XFEM

An extended finite element library This paper presents and exercises a general structure for an object-oriented-enriched finite element code. The programming environment provides a robust tool for extended finite element (XFEM) computations and a modular and extensible system. The programme structure has been designed to meet all natural requirements for modularity, extensibility, and robustness. To facilitate mesh -- geometry interactions with hundreds of enrichment items, a mesh generator and mesh database are included. The salient features of the programme are: flexibility in the integration schemes (subtriangles, subquadrilaterals, independent near-tip, and discontinuous quadrature rules); domain integral methods for homogeneous and bi-material interface cracks arbitrarily oriented with respect to the mesh; geometry is described and updated by level sets, vector level sets or a standard method; standard and enriched approximations are independent; enrichment detection schemes: topological, geometrical, narrow-band, etc.; multi-material problem with an arbitrary number of interfaces and slip-interfaces; nonlinear material models such as J2 plasticity with linear, isotropic and kinematic hardening. To illustrate the possible applications of our paradigm, we present 2D linear elastic fracture mechanics for hundreds of cracks with local near-tip refinement, and crack propagation in two dimensions as well as complex 3D industrial problems.


References in zbMATH (referenced in 196 articles , 1 standard article )

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  1. Beirão da Veiga, Lourenço; Brezzi, Franco; Marini, Luisa Donatella; Russo, Alessandro: Mixed virtual element methods for general second order elliptic problems on polygonal meshes (2016)
  2. Bodart, Olivier; Cayol, Valérie; Court, Sébastien; Koko, Jonas: XFEM-based fictitious domain method for linear elasticity model with crack (2016)
  3. Elgeti, S.; Sauerland, H.: Deforming fluid domains within the finite element method: five mesh-based tracking methods in comparison (2016)
  4. Malekan, Mohammad; Barros, Felicio Bruzzi: Well-conditioning global-local analysis using stable generalized/extended finite element method for linear elastic fracture mechanics (2016)
  5. Nguyen, Vinh Phu; Nguyen, Chi Thanh; Bordas, Stéphane; Heidarpour, Amin: Modelling interfacial cracking with non-matching cohesive interface elements (2016)
  6. Stapór, Pawel: A two-dimensional simulation of solidification processes in materials with thermo-dependent properties using XFEM (2016)
  7. Yang, Gang; Hu, Dean; Ma, Guowei; Wan, Detao: A novel integration scheme for solution of consistent mass matrix in free and forced vibration analysis (2016)
  8. Cano, Alfredo; Moreno, Carlos: A new method for numerical integration of singular functions on the plane (2015)
  9. Élie-Dit-Cosaque, Xavier J.-G.; Gakwaya, Augustin; Naceur, Hakim: Smoothed finite element method implemented in a resultant eight-node solid-shell element for geometrical linear analysis (2015)
  10. Haeri, Hadi; Khaloo, Alireza; Marji, Mohammad Fatehi: Fracture analyses of different pre-holed concrete specimens under compression (2015)
  11. Lins, R.M.; Ferreira, M.D.C.; Proença, S.P.B.; Duarte, C.A.: An a-posteriori error estimator for linear elastic fracture mechanics using the stable generalized/extended finite element method (2015)
  12. Singh, Sonam; Bhargava, Rama: Numerical simulation of a phase transition problem with natural convection using hybrid FEM/EFGM technique (2015)
  13. Stapór, Pawel: The XFEM for nonlinear thermal and phase change problems (2015)
  14. Amiri, F.; Anitescu, C.; Arroyo, M.; Bordas, S.P.A.; Rabczuk, T.: XLME interpolants, a seamless bridge between XFEM and enriched meshless methods (2014)
  15. Duddu, Ravindra: Numerical modeling of corrosion pit propagation using the combined extended finite element and level set method (2014)
  16. González-Estrada, O.A.; Nadal, E.; Ródenas, J.J.; Kerfriden, P.; Bordas, S.P.A.; Fuenmayor, F.J.: Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery (2014)
  17. Holl, Matthias; Rogge, Timo; Loehnert, Stefan; Wriggers, Peter; Rolfes, Raimund: 3D multiscale crack propagation using the XFEM applied to a gas turbine blade (2014)
  18. Lang, Christapher; Makhija, David; Doostan, Alireza; Maute, Kurt: A simple and efficient preconditioning scheme for Heaviside enriched XFEM (2014)
  19. Liu, J.T.; Gu, S.T.; Monteiro, E.; He, Q.C.: A versatile interface model for thermal conduction phenomena and its numerical implementation by XFEM (2014)
  20. Loehnert, Stefan: A stabilization technique for the regularization of nearly singular extended finite elements (2014)

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Further publications can be found at: http://www.xfem.rwth-aachen.de/Project/Publications/PRJ_Publications.php