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. Lee, Chaemin; Kim, San; Lee, Phill-Seung: The strain-smoothed 4-node quadrilateral finite element (2021)
  2. Li, X. F.; Li, H. B.; Zhao, J.: Transgranular fracturing of crystalline rocks and its influence on rock strengths: insights from a grain-scale continuum-discontinuum approach (2021)
  3. Muixí, Alba; Marco, Onofre; Rodríguez-Ferran, Antonio; Fernández-Méndez, Sonia: A combined XFEM phase-field computational model for crack growth without remeshing (2021)
  4. Wang, Zihao; Yao, Weian; Zuo, Chong; Hu, Xiaofei: Solving phase change problems via a precise time-domain expanding boundary element method combined with the level set method (2021)
  5. Xiao, Guizhong; Wen, Longfei; Tian, Rong: Arbitrary 3D crack propagation with improved XFEM: accurate and efficient crack geometries (2021)
  6. Cui, X.; Qie, Y. H.: Using axisymmetric smoothed finite element method (S-FEM) to analyze pressure piping with defect in ABAQUS (2020)
  7. 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)
  8. Deng, Quanling; Calo, Victor: Higher order stable generalized finite element method for the elliptic eigenvalue and source problems with an interface in 1D (2020)
  9. Hou, Wenbin; Jiang, Kai; Zhu, Xuefeng; Shen, Yuanxing; Li, Yongcheng; Zhang, Xiangkui; Hu, Ping: Extended isogeometric analysis with strong imposing essential boundary conditions for weak discontinuous problems using B++ splines (2020)
  10. 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)
  11. Jahn, Mischa; Montalvo-Urquizo, Jonathan: Modeling and simulation of keyhole-based welding as multi-domain problem using the extended finite element method (2020)
  12. Johansson, August; Larson, Mats G.; Logg, Anders: Multimesh finite elements with flexible mesh sizes (2020)
  13. Liu, Feng; Zhang, Kaiyu; Xu, Dongdong: Crack analysis using numerical manifold method with strain smoothing technique and corrected approximation for blending elements (2020)
  14. 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)
  15. Loew, Pascal J.; Poh, Leong H.; Peters, Bernhard; Beex, Lars A. A.: Accelerating fatigue simulations of a phase-field damage model for rubber (2020)
  16. 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)
  17. Rao, S. S. Durga; Raju, Sethuraman: Orthogonalized generalized iso-geometric analysis (OGIGA) and its applications to problems of fracture mechanics (2020)
  18. Ren, Huilong; Zhuang, Xiaoying; Rabczuk, Timon: A nonlocal operator method for solving partial differential equations (2020)
  19. Sanchez-Rivadeneira, A. G.; Duarte, C. A.: A simple, first-order, well-conditioned, and optimally convergent generalized/extended FEM for two- and three-dimensional linear elastic fracture mechanics (2020)
  20. 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)

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