable Generalized Finite Element Method (SGFEM) (2011, methodology): “For example, XFEM has been used recently to address two-phase fluid flow problems ([19]), mechanical behavior of nano-structures ([20]), and heterogeneous material with random interfaces ([36]); GFEM has been used to address heat transfer problems with sharp thermal gradient ([40]), grain boundary i”
Numerically determined enrichment functions for the extended finite element method and applications to bi‐material anisotropic fracture and polycrystals (2010, methodology): “[16] described a method where a Heaviside function was used to describe grain boundaries.”
Modeling complex crack problems using the numerical manifold method (2009, background): “Fig. 8 Treatment of a triple junction in the GFEM from Simone et al. (2006)”