An extended finite element method with higher-order elements for curved cracks

By F. Stazi, Elisa Budyn, J. Chessa, Ted Belytschko. 2003

254 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/2b2d9a084d996356c8f866503bdc25173411a526

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE (2004, methodology): “Using polynomial functions together with other special functions we get the XFEM (see [ 36 , 41]), which is a special case of the GFEM.”
Studied X-FEM enrichment to handle material interfaces with higher order finite element (2010, background): “In [27], higher order elements are applied to curved cracks problems (six-node triangular elements) with quadratic shape functions.”
Thermodynamically consistent algorithms for a finite‐deformation phase‐field approach to fracture (2014, methodology): “Discretization methods include both classical discontinuous methods, such as interface (cohesive) element formulations [9–11] or local enrichment strategies [12, 13] and continuous methods with discontinuities replaced by sharp gradients [8, 14].”
XLME interpolants, a seamless bridge between XFEM and enriched meshless methods (2014, unknown): “If t · ∇r > 0, θ is considered as in [28]:”
A study of the representation of cracks with level sets (2007, methodology): “Similar methods with scalar level set functions are used in References [26–28].”
High‐order extended finite element method for cracked domains (2005, unknown): “F1 r sin θ2 F2 r cos θ2 F3 r sin θ2 cosθ F4 r cos θ2 cosθ (2) 2.”
On Approximation in Meshless Methods (2005, methodology): “A few examples frequently mentioned in this context are the diffuse element method, [87], the element-free Galerkin (EFG, [11, 13, 14]), the X-FEM (extended FEM), [29, 84, 98 ], the RKPM (reproducing kernel particle method, [70, 72–75]), the generalized FEM/partition of unity method ( [7, 9, 78, 79”
Optimal convergence analysis for the extended finite element method (2011, background): “O( √ h), see [31, 25]) since the area of enrichment tends to vanish when the mesh parameter decreases.”