Smooth Generalized/eXtended FEM approximations in the computation of configurational forces in linear elastic fracture mechanics

Torres, Diego Amadeu F.; Barcellos, Clóvis Sperb de; Mendonça, Paulo de Tarso R.

doi:10.1007/s10704-019-00353-1

Cited by 1 publication

(3 citation statements)

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“…The energy release rate G in the case of LEFM is equal to the J -integral (Anderson, 2005;Rice, 1968) and, in turn, this last can be related to stress intensity factors (Irwin, 1957). The J -integral, in turn, can be related to nodal configurational forces, using the Eshelbian mechanics formalism, as discussed in Torres et al, 2019, where a more detailed discussion on the configurational mechanics and its relation to other conventional procedures to evaluate crack severity parameters can be found.…”

Section: Quality Assessment Via Materials Forces Methodsmentioning

confidence: 99%

“…The crack severity parameters computation can be improved summing all material forces within a defined area around the crack tip (Torres et al, 2019;Glaser and Steinmann, 2007;Denzer et al, 2003). One would expect that by enlarging the extraction zone, and consequently aggregating more nodal configurational forces, it would be possible to estimate the crack severity parameters better, for a given solution.…”

Section: Quality Assessment Via Materials Forces Methodsmentioning

confidence: 99%

“…Recently, the smooth version of the GFEM (Duarte et al, 2006) has shown to be very appropriate to model sharp gradients around crack tips in linear elastic fracture mechanics (LEFM) (Torres et al, 2015). Continuous stress fields around the singularity favor the estimation of crack severity parameters (Torres et al, 2019). The findings also indicate that the singular enrichment, via geometrical pattern, is better availed when applied over a smooth partition of unity (PoU) endowed with a flat-top.…”

Section: Introductionmentioning

confidence: 99%

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On the topological enrichment for crack modeling via the generalized/extended FEM: a novel discussion considering smooth partitions of unity

Torres

2021

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Purpose It has been usual to prefer an enrichment pattern independent of the mesh when applying singular functions in the generalized/eXtended finite element method (G/XFEM). This choice, when modeling crack tip singularities through extrinsic enrichment, has been understood as the only way to surpass the typical poor convergence rate obtained with the finite element method (FEM), on uniform or quasi-uniform meshes conforming to the crack. Herein, the topological enrichment pattern is revisited in the light of a higher-order continuity obtained with a smooth partition of unity (PoU). Aiming to verify the smoothness' impacts on the blending phenomenon, a series of numerical experiments is conceived to compare the two GFEM versions: the conventional one, based on piecewise continuous PoU's, and another which considers PoU's with high-regularity. Design/methodology/approach The stress approximations right at the crack tip vicinity are qualified by focusing on crack severity parameters. For this purpose, the material forces method originated from the configurational mechanics is used. Some attempts to improve solution using different polynomial enrichment schemes, besides the singular one, are discussed aiming to verify the transition/blending effects. A classical two-dimensional problem of the linear elastic fracture mechanics (LEFM) is solved, considering the pure Mode I and the mixed-mode loading. Findings The results reveal that, in the presence of smooth PoU's, the topological enrichment can still be considered as a suitable strategy for extrinsic enrichment. First, because such an enrichment pattern still can treat the crack independently of the mesh and deliver some advantage in terms of convergence rates, under certain conditions, when compared to the conventional FEM. Second, because the topological pattern demands fewer degrees of freedom and impacts conditioning less than the geometrical strategy. Originality/value Several outputs are presented, considering estimations for the J–integral and the angle of probable crack advance, this last computed from two different strategies to monitoring blending/transition effects, besides some comments about conditioning. Both h- and p-behaviors are displayed to allow a discussion from different points of view concerning the topological enrichment in smooth GFEM.

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Section: Quality Assessment Via Materials Forces Methodsmentioning

confidence: 99%

Section: Quality Assessment Via Materials Forces Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Smooth Generalized/eXtended FEM approximations in the computation of configurational forces in linear elastic fracture mechanics

Cited by 1 publication

References 83 publications

On the topological enrichment for crack modeling via the generalized/extended FEM: a novel discussion considering smooth partitions of unity

On the topological enrichment for crack modeling via the generalized/extended FEM: a novel discussion considering smooth partitions of unity

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