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. da Costa, R. O. S. S.; Pinho, S. T.: A novel formulation for the explicit discretisation of evolving boundaries with application to topology optimisation (2020)
  2. Deng, Quanling; Calo, Victor: Higher order stable generalized finite element method for the elliptic eigenvalue and source problems with an interface in 1D (2020)
  3. Hu, Qingyuan; Xia, Yang; Natarajan, Sundararajan; Zilian, Andreas; Hu, Ping; Bordas, Stéphane P. A.: Isogeometric analysis of thin Reissner-Mindlin shells: locking phenomena and B-bar method (2020)
  4. Jahn, Mischa; Montalvo-Urquizo, Jonathan: Modeling and simulation of keyhole-based welding as multi-domain problem using the extended finite element method (2020)
  5. Liu, Feng; Zhang, Kaiyu; Xu, Dongdong: Crack analysis using numerical manifold method with strain smoothing technique and corrected approximation for blending elements (2020)
  6. Liu, Yang; Sussman, Mark; Lian, Yongsheng; Yousuff Hussaini, M.: A moment-of-fluid method for diffusion equations on irregular domains in multi-material systems (2020)
  7. Lv, Jia-He; Jiao, Yu-Yong; Rabczuk, Timon; Zhuang, Xiao-Ying; Feng, Xia-Ting; Tan, Fei: A general algorithm for numerical integration of three-dimensional crack singularities in PU-based numerical methods (2020)
  8. Ren, Huilong; Zhuang, Xiaoying; Rabczuk, Timon: A nonlocal operator method for solving partial differential equations (2020)
  9. Sanchez-Rivadeneira, A. G.; Shauer, N.; Mazurowski, B.; Duarte, C. A.: A stable generalized/extended (p)-hierarchical FEM for three-dimensional linear elastic fracture mechanics (2020)
  10. Schätzer, Markus; Fries, Thomas-Peter: Loaded crack surfaces in two and three dimensions with XFEM (2020)
  11. Schuler, Louis; Ilgen, Anastasia G.; Newell, Pania: Chemo-mechanical phase-field modeling of dissolution-assisted fracture (2020)
  12. Agathos, Konstantinos; Bordas, Stéphane P. A.; Chatzi, Eleni: Improving the conditioning of XFEM/GFEM for fracture mechanics problems through enrichment quasi-orthogonalization (2019)
  13. Agathos, Konstantinos; Chatzi, Eleni; Bordas, Stéphane P. A.: A unified enrichment approach addressing blending and conditioning issues in enriched finite elements (2019)
  14. Amiri, Erfan A.; Craig, James R.; Hirmand, M. Reza: A trust region approach for numerical modeling of non-isothermal phase change (2019)
  15. Bansal, Manik; Singh, I. V.; Mishra, B. K.; Bordas, S. P. A.: A parallel and efficient multi-split XFEM for 3-D analysis of heterogeneous materials (2019)
  16. Benvenuti, E.; Chiozzi, A.; Manzini, G.; Sukumar, N.: Extended virtual element method for the Laplace problem with singularities and discontinuities (2019)
  17. Bulling, Jannis; Gravenkamp, Hauke; Birk, Carolin: A high-order finite element technique with automatic treatment of stress singularities by semi-analytical enrichment (2019)
  18. Cheng, Zhenxing; Wang, Hu: An exact and efficient X-FEM-based reanalysis algorithm for quasi-static crack propagation (2019)
  19. Chen, Haodong; Wang, Qingsong; Zeng, W.; Liu, G. R.; Sun, Jinhua; He, Linghui; Bui, Tinh Quoc: Dynamic brittle crack propagation modeling using singular edge-based smoothed finite element method with local mesh rezoning (2019)
  20. Chen, Juan; Li, Chong-Jun: A 3D triangular prism spline element using B-net method (2019)

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