X-FEM modeling of large plasticity deformation; a convergence study on various blending strategies for weak discontinuities
Keywords:
X-FEM model, large deformations, blending elements, weak discontinuitiesAbstract
In the extended finite element method (FEM), the transition elements between the enriched and standard elements, which are generally referred as the blending, or partially enriched elements, are often crucial for a good performance of the local partition of unity enrichments. In these elements, the enrichment function cannot be reproduced exactly due to the lack of a partition of unity, and blending elements produce unwanted terms into the approximation that cannot be compensated by the standard finite element part of the approximation. In this paper, some optimal X-FEMtype methods reported in literature are employed to study the performance of blending elements in large plastic deformation problems with weak discontinuities. Several numerical examples are solved using the standard X-FEM, the X-FEM with modified enrichment function, the hierarchical X-FEM and the corrected X-FEM technique, and the results are compared with an alternative intrinsic enrichment strategy in large deformation problems.
Downloads
References
Belytschko, T., & Black, T. (1999). Elastic crack growth in finite elements with minimal
remeshing. International Journal for Numerical Methods in Engineering, 45, 601–620.
Belytschko, T., Black, T., Moës, N., Sukumar, N., & Usui, S. (2003). Structured extended finite
element methods of solids defined by implicit surfaces. International Journal for Numerical
Methods in Engineering, 56, 609–635.
Bordas, S. P. A., Rabczuk, T., Nguyen-Xuan, H., Nguyen, V. P., Natarajan, S., Bog, T., … Hiep,
N. V. (2010). Strain smoothing in FEM and XFEM. Computers & Structures, 88, 1419–1443.
Broumand, P., & Khoei, A. R. (2013). The extended finite element method for large deformation
ductile fracture problems with a non-local damage–plasticity model. Engineering Fracture
Mechanics, 112, 97–125.
Chen, L., Rabczuk, T., Bordas, S. P. A., Liu, G. R., Zeng, K. Y., & Kerfriden, P. (2012). Extended
finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic
crack growth. Computer Methods in Applied Mechanics and Engineering, 209–212, 250–265.
Chessa, J., Wang, H., & Belytschko, T. (2003). On the construction of blending elements for
local partition of unity enriched finite elements. International Journal for Numerical Methods
in Engineering, 57, 1015–1038.
Fries, T. P. (2008). A corrected XFEM approximation without problems in blending elements.
International Journal for Numerical Methods in Engineering, 75, 503–532.
Fries, T. P., & Belytschko, T. (2006). The intrinsic XFEM: A method for arbitrary discontinuities
without additional unknowns. International Journal for Numerical Methods in Engineering,
, 1358–1385.Gracie, R., Wang, H., & Belytschko, T. (2008). Blending in the extended finite element method
by discontinuous Galerkin and assumed strain methods. International Journal for Numerical
Methods in Engineering, 74, 1645–1669.
Gupta, V., Duarte, C. A., Babuška, I., & Banerjee, U. (2015). Stable GFEM (SGFEM): Improved
conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics.
Computer Methods in Applied Mechanics and Engineering, 289, 355–386.
Khoei, A. R. (2005) Computational plasticity in powder forming process. Oxford, UK: Elsevier.
Khoei, A. R. (2015). Extended finite element method, theory and applications. Sussex, UK:
John Wiley.
Khoei, A. R., Biabanaki, S. O. R., & Anahid, M. (2008). Extended finite element method for
three-dimensional large plasticity deformations on arbitrary interfaces. Computer Methods
in Applied Mechanics and Engineering, 197, 1100–1114.
Khoei, A. R., Biabanaki, S. O. R., & Anahid, M. (2009). A Lagrangian-extended finite-element
method in modeling large-plasticity deformations and contact problems. International
Journal of Mechanical Sciences, 51, 384–401.
Laborde, P., Pommier, J., Renard, Y., & Salaün, M. (2005). High-order extended finite element
method for cracked domains. International Journal for Numerical Methods in Engineering,
, 354–381.
Loehnert, S., Mueller-Hoeppe, D. S., & Wriggers, P. (2011). 3D corrected XFEM approach
and extension to finite deformation theory. International Journal for Numerical Methods in
Engineering, 86, 431–452.
Moës, N., Cloirec, M., Cartraud, P., & Remacle, J. F. (2003). A computational approach to
handle complex microstructure geometries. Computer Methods in Applied Mechanics and
Engineering, 192, 3163–3177.
Natarajan S., Bordas S. P. A., Minh Q. D., Nguyen-Xuan H., Rabczuk T., Cahill L., McCarthy C. T.
(2008). The smoothed extended finite element method. Proceedings of the 6th International
Conference on Engineering Computational Technology, Greece.
Nguyen-Xuan, H., Bordas, S. P. A., & Nguyen-Dang, H. (2007). Smooth finite element methods:
Convergence, accuracy and properties. International Journal for Numerical Methods in
Engineering, 74, 175–208.
Shibanuma, K., & Utsunomiya, T. (2009). Reformulation of XFEM based on PUFEM for solving
problem caused by blending elements. Finite Elements in Analysis and Design, 45, 806–816.
Stazi, F. L., Budyn, E., Chessa, J., & Belytschko, T. (2003). An extended finite element method
with higher-order elements for curved cracks. Computational Mechanics, 31, 38–48.
Sukumar, N., Chopp, D. L., Moës, N., & Belytschko, T. (2001). Modeling holes and inclusions
by level sets in the extended finite-element method. Computer Methods in Applied Mechanics
and Engineering, 190, 6183–6200.
Szabó, B., & Babuška, I. (1991). Finite element analysis. New York, NY: Wiley.
Tarancón, J. E., Vercher, A., Giner, E., & Fuenmayor, F. J. (2009). Enhanced blending elements
for XFEM applied to linear elastic fracture mechanics. International Journal for Numerical
Methods in Engineering, 77, 126–148.
Ventura, G., Gracie, R., & Belytschko, T. (2009). Fast integration and weight function blending
in the extended finite element method. International Journal for Numerical Methods in
Engineering, 77, 1–29.
