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.

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  1. Beese, Steffen; Loehnert, Stefan; Wriggers, Peter: 3D ductile crack propagation within a polycrystalline microstructure using XFEM (2018)
  2. Bhowmick, Sauradeep; Liu, GR.: On singular ES-FEM for fracture analysis of solids with singular stress fields of arbitrary order (2018)
  3. Chai, Yingbin; Gong, Zhixiong; Li, Wei; Li, Tianyun; Zhang, Qifan; Zou, Zhihong; Sun, Yangbin: Application of smoothed finite element method to two-dimensional exterior problems of acoustic radiation (2018)
  4. Yang, Yongtao; Tang, Xuhai; Zheng, Hong; Liu, Quansheng: Four-node quadrilateral element with continuous nodal stress for geometrical nonlinear analysis (2018)
  5. Zeng, W.; Liu, G. R.: Smoothed finite element methods (S-FEM): an overview and recent developments (2018)
  6. Zonca, Stefano; Vergara, Christian; Formaggia, Luca: An unfitted formulation for the interaction of an incompressible fluid with a thick structure via an XFEM/DG approach (2018)
  7. Chau-Dinh, Thanh; Nguyen-Duy, Quang; Nguyen-Xuan, Hung: Improvement on MITC3 plate finite element using edge-based strain smoothing enhancement for plate analysis (2017)
  8. Davari, M.; Rossi, R.; Dadvand, P.: Three embedded techniques for finite element heat flow problem with embedded discontinuities (2017)
  9. Hattori, Gabriel; Trevelyan, Jon; Augarde, Charles E.; Coombs, William M.; Aplin, Andrew C.: Numerical simulation of fracking in shale rocks: current state and future approaches (2017)
  10. Martínez-Pañeda, E.; Natarajan, S.; Bordas, S.: Gradient plasticity crack tip characterization by means of the extended finite element method (2017)
  11. Nguyen-Thoi, T.; Rabczuk, T.; Ho-Huu, V.; Le-Anh, L.; Dang-Trung, H.; Vo-Duy, T.: An extended cell-based smoothed three-node Mindlin plate element (XCS-MIN3) for free vibration analysis of cracked FGM plates (2017)
  12. Schroeder, Philipp W.; Lube, Gert: Stabilised DG-FEM for incompressible natural convection flows with boundary and moving interior layers on non-adapted meshes (2017)
  13. Wan, Detao; Hu, Dean; Natarajan, Sundararajan; Bordas, Stéphane P. A.; Long, Ting: A linear smoothed higher-order CS-FEM for the analysis of notched laminated composites (2017)
  14. Wan, Detao; Hu, Dean; Natarajan, Sundararajan; Bordas, Stéphane P. A.; Yang, Gang: A fully smoothed XFEM for analysis of axisymmetric problems with weak discontinuities (2017)
  15. Yang, Yongtao; Sun, Guanhua; Zheng, Hong: Application of the `FE-meshfree’ QUAD4 with continuous nodal stress using radial-polynomial basis functions for vibration and geometric nonlinear analyses (2017)
  16. 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)
  17. Bodart, Olivier; Cayol, Valérie; Court, Sébastien; Koko, Jonas: XFEM-based fictitious domain method for linear elasticity model with crack (2016)
  18. Cen, Song; Bao, Yi; Li, Chen-Feng: Quasi-static crack propagation modeling using shape-free hybrid stress-function elements with drilling degrees of freedom (2016)
  19. Elgeti, S.; Sauerland, H.: Deforming fluid domains within the finite element method: five mesh-based tracking methods in comparison (2016)
  20. Feng, H.; Cui, X. Y.; Li, G. Y.: A stable nodal integration method with strain gradient for static and dynamic analysis of solid mechanics (2016)

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