Appropriate extended functions for X-FEM simulation of plastic fracture mechanics

By Thomas Elguedj, Anthony Gravouil, Alain Combescure. 2006

260 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/06bd9506686f7b47577ad744f0e320fe6d2e73f1

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Damage growth modeling using the Thick Level Set (TLS) approach: Efficient discretization for quasi-static loadings (2012, background): “[36,40,6,3]), quickly becomes a tedious task as the number of cracks grows.”
Strength prediction of single- and double-lap joints by standard and extended finite element modelling (2011, unknown): “[32], which used a new enriched basis function to capture the singular fields in elasto-plastic fracture mechanics.”
Generalized Duffy transformation for integrating vertex singularities (2009, background): “The development of meshfree [8] and partition of unity finite element methods [9] for modeling singularities—cracks in isotropic media (λ = 1/2) [10–13], strong and weak singularities for a crack perpendicular to a bimaterial interface [14], complete sliding contact [15], HRR crack-tip fields with λ”
Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method (2013, methodology): “The XFEM has also been employed in elasto-plastic problems, including plastic fracture mechanics [30], plasticity of frictional contact [31], large plastic deformations [32–34], localization phenomenon in higher-order Cosserat theory [35] and porous media with arbitrary interfaces [36].”
A stable 3D contact formulation using X-FEM (2007, background): “…methods is its easy implementation in a general finite element software, and its capacities to be applied to various fields: large transformations (Legrain et al., 2005), plasticity (Elguedj et al., 2006)… One can say that X-FEM extends the possibilities of the FEM, keeping all its advantages.”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, unknown): “Examples of recent attempts to identify suitable near-tip enrichment functions can be found in Elguedj et al. (2006) for plasticity and in Karoui et al. (2014) for compressible hyperelasticity.”
Thermo-hydro-mechanical modeling of impermeable discontinuity in saturated porous media with X-FEM technique (2012, methodology): “The technique was then employed in elastoplasticity problems, including: the crack propagation in plastic fracture mechanics [40], the plasticity of frictional contact on arbitrary interfaces [41, 42], the plasticity of large deformations”
Isogeometric analysis: An overview and computer implementation aspects (2012, methodology): “In addition to this popular technique, a simple integration rule is also provided – elements crossed by the crack and tip-enriched elements are numerically integrated using a regular Gauss-Legendre quadrature with a large number of Gauss points as done in [44].”
Investigation of mixed-mode stress intensity factors for nonhomogeneous materials using an interaction integral method (2009, methodology): “For the elements containing discontinuous material interfaces, we employ the integration strategy given by Elguedj et al. (2006): each element is divided into 3 3 sub-domains and 3 3 Gauss quadrature is used in each sub-domain.”
A mixed augmented Lagrangian‐extended finite element method for modelling elastic–plastic fatigue crack growth with unilateral contact (2007, unknown): “The main results to obtain an appropriate elastic–plastic enrichment basis, presented in Reference [19], are given.”
An extended finite element method for fluid flow in partially saturated porous media with weak discontinuities; the convergence analysis of local enrichment strategies (2013, methodology): “The XFEM was also implemented in nonlinear problems including the plastic fracture mechanics [18], the frictional contact [19], the large plastic deformation of arbitrary interfaces [20,21], and the localization phenomenon in higher-order Cosserat theory [22] and in the treatment of incompressible o”